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  • Numerical Methods and Modeling  (293)
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  • 1
    Electronic Resource
    Electronic Resource
    A MULTI-LEVEL NUMERICAL MODEL OF COASTAL UPWELLING: A DIAGNOSTIC STUDY (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 17-59 
    Details
    ISSN: 0271-2091
    Keywords: radiation boundary condition ; numerical model ; coastal upwelling ; baroclinic model ; coastal jet ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A two-dimensional baroclinic model is described for coastal upwelling in a vertical plane perpendicular to the coast. The model consists of equations of motion, continuity and turbulence energy along with equations for salinity and thermal energy and an equation of state. The role of density gradient in the baroclinic pressure gradient is investigated to understand the dynamics during the upwelling process. To represent the surface and bottom boundaries corresponding to a fixed computational level in the discretized equations, a set of non-dimensional co-ordinates is used. These co-ordinates are then transformed onto logarithmic co-ordinate axes to resolve effectively the boundary layers.The first experiment is carried out with a flat bottom to understand the dynamics of the upwelling and the structural features of the process by diagnostic analysis of the balance between various terms of the momentum equation. Starting from a state of rest, a spatially uniform alongshore wind stress corresponding to the mean monthly wind stress for the month of May is applied and held constant thereafter. The fluid is assumed to be incompressible and stratified, with the initial temperature and salinity having no horizontal variations but a uniform vertical gradient. As the upwelling phenomenon is transient in nature and keeping in mind the additional computational overheads, the response of the model is studied day-wise up to 4 days.In the second experiment the model is applied to study the upwelling off the east coast of India in a plane normal to the coast of Visakhapatnam. The analysis area extends to 100 km offshore with real topography. The results are presented day-wise for 4 days, comparing the balance between various terms in the upwelling region and in the open sea, and the dynamics of the baroclinic coastal jet is explained. © 1997 John Wiley & Sons, Ltd.
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  • 2
    Electronic Resource
    Electronic Resource
    Parallel computation of incompressible flows with complex geometries (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 1321-1340 
    Details
    ISSN: 0271-2091
    Keywords: parallel flow simulation ; complex geometries ; mesh generation ; automobile ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We present our numerical methods for the solution of large-scale incompressible flow applications with complex geometries. These methods include a stabilized finite element formulation of the Navier-Stokes equations, implementation of this formulation on parallel architectures such as the Thinking Machines CM-5 and the CRAY T3D, and automatic 3D mesh generation techniques based on Delaunay-Voronoi methods for the discretization of complex domains. All three of these methods are required for the numerical simulation of most engineering applications involving fluid flow.We apply these methods to the simulation of airflow past an automobile and fluid-particle interactions. The simulation of airflow past an automobile is of very large scale with a high level of detail and yielded many interesting airflow patterns which help in understanding the aerodynamic characteristics of such vehicles. © 1997 John Wiley & Sons, Ltd.
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  • 3
    Electronic Resource
    Electronic Resource
    Parallel finite element methods for large-scale computation of storm surges and tidal flows (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 1371-1389 
    Details
    ISSN: 0271-2091
    Keywords: parallel finite element method ; three-step explicit formulation ; implicit space-time formulation ; storm surge ; tidal flow ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Massively parallel finite element methods for large-scale computation of storm surges and tidal flows are discussed here. The finite element computations, carried out using unstructured grids, are based on a three-step explicit formulation and on an implicit space-time formulation. Parallel implementations of these unstructured grid-based formulations are carried out on the Fujitsu Highly Parallel Computer AP1000 and on the Thinking Machines CM-5. Simulations of the storm surge accompanying the Ise-Bay typhoon in 1959 and of the tidal flow in Tokyo Bay serve as numerical examples. The impact of parallelization on this type of simulation is also investigated. The present methods are shown to be useful and powerful tools for the analysis of storm surges and tidal flows. © 1997 John Wiley & Sons, Ltd.
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  • 4
    Electronic Resource
    Electronic Resource
    Simulation of flow problems with moving mechanical components, fluid-structure interactions and two-fluid interfaces (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 1433-1448 
    Details
    ISSN: 0271-2091
    Keywords: flow simulation ; moving mechanical components ; fluid-structure interactions ; two-fluid interfaces ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The application of a stabilized space-time finite element formulation to problems involving fluid-structure interactions and two-fluid interfaces is discussed. Two sample problems are presented and the method is validated by comparison with a test problem. © 1997 John Wiley & Sons, Ltd.
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  • 5
    Electronic Resource
    Electronic Resource
    DNS OF 2D TURBULENT FLOW AROUND A SQUARE CYLINDER (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 51-62 
    Details
    ISSN: 0271-2091
    Keywords: two-dimensional turbulence ; DNS ; vortex dynamics ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Two-dimensional ‘turbulent’ flow around a rectangular cylinder has been simulated at Re=10,000 using a sixth- order-accurate finite volume method for the discretization of convection and diffusion. The spatial discretization consists of a combination of a seventh- order upwind-biased method for the convective terms and an eighth-order central method for the diffusive terms, discretized on a stretched and staggered grid. To cope with the stretching of the grid, Lagrange interpolations are used.The method applied to obtain a boundary condition for the velocity in the x-direction at the outflow boundary is shown not to affect the flow in the interior of the computational domain in a way that is visible in various snapshots of the vorticity field. The variation in the velocity in the x-direction with time is itself found to be relatively small near the outflow boundary.Several turbulence statistics have been gathered from a simulation of the flow developed during 77 dimensionless time units. Snapshots of the vorticity field of the developed flow show the presence of a vortex-street- like structure. Typical 2D turbulent behaviour, such as the appearance of monopolar, dipolar and tripolar vortices due to the amalgamation of vorticity in the wake and the x-1/2 scaling of the velocity defect in the wake, has been obtained. © 1997 John Wiley & Sons, Ltd.
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  • 6
    Electronic Resource
    Electronic Resource
    A PRESSURE-BASED ALGORITHM FOR HIGH-SPEED TURBOMACHINERY FLOWS (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 63-80 
    Details
    ISSN: 0271-2091
    Keywords: turbulent flows ; compressible flows ; pressure correction ; approximate factorization ; density biasing ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The steady state Navier-Stokes equations are solved in transonic flows using an elliptic formulation. A segregated solution algorithm is established in which the pressure correction equation is utilized to enforce the divergence-free mass flux constraint. The momentum equations are solved in terms of the primitive variables, while the pressure correction field is used to update both the convecting mass flux components and the pressure itself. The velocity components are deduced from the corrected mass fluxes on the basis of an upwind-biased density, which is a mechanism capable of overcoming the ellipticity of the system of equations, in the transonic flow regime. An incomplete LU decomposition is used for the solution of the transport-type equations and a globally minimized residual method resolves the pressure correction equation. Turbulence is resolved through the k-ε model. Dealing with turbomachinery applications, results are presented in two-dimensional compressor and turbine cascades under design and off-design conditions. © 1997 John Wiley & Sons, Ltd.
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  • 7
    Electronic Resource
    Electronic Resource
    UNSTEADY DETACHED SEPARATION FROM A CIRCULAR CYLINDER PERFORMING ROTATIONAL OSCILLATIONS IN A UNIFORM VISCOUS INCOMPRESSIBLE FLOW (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 125-142 
    Details
    ISSN: 0271-2091
    Keywords: viscous ; vorticity ; detached separation ; cylinder ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The origination of detached separation is studied on the basis of a numerical solution of the full Navier-Stokes equations. Fluxes of vorticity with different signs generated with twice the frequency of cylinder oscillation move from the cylinder to the outer surface of a detached liquid layer in the form of concentric rings. Near the critical layer between the attached layer and the main flow these rings are torn and crimped to the regions of separated vortices of the corresponding sign. The form of detached separated vortices is similar to that of vortices originating from a stationary circular cylinder in a uniform flow. Transition of the flow to a non-symmetric form with Karman vortex street generation at a Reynolds number (based on the radius) greater than 17 is revealed. This critical Reynolds number is smaller than that for a stationary circular cylinder in a viscous stream (where Re=20 has been determined to be a critical value) and corresponds to the Reynolds number extrapolated from the critical value for the stationary cylinder by increasing the cylinder radius by the attached layer thickness. The vorticity flux from the cylinder surface immediately into the separation region decreases as the frequency of cylinder oscillation increases. Violation of the flow potentiality in the detached separation region is the main cause of the vorticity generation on the outer surface of the attached liquid layer. © 1997 John Wiley & Sons, Ltd.
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  • 8
    Electronic Resource
    Electronic Resource
    NUMERICAL SOLUTIONS OF OPTIMAL CONTROL FOR THERMALLY CONVECTIVE FLOWS (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 205-223 
    Details
    ISSN: 0271-2091
    Keywords: optimal control ; Navier-Stokes equations ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We study the numerical solution of optimal control problems associated with two-dimensional viscous incompressible thermally convective flows. Although the techniques apply to more general settings, the presentation is confined to the objectives of minimizing the vorticity in the steady state case and tracking the velocity field in the non-stationary case with boundary temperature controls. In the steady state case we develop a systematic way to use the Lagrange multiplier rules to derive an optimality system of equations from which an optimal solution can be computed; finite element methods are used to find approximate solutions for the optimality system of equations. In the time-dependent case a piecewise-in-time optimal control approach is proposed and the fully discrete approximation algorithm for solving the piecewise optimal control problem is defined. Numerical results are presented for both the steady state and time-dependent optimal control problems. © 1997 John Wiley & Sons, Ltd.
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  • 9
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    Electronic Resource
    UNSTEADY TWO-DIMENSIONAL TURBULENT VISCOUS FLOW PAST AEROFOILS (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 315-366 
    Details
    ISSN: 0271-2091
    Keywords: viscous flow ; dynamic stall ; turbulent flow ; aerofoils ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The so-called CPI finite volume method is applied to the computation of the deep dynamic stall of a pitching NACA 0012 aerofoil. The evolution of flow sequences is analysed for two turbulence models, the so-called Baldwin-Barth and K-ω SST models, and compared with available data of McAlister et al. The hysteresis loops for the force coefficients are presented for three different reduced frequencies of the pitching motion and compared with experimental data. The agreement with available data is good during the upstroke phase and it is found that the level of disagreement during the downstroke phase can be attributed to the overestimation of the pressure minima within shed vortices. © 1997 John Wiley & Sons, Ltd.
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  • 10
    Electronic Resource
    Electronic Resource
    A deforming finite element mesh for use in moving one-dimensional boundary wave problems (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 407-420 
    Details
    ISSN: 0271-2091
    Keywords: wave ; finite element ; deforming mesh ; run-up ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The finite element method is developed to solve the problem of wave run-up on a mild, plane slope. A novel approach to implementing a deforming mesh of one-dimensional, three-node, isoparametric elements is described and demonstrated. The discrete time interval (DTI), arbitrary Lagrangian-Eulerian (ALE) and space-time element (STE) methods are used to solve the unsteady one-dimensional shallow water wave equations. The boundary condition required is simply the seaward water surface elevation, and although the method has only been tested for monochromatic waves, it should be equally valid for any sea state which can be described as a water surface elevation as a function of time. All three solution methods are shown to given good results. Time histories of the terms of the governing equations are calculated and used to demonstrate how the ALE and STE methods account for mesh deformation. The model could be extended to two dimensions, which would have practical application to the run-up of obliquely incident waves. © 1997 John Wiley & Sons, Ltd.
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  • 11
    Electronic Resource
    Electronic Resource
    Anisotropic unstructured mesh adaption for flow simulations (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 475-491 
    Details
    ISSN: 0271-2091
    Keywords: mesh ; anisotropic ; adaptation ; Delaunay ; metric ; CFD ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Three new ideas for anisotropic adaption of unstructured triangular grids are presented, with particular emphasis on fluid flow computations. © 1997 John Wiley & Sons, Ltd.
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  • 12
    Electronic Resource
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    Development of an artificial compressibility methodology using flux vector splitting (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 523-545 
    Details
    ISSN: 0271-2091
    Keywords: incompressible Navier-Stokes equations ; flux-vector-splitting method ; artificial compressibility ; upwind schemes ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An implicit, upwind arithmetic scheme that is efficient for the solution of laminar, steady, incompressible, two-dimensional flow fields in a generalised co-ordinate system is presented in this paper. The developed algorithm is based on the extended flux-vector-splitting (FVS) method for solving incompressible flow fields. As in the case of compressible flows, the FVS method consists of the decomposition of the convective fluxes into positive and negative parts that transmit information from the upstream and downstream flow field respectively. The extension of this method to the solution of incompressible flows is achieved by the method of artificial compressibility, whereby an artificial time derivative of the pressure is added to the continuity equation. In this way the incompressible equations take on a hyperbolic character with pseudopressure waves propagating with finite speed. In such problems the ‘information’ inside the field is transmitted along its characteristic curves. In this sense, we can use upwind schemes to represent the finite volume scheme of the problem's governing equations. For the representation of the problem variables at the cell faces, upwind schemes up to third order of accuracy are used, while for the development of a time-iterative procedure a first-order-accurate Euler backward-time difference scheme is used and a second-order central differencing for the shear stresses is presented. The discretized Navier-Stokes equations are solved by an implicit unfactored method using Newton iterations and Gauss-Siedel relaxation. To validate the derived arithmetical results against experimental data and other numerical solutions, various laminar flows with known behaviour from the literature are examined. © 1997 John Wiley & Sons, Ltd.
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  • 13
    Electronic Resource
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    A FINITE ELEMENT MODEL FOR THE SIMULATION OF DENSE GAS DISPERSION IN THE ATMOSPHERE (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 291-317 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; dense gas dispersion ; density stratification ; anisotropic turbulent viscosity ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A state-of-the-art model is developed for the simulation of the dispersion of hazardous toxic or flammable gases heavier than air in the atmosphere. The model depends on solving the Reynolds-averaged Navier-Stokes equations in addition to the energy equation and a species concentration equation for the contaminant gas. Turbulence closure is achieved by using a buoyancy-extended version of the standard k- ∊ two-equation model. The buoyancy extension is introduced to account for the anisotropic turbulent viscosity resulting from the strong stratification introduced by the dense gas clouds. The spatial discretization is achieved via the Galerkin finite element method, while the solution is advanced in time using the forward Euler method. A special element layer is introduced in the near-ground region to bridge the gap between the solid wall and the main solution domain where the turbulence model can be applied. This special element layer eliminates the need to apply the wall function in the standard way where any oscillations in the pressure field could contaminate the velocity solution. The model was tested against the Burro-8 field trial and could predict the experiment satisfactorily to within the experimental uncertainties of the reported results. © by 1997 John Wiley & Sons, Ltd.
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  • 14
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    SUBGRID VOLUMETRIC QUADRATURE ACCURACY FOR TRANSIENT COMPRESSIBLE FLOW PREDICTIONS (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 143-149 
    Details
    ISSN: 0271-2091
    Keywords: transient compressible flow ; finite element ; quadrature ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite volume-element formulation of the Navier-Stokes equations for compressible flows is applied to the transient shock tube problem. A second-order spatial quadrature for volumetric integration is studied because of its effects on the shock wave resolution and positioning. Low quadrature order is shown to produce solution anomalies in regions with a transonic character as well as poor predictions of shock wave propagation. The second-order volumetric quadrature includes the proper upstream and downstream solution behaviour and eliminates both the transonic and shock speed errors in the transient shock tube problem. © 1997 John Wiley & Sons, Ltd.
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  • 15
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    A NEW OPTIMAL SHAPE DESIGN PROCEDURE FOR INVISCID AND VISCOUS TURBULENT FLOWS (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 183-203 
    Details
    ISSN: 0271-2091
    Keywords: shape design ; turbulent flow ; automatic differentiation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new approach for optimal shape design is introduced. The main ingredients are an unstructured CAD-free framework for geometry deformation and automatic differentiation (AD) in reverse mode. Transonic inviscid and viscous turbulent flows are investigated. Both two- and three- dimensional configurations are considered. These cases involve up to several thousand control parameters. © 1997 John Wiley & Sons, Ltd.
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  • 16
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    AN EVALUATION OF THE BOUNCE-BACK BOUNDARY CONDITION FOR LATTICE BOLTZMANN SIMULATIONS (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 249-263 
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    ISSN: 0271-2091
    Keywords: lattice Boltzmann ; boundary conditions ; bounce-back; accuracy ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The bounce-back boundary condition for lattice Boltzmann simulations is evaluated for flow about an infinite periodic array of cylinders. The solution is compared with results from a more accurate boundary condition formulation for the lattice Boltemann method and with finite difference solutions. The bounce-back boundary condition is used to simulate boundaries of cylinders with both circular and octagonal cross-sections. The convergences of the velocity and total drag associated with this method are slightly sublinear with grid spacing. Error is also a function of relaxation time, increasing exponentially for large relaxation times. However, the accuracy does not exhibit a trend with Reynolds number between 0·1 and 100. The square lattice Boltzmann grid conforms to the octagonal cylinder but only approximates the circular cylinder, and the resulting error associated with the octagonal cylinder is half the error of the circular cylinder. The bounce-back boundary condition is shown to yield accurate lattice Boltzmann simulations with reduced computational requirements for computational grids of 170×170 or finer, a relaxation time less than 1·5 and any Reynolds number from 0·1 to 100. For this range of parameters the root mean square error in velocity and the relative error in drag coefficient are less than 1 per cent for the octagonal cylinder and 2 per cent for the circular cylinder. © 1997 John Wiley & Sons, Ltd.
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  • 17
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    The three-dimensional prolonged adaptive unstructured finite element multigrid method for the Navier-Stokes equations (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 371-392 
    Details
    ISSN: 0271-2091
    Keywords: adaptive grids ; finite element method ; iterative solvers ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents the development of the three- dimensional prolonged adaptive finite element equation solver for the Navier-Stokes equations. The finite element used is the tetrahedron with quadratic approximation of the velocities and linear approximation of the pressure. The equation system is formulated in the basic variables. The grid is adapted to the solution by the element Reynolds number. An element in the grid is refined when the Reynolds number of the element exceeds a preset limit. The global Reynolds number in the investigation is increased by scaling the solution for a lower Reynolds number. The grid is refined according to the scaled solution and the prolonged solution for the lower Reynolds number constitutes the start vector for the higher Reynolds number. Since the Reynolds number is the ratio of convection to diffusion, the grid refinements act as linearization and symmetrization of the equation system. The linear equation system of the Newton formulation is solved by CGSTAB with coupled node fill-in preconditioner. The test problem considered is the three-dimensional driven cavity flow. © 1997 John Wiley & Sons, Ltd.
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  • 18
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    Transient 1D transport equation simulated by a mixed Green element formulation (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 437-454 
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    ISSN: 0271-2091
    Keywords: Green element method ; diffusion-advection ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: New discrete element equations or coefficients are derived for the transient 1D diffusion-advection or transport equation based on the Green element replication of the differential equation using linear elements. The Green element method (GEM), which solves the singular boundary integral theory (a Fredholm integral equation of the second kind) on a typical element, gives rise to a banded global coefficient matrix which is amenable to efficient matrix solvers. It is herein derived for the transient 1D transport equation with uniform and non-uniform ambient flow conditions and in which first-order decay of the containment is allowed to take place. Because the GEM implements the singular boundary integral theory within each element at a time, the integrations are carried out in exact fashion, thereby making the application of the boundary integral theory more utilitarian. This system of discrete equations, presented herein for the first time, using linear interpolating functions in the spatial dimensions shows promising stable characteristics for advection-dominant transport. Three numerical examples are used to demonstrate the capabilities of the method. The second-order-correct Crank-Nicolson scheme and the modified fully implicit scheme with a difference weighting value of two give superior solutions in all simulated examples. © 1997 John Wiley & Sons, Ltd.
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  • 19
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    On a compact mixed-order finite element for solving the three-dimensional incompressible Navier-Stokes equations (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 513-522 
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    ISSN: 0271-2091
    Keywords: compact ; multivariant ; compressed row storage ; univariant ; multifrontal ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Our work is an extension of the previously proposed multivariant element. We assign this refined element as a compact mixed-order element in the sense that use of this element offers a much smaller bandwidth. The analysis is implemented on quadratic hexahedral elements with a view to analysing a three-dimensional incompressible viscous flow problem using a method formulated within the mixed finite element context. The idea of constructing such a stable element is to bring the marker-and-cell (MAC) grid lay-out to the finite element context. This multivariant element can thus be classified as a discontinuous pressure element. We have several reasons for advocating the proposed multivariant element. The primary advantage gained is its ability to reduce the bandwidth of the matrix equation, as compared with its univariant counterparts, so that it can be effectively stored in a compressed row storage (CRS) format. The resulting matrix equation can be solved efficiently by a multifrontal solver owing to its reduced bandwidth. The coding is, however, complicated by the appearance of restricted degrees of freedom at mid-face nodes. Through analytic study this compact multivariant element has a marked advantage over the multivariant element of Gupta et al. in that both bandwidth and computation time have been drastically reduced. © 1997 John Wiley & Sons, Ltd.
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    Numerical computations of internal flows for axisymmetric and two-dimensional nozzles (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 599-610 
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    ISSN: 0271-2091
    Keywords: axisymmetric nozzles ; two-dimensional nozzles ; Navier-Stokes solver ; internal flows ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: MacCormack's explicit time-marching scheme is used to solve the full Navier-Stokes unsteady, compressible equations for internal flows. The requirement of a very fine grid to capture shock as well as separated flows is circumvented by employing grid clustering. The numerical scheme is applied for axisymmetric as well as two-dimensional flows. Numerical predictions are compared with experimental data and the qualitative as well as the quantitative agreement is found to be quite satisfactory. © 1997 John Wiley & Sons, Ltd.
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    Parallel finite element calculation of flow in a three-dimensional lid-driven cavity using the CM-5 and T3D (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 1449-1461 
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    ISSN: 0271-2091
    Keywords: parallel finite element ; three-dimensional ; incompressible ; steady ; flow ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Steady flows in a three-dimensional lid-driven cavity at moderate Reynolds number are studied using various methods of parallel programming on the Cray T3D and Thinking Machines CM-5. These three-dimensional flows are compared with flows computed in a two-dimensional cavity. Solutions at Reynolds number up to 500 agree well with the experimental data of Aidun et al. (Phys. Fluids A, 3, 2081-2091 (1991)) for the location of separation of the secondary eddy at the downstream wall. Convergence of the three-dimensional problem using GMRES with diagonal preconditioning could not be obtained at Reynolds number greater than about 500. We speculate that the source of the difficulty is the loss of stability via pitchfork and Hopf bifurcations identified by Aidun et al. The relative performance of various methods of message passing on the Cray T3D is compared with the data-parallel mode of programming on the CM-5. No clear advantage between machines or message-passing methods is distinguished. © 1997 John Wiley & Sons, Ltd.
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    A PSEUDOSPECTRAL CODE FOR CONVECTION WITH AN ANALYTICAL/NUMERICAL IMPLEMENTATION OF HORIZONTAL BOUNDARY CONDITIONS (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 151-166 
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    ISSN: 0271-2091
    Keywords: convection ; shear flow ; boundary conditions ; pseudospectral ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new code for simulating convection in a horizontal layer of fluid is described. The code can be used to study the usual Rayleigh -Bénard convection problem but can also incorporate internal heating, rotation and the vortex force responsible for Langmuir circulation. Boundary conditions in the horizontal directions are periodic, but a wide range of conditions may be imposed on the upper and lower boundaries.A novel feature of the method is the way in which these boundary conditions are implemented through the following analytical/numerical technique. The governing partial differential equations are reduced to a number of inhomogeneous second-order ODEs for the horizontal Fourier modes. The solutions to these are then written as the sum of a particular integral and a complementary function. The former is easily computed (numerically) without regard to the boundary conditions and the latter is then selected (analytically/numerically) to ensure that the boundary conditions are met.We apply our code to the problem of highly supercritical thermal convection in a shear flow. We compare our results with simulations in the literature and, by integrating over a longer time interval, find flow features not observed in the previous simulations, including stable time-dependent states, multiple stable equilibria and chaos. © 1997 John Wiley & Sons, Ltd.
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    SOLUTION ALGORITHM FOR LOW-PECLET-NUMBER REACTING FLOW (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 225-243 
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    ISSN: 0271-2091
    Keywords: Navier-Stokes ; low Peclet number ; chemical vapour deposition ; low Mach number ; finite volume ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An enhanced solution strategy based on the SIMPLER algorithm is presented for low-Peclet-number mass transport calculations with applications in low-pressure material processing. The accurate solution of highly diffusive flows requires boundary conditions that preserve specified chemical species mass fluxes. The implementation of such boundary conditions in the standard SIMPLER solution procedure leads to degraded convergence that scales with the Peclet number. Modifications to both the non-linear and linear parts of the solution algorithm remove the slow convergence problem. In particular, the linearized species transport equations must be implicitly coupled to the boundary condition equations and the combined system must be solved exactly at each non-linear iteration. The pressure correction boundary conditions are reformulated to ensure that continuity is preserved in each finite volume at each iteration. The boundary condition scaling problem is demonstrated with a simple linear model problem. The enhanced solution strategy is implemented in a baseline computer code that is used to solve the multicomponent Navier-Stokes equations on a generalized, multiple-block grid system. Accelerated convergence rates are demonstrated for several material-processing example problems. © 1997 John Wiley & Sons, Ltd.
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    SEMI-IMPLICIT FINITE VOLUME SHALLOW-WATER FLOW AND SOLUTE TRANSPORT SOLVER WITH k-ε TURBULENCE MODEL (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 285-313 
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    ISSN: 0271-2091
    Keywords: shallow-water ; soluteep ; solver ; turbulence ; model ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A 3D semi-implicit finite volume scheme for shallow- water flow with the hydrostatic pressure assumption has been developed using the σ-co-ordinate system, incorporating a standard k-ε turbulence transport model and variable density solute transport with the Boussinesq approximation for the resulting horizontal pressure gradients. The mesh spacing in the vertical direction varies parabolically to give fine resolution near the bed and free surface to resolve high gradients of velocity, k and ε. In this study, wall functions are used at the bed (defined by the bed roughness) and wind stress at the surface is not considered. Surface elevation gradient terms and vertical diffusion terms are handled implicitly and horizontal diffusion and source terms explicitly, including the Boussinesq pressure gradient term due to the horizontal density gradient. The advection terms are handled in explicit (conservative) form using linear upwind interpolation giving second-order accuracy. A fully coupled solution for the flow field is obtained by substi- tuting for velocity in the depth-integrated continuity equation and solving for surface elevation using a conjugate gradient equation solver. Evaluation of horizontal gradients in the σ-co-ordinate system requires high-order derivatives which can cause spurious flows and this is avoided by obtaining these gradients in real space. In this paper the method is applied to parallel oscillatory (tidal) flow in deep and shallow water and compared with field measurements. It is then applied to current flow about a conical island of small side slope where vortex shedding occurs and velocities are compared with data from the laboratory. Computed concentration distributions are also compared with dye visualization and an example of the influence of temperature on plume dispersion is presented. © 1997 John Wiley & Sons, Ltd.
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    Stability analysis of numerical interface conditions in fluid-structure thermal analysis (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 421-436 
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    ISSN: 0271-2091
    Keywords: numerical analysis ; boundary conditions ; aerothermal coupling ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper analyses the numerical stability of coupling procedures in modelling the thermal diffusion in a solid and a fluid with continuity of temperature and heat flux at the interface. A simple one-dimensional model is employed with uniform material properties and grid density in each domain. A number of different explicit and implicit algorithms are considered for both the interior equations and the boundary conditions. The analysis shows that in general these are stable provided that Dirichlet boundary conditions are imposed on the fluid and Neumann boundary conditions are imposed on the solid; in each case the imposed values are obtained from the other domains. © 1997 John Wiley & Sons, Ltd.
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    Computer-aided analysis of flow past a surface-mounted obstacle (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 495-512 
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    ISSN: 0271-2091
    Keywords: separated flows ; recirculation length ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The incompressible, laminar, isothermal flow of a Newtonian fluid at steady state past a surface-mounted obstacle (flow over a step) is studied in a two-dimensional numerical experiment using the Galerkin finite element method. The dimensionless Navier-Stokes equations are solved in the whole range of the laminar flow regime. The numerical predictions are compared with available experimental data. The emphasis in the discussion of the results is on the presentation of the streamlines for various Reynolds numbers, the pressure distribution over and downstream of the step, the shear stress distribution along the surface of the step and the length of the recirculation region as a function of the Reynolds number. This analysis may be used in numerous applications from agricultural to civil, mechanical and chemical engineering. © 1997 John Wiley & Sons, Ltd.
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    A numerical investigation of 2d, steady free surface flows (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 567-598 
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    ISSN: 0271-2091
    Keywords: free surface flows ; finite volumes ; k-ε model ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Systematic tests have been performed to study the behaviour of a numerical method developed to calculate 2D, steady free surface flows. The Reynolds equations are solved in the physical space by employing a non-orthogonal staggered grid, while the k-ε model is adopted to approximate the Reynolds stresses. The free surface is calculated following an iterative procedure and various parameters that affect convergence and accuracy of the numerical solution have been examined. Calculated results are compared with measured data for two cases, i.e. the wave generation above a bottom topography at various Froude numbers and the free surface formation above a submerged hydrofoil. © 1997 John Wiley & Sons, Ltd.
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    A numerical study of turbulent line puffs via the renormalization group (RNG) k-∊ model (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 217-247 
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    ISSN: 0271-2091
    Keywords: puffs and thermals ; turbulence modelling ; jets and plumes ; environmental fluid mechanics ; vortex flow ; added mass ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The time evolution of a line puff, a turbulent non-buoyant element with significant momentum, is studied using the renormalization group (RNG) k-∊ model. The numerical results show that the puff motion is characterized by a vortex pair flow; the computed flow details and scalar mixing characteristics can be described by self-similar relations beyond a dimensionless time of around 30. The added mass coefficient of the puff motion is found to be approximately unity. The predicted puff flow and mixing rate are substantially similar to those obtained from the standard k-∊ model and are well supported by experimental data. The computed scalar field reveals significant secondary concentration peaks trailing behind in the wake of the puff. The present results suggest that the overall mixing rate of a puff is primarily determined by the large-scale motion and that streamline curvature probably plays a minor role. © 1998 John Wiley & Sons, Ltd.
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    Grid convergence studies for the prediction of hurricane storm surge (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 369-401 
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    ISSN: 0271-2091
    Keywords: storm surge ; shallow water model ; grid convergence ; coastal ocean ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The focus of this paper is a systematic determination of the relationship between grid resolution and errors associated with computations of hurricane storm surge. A grid structure is sought that provides the spatial resolution necessary to capture pertinent storm surge physics and does not overdiscretize. A set of numerical experiments simulating storm surge generation over 14 grid discretizations of idealized domains examines the influence of grid spacing, shoreline detail, coastline resolution and characteristics of the meteorological forcing on storm surge computations. Errors associated with a given grid are estimated using a Richardson-based error estimator. Analysis of the magnitude and location of estimated errors indicates that underresolution on the continental shelf leads to significant overprediction of the primary storm surge. In deeper waters, underresolution causes smearing or damping of the inverted barometer forcing function, which in turn results in underprediction of the surge elevation. In order to maintain a specified error level throughout the duration of the storm, the highest grid resolution is required on the continental shelf and particularly in nearshore areas. The disparity of discretization requirements between deep waters and coastal regions is best met using a graded grid. Application of the graded gridding strategy to the hindcast of Hurricane Camille reinforces the necessity of using a grid that has high levels of resolution in nearshore regions and areas of complex coastal geometry. © 1998 John Wiley & Sons, Ltd.
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    Viscous oscillatory flow around a circular cylinder at low Keulegan-Carpenter numbers and frequency parameters (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 403-442 
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    ISSN: 0271-2091
    Keywords: oscillating flow ; Keulegan-Carpenter number ; finite element method ; in-line force ; transverse force ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The results of a numerical study of the viscous oscillating flow around a circular cylinder at low Keulegan-Carpenter numbers (KC) and frequency parameters (β) are presented in this paper. The finite element method was used for the solution of the Navier-Stokes equations in the formulation where the streamfunction and vorticity are the field variables. The computation was conducted at Keulegan-Carpenter numbers extending up to KC=15 and frequency parameters ranging between β=6 and 100. At low values of the Keulegan-Carpenter number the flow remains symmetrical. As the Keulegan-Carpenter number is increased over a certain value which depends also on the frequency parameter, asymmetries appear in the flow which are eventually amplified and lead finally to complex vortex-shedding patterns, some of which are markedly different from those observed at higher frequency parameters. The solution revealed that although for certain values of KC and β the shedding of vortices is periodic, there also exists a complicated flow regime in which the flow is not periodic but switches between different modes in consecutive cycles of flow oscillation. For the various flow cases examined, the traces of the hydrodynamic forces are presented and the hydrodynamic coefficients and RMS values of the in-line force are compared with experimental evidence. © 1998 John Wiley & Sons, Ltd.
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    Direct numerical simulation of the amplification of a 2D temporal disturbance in plane Poiseuille flow (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 443-457 
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    ISSN: 0271-2091
    Keywords: direct numerical simulation ; 2D temporal disturbance ; plane Poiseuille flow ; finite difference method ; transient non-linear equation ; stream-function-vorticity equation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A direct numerical scheme is developed to study the temporal amplification of a 2D disturbance in plane Poiseuille flow. The transient non-linear Navier-Stokes equations are applied in a region of wavelength moving with the wave propagation speed. The complex amplitude involved in the perturbation functions is considered as the initial input of the non-linear stability equations. In this study a fully implicit finite difference scheme with five points in the flow direction and three points in the normal direction is developed so that numerical simulation of the amplification of a two-dimensional temporal disturbance in plane Poiseuille flow can be investigated. The growth and decay of the disturbance with time are presented and neutral stability curves which are in good agreement with existing solutions can be determined. The critical conditions as a function of the amplitude A0 of the disturbance are presented. Fixing the wavelength, the Navier-Stokes equations are solved up to Re=10,000 a friction factor increasing with Reynolds number is observed. The 2D non-linear behaviour of the streamfunction, vorticity and velocity components at Re=10,000 are also exhibited. © 1998 John Wiley & Sons, Ltd.
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    Effect of Reynolds number on the eddy structure in a lid-driven cavity (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 557-579 
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    ISSN: 0271-2091
    Keywords: lid-driven cavity ; Taylor-Görtler-like vortices ; instabilities ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper we apply a finite volume method, together with a cost-effective segregated solution algorithm, to solve for the primitive velocities and pressure in a set of incompressible Navier-Stokes equations. The well-categorized workshop problem of lid-driven cavity flow is chosen for this exercise, and results focus on the Reynolds number. Solutions are given for a depth-to-width aspect ration of 1:1 and a span-to width aspect ratio of 3:1. Upon increasing the Reynolds number, the flows in the cavity of interest were found to comprise a transition from a strongly two-dimensional character to a truly three-dimensional flow and, subsequently, a bifurcation from a stationary flow pattern to a periodically oscillatory state. Finally, viscous (Tollmien-Schlichting) travelling wave instability further induced longitudinal vortices, which are essentially identical to Taylor-Görtler vortices. The objective of this study was to extend our understanding of the time evolution of a recirculatory flow pattern against the Reynolds number. The main goal was to distinguish the critical Reynolds number at which the presence of a spanwise velocity makes the flow pattern become three-dimensional. Secondly, we intended to learn how and at what Reynolds number the onset of instability is generated. © 1998 John Wiley & Sons, Ltd.
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    A fast algorithm to solve viscous two-phase flow in an axisymmetric rocket nozzle (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 501-517 
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    ISSN: 0271-2091
    Keywords: Multiphase ; turbulent ; finite volumes ; structured grids ; compressible flows ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerically fast algorithm has been developed to solve the viscous two-phase flow in an axisymmetric rocket nozzle. A Eulerian-Eulerian approach is employed in the computation to couple the gas-particle flow. Turbulence closure is achieved using a Baldwin-Lomax model. The numerical procedure employs a multistage time-stepping Runge-Kutta scheme in conjunction with a finite volume method and is made computationally fast for the axisymmetric nozzle. The present numerical scheme is applied to compute the flow field inside JPL and AGARD nozzles. © 1998 John Wiley & Sons, Ltd.
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    Non-singular direct formulation of boundary integral equations for potential flows (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 627-635 
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    ISSN: 0271-2091
    Keywords: arbitrary-order boundary element method ; non-singular formulation ; potential problems ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents a general direct integral formulation for potential flows. The singularities of Green's functions are desingularized theoretically, using a subtracting and adding back technique, so that Gaussian quadrature or any other numerical integration methods can be applied directly to evaluate all the integrals without any difficulty. When high-order quadrature formulas are applied globally, the number of unknowns can be reduced. Interpolation functions are not necessary for unknown variables in the present paper. Therefore, the present method is much simpler and more efficient than the conventional one. Several numerical examples are calculated and compared satisfactorily with analytical solutions or published results. © 1998 John Wiley & Sons, Ltd.
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    Parallel computation of atmospheric pollutant dispersion under unstably stratified atmosphere (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 677-696 
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    ISSN: 0271-2091
    Keywords: second-order closure model ; pollutant dispersion ; finite element method ; unstably stratified atmosphere ; parallel computation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Pollutant dispersion under unstably stratified atmosphere was investigated numerically using the finite element method. The effects of atmospheric stability on plume trajectory were studied using a three-dimensional second-order closure dispersion model. The numerical model was implemented using domain decomposition method and carried out using a parallel computer. The computation accelerates significantly and the size of computation can be largely increased as a result of the parallelism. A passive contaminant point source was placed at the middle of the convective boundary layer to simulate the atmospheric dispersion. The requirement of the input of dispersion coefficients in k-theory and Gaussian models was replaced with direct input of turbulence flow data. It was found that the present numerical model can predict several non-Gaussian plume behaviours and the computed results agreed well with findings from experimental observations. © 1998 John Wiley & Sons, Ltd.
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    Computation of viscoelastic cable coating flows (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 697-712 
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    ISSN: 0271-2091
    Keywords: viscoelastic ; boundary conditions ; tube tooling ; cable-coating ; finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A viscoelastic analysis is presented for model tube tooling, draw-down and combined geometry flows encountered in the cable coating industries. The work investigates the development of stress fields and studies the effect of varying entry flow stress boundary conditions. The analysis takes into account tube tooling and draw-down flow sections individually, and in combination. The flow behaviour of cable-coating grade low density polyethylene is studied assuming a viscoelastic, isothermal flow, and employing a Taylor-Petrov-Galerkin finite element scheme with an exponential Phan-Thien-Tanner constitutive model. © 1998 John Wiley & Sons, Ltd.
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    Numerical analysis of breaking waves using the moving particle semi-implicit method (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 751-769 
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    ISSN: 0271-2091
    Keywords: MPS ; particle method ; incompressible flow ; free surface ; breaking wave ; surf similarity parameter ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The numerical method used in this study is the moving particle semi-implicit (MPS) method, which is based on particles and their interactions. The particle number density is implicitly required to be constant to satisfy incompressibility. A semi-implicit algorithm is used for two-dimensional incompressible non-viscous flow analysis. The particles whose particle number densities are below a set point are considered as on the free surface. Grids are not necessary in any calculation steps. It is estimated that most of computation time is used in generation of the list of neighboring particles in a large problem. An algorithm to enhance the computation speed is proposed. The MPS method is applied to numerical simulation of breaking waves on slopes. Two types of breaking waves, plunging and spilling breakers, are observed in the calculation results. The breaker types are classified by using the minimum angular momentum at the wave front. The surf similarity parameter which separates the types agrees well with references. Breaking waves are also calculated with a passively moving float which is modelled by particles. Artificial friction due to the disturbed motion of particles causes errors in the flow velocity distribution which is shown in comparison with the theoretical solution of a cnoidal wave. © 1998 John Wiley & Sons, Ltd.
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    An efficient operator splitting scheme for three-dimensional hydrodynamic computations (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 771-789 
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    ISSN: 0271-2091
    Keywords: three-dimensional numerical method ; hybrid method ; splitting method ; Eulerian-Lagrangian method ; shallow water equations ; sigma co-ordinate transformation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new efficient numerical method for three-dimensional hydrodynamic computations is presented and discussed in this paper. The method is based on the operator splitting method and combined with Eulerian-Lagrangian method, finite element method and finite difference method. To increase the efficiency and stability of the numerical solutions, the operator splitting method is employed to partition the momentum equations into three parts, according to physical phenomena. A time step is divided into three time substeps. In the first substep, advection and Coriolis force are solved using the explicit Eulerian-Lagrangian method. In the second substep, horizontal diffusion is approximated by implicit FEM in each horizontal layer. In the last substep, the continuity equation is solved by implicit FEM, and vertical diffusion and pressure gradient are discretized by implicit FDM in each nodal column. The stability analysis shows that this method is unconditionally stable. A number of numerical experiments have been performed. The results simulated by the present scheme agree well with analytical solutions and the other documented model results. The method is efficient for 3D shallow water flow computations and fully fits complicated configurations. © 1998 John Wiley & Sons, Ltd.
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    A numerical simulation of hydrodynamic forces of ground-effect problem using Lagrange's equation of motion (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 725-747 
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    ISSN: 0271-2091
    Keywords: unsteady two-body interaction ; potential flow theory ; boundary-integral method ; Lagrange's equation of motion ; generalized Taylor's formula ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: On the basis of the potential flow theory, Lagrange's equation of motion is used to study the unsteady ground-effect problem. The forces and moments acting on the moving body are solved in terms of the derivatives of added masses in which the generalized Taylor's formulae are applied. The singular integral equations used to solve the surface source intensities and their derivatives are regularized by the Gauss flux theorem and are therefore amenable to the direct use of the Gaussian quadrature formula. In illustration, the condition of a prolate spheroid moving in the fore-and-aft direction at constant speed past a flat ground with a protrusion is considered. The hydrodynamic forces and moments acting on the moving spheroid are investigated systematically by varying the size of the protrusion and the cruising height of the spheroid. © 1998 John Wiley & Sons, Ltd.
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    Numerical analysis of secondary instabilities of the incompressible boundary layer flow with suction (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 811-835 
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    ISSN: 0271-2091
    Keywords: Floquet ; subharmonic ; fundamental ; secondary instability ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Based on the Euler-Maclaurin formula, a compact finite difference scheme is employed to solve a two-point boundary value problem for studying the secondary instabilities of the boundary layer flow. The parametric resonance of unstable waves is explored using the Floquet method. For both subharmonic and fundamental modes, two additional Fourier terms are added in the analysis, and the spatial growth rates are determined. The effect of suction mechanism on the secondary instability waves is also investigated. From numerical experiments, it is shown that the proposed numerical scheme is very promising. © 1998 John Wiley & Sons, Ltd.
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    Calculation of laminar flows with second-order schemes and collocated variable arrangement (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 887-905 
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    ISSN: 0271-2091
    Keywords: laminar flows ; incompressible flows ; second-order schemes ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical study of laminar flows is carried out to examine the performance of two second-order discretization schemes: a total variation diminishing scheme and a second-order upwind scheme. The former has the same form as the standard first-order hybrid central upwind scheme, but with a numerical diffusion reduced by the Van Leer limiter; the latter is based on the linear extrapolation of cell face values using the two upwind neighbors. A collocated grid arrangement is used; oscillations which could be generated by pressure-velocity decoupling are avoided via the Rhie-Chow interpolation. Two iterative solution methods are used: (i) the deferred correction procedure proposed by Khosla and Rubin and (ii) implicit treatment of the second-order upwind contribution. Three two-dimensional laminar test cases are considered for assessment: the plane lid-driven cavity, the plane backward facing step and the axisymmetric pipe with sudden contraction. Experimental data are available for the two last cases. Both the total variation diminishing and the second-order upwind schemes give wiggle-free results and can predict the flowfields more accurately than the standard first-order hybrid central upwind scheme. © 1998 John Wiley & Sons, Ltd.
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    A semi-coarsening strategy for unstructured multigrid based on agglomeration (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 927-957 
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    ISSN: 0271-2091
    Keywords: multigrid methods ; finite elements ; finite volumes ; semi-coarsening ; numerical analysis ; turbulent flows ; compressible flows ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Extending multigrid concepts to the calculation of complex compressible flow is usually not straightforward. This is especially true when non-embedded grid hierarchies or volume agglomeration strategies are used to construct a gradation of unstructured grids. In this work, a multigrid method for solving second-order PDE's on stretched unstructured triangulations is studied. The finite volume agglomeration multigrid technique originally developed for solving the Euler equations is used (M.-H. Lallemand and A. Dervieux, in Multigrid Methods, Theory, Applications and Supercomputing, Marcel Dekker, 337-363 (1988)). First, a directional semi-coarsening strategy based on Poisson's equation is proposed. The second-order derivatives are approximated on each level by introducing a correction factor adapted to the semi-coarsening strategy. Then, this method is applied to solve the Poisson equation. It is extended to the 2D Reynolds-averaged Navier-Stokes equations with appropriate boundary treatment for low-Reynolds number turbulent flows. © 1998 John Wiley & Sons, Ltd.
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    A three-dimensional simulation of a steady approach flow past a circular cylinder at low Reynolds number (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 1003-1022 
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    ISSN: 0271-2091
    Keywords: steady approach flow ; low Reynolds numbers ; 3D simulation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The three-dimensional (3D) unsteady viscous wake of a circular cylinder exposed to a steady approach flow is calculated using a fractional-step finite-difference/spectral-element method. The calculated flow fields at Reynolds numbers of 100 (2D) and 200 (3D) are examined in detail. The flow field at Re = 100 is 2D as expected, while the flow field at Re = 200 has distinct 3D features, with spanwise wavelengths of about 3.75 cylinder diameters. The calculated results produce drag and lift coefficients and Strouhal numbers that agree extremely well with the experimental values. These 3D values at Re = 200 are in better agreement with experimental values than the results of a 2D calculation at Re = 200, which is expected. © 1998 John Wiley & Sons, Ltd.
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    Domain decomposition for the incompressible Navier-Stokes equations: solving subdomain problems accurately and inaccurately (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 1217-1237 
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    ISSN: 0271-2091
    Keywords: domain decomposition ; GCR ; Krylov-Schwarz ; incompressible Navier-Stokes ; boundary-fitted co-ordinates ; finite volume ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: For the solution of practical flow problems in arbitrarily shaped domains, simple Schwarz domain decomposition methods with minimal overlap are quite efficient, provided Krylov subspace methods, e.g. the GMRES method, are used to accelerate convergence. With an accurate subdomain solution, the amount of time spent solving these problems may be quite large. To reduce computing time, an inaccurate solution of subdomain problems is considered, which requires a GCR-based acceleration technique. Much emphasis is put on the multiplicative domain decomposition algorithm since we also want an algorithm which is fast on a single processor. Nevertheless, the prospects for parallel implementation are also investigated. © 1998 John Wiley & Sons, Ltd.
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    A general algorithm for compressible and incompressible flows. Part III: The semi-implicit form (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 27 (1998), S. 13-32 
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    ISSN: 0271-2091
    Keywords: splitting ; pressure stabilization ; characteristic schemes ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper we consider some particular aspects related to the semi-implicit version of a fractional step finite element method for compressible flows that we have developed recently. The first is the imposition of boundary conditions. We show that no boundary conditions at all need to be imposed in the first step where an intermediate momentum is computed. This allows us to impose the real boundary conditions for the pressure, a point that turns out to be very important for compressible flows.The main difficulty of the semi-implicit form of the scheme arises in the solution of the continuity equation, since it involves both the density and the pressure. These two variables can be related through the equation of state, which in turn introduces the temperature as a variable in many cases. We discuss here the choice of variables (pressure or density) and some strategies to solve the continuity equation.The final point that we study is the behaviour of the scheme in the incompressible limit. It is shown that the method has an inherent pressure dissipation that allows us to reach this limit without having to satisfy the classical compatibility conditions for the interpolation of the velocity and the pressure. © 1998 John Wiley & Sons, Ltd.
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    Unstructured mesh procedures for the simulation of three-dimensional transient compressible inviscid flows with moving boundary components (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 27 (1998), S. 41-55 
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    ISSN: 0271-2091
    Keywords: unstructured mesh ; compressible flow ; transient flow ; mesh adaptation ; moving boundaries ; Delaunay triangulation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The solution of high-speed transient inviscid compressible flow problems in three dimensions is considered. Discretization of the spatial domain is accomplished by the use of tetrahedral elements generated by Delaunay triangulation with automatic point creation. Methods of adapting the mesh to allow for boundary movement are considered and a strategy for ensuring boundary recovery is proposed. An explicit multistage time-stepping algorithm is employed to advance the flow solution. A number of examples are included to illustrate the numerical performance of the proposed procedures. © 1998 John Wiley & Sons, Ltd.
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    On a multilevel approach for the two dimensional Navier-Stokes equations with finite elements (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 27 (1998), S. 241-258 
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    ISSN: 0271-2091
    Keywords: multilevel algorithm ; 2D Navier-Stokes equations ; finite element ; large eddy simulations ; long time integration ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We study if the multilevel algorithm introduced in Debussche et al. (Theor. Comput. Fluid Dynam., 7, 279-315 (1995)) and Dubois et al. (J. Sci. Comp., 8, 167-194 (1993)) for the 2D Navier-Stokes equations with periodic boundary conditions and spectral discretization can be generalized to more general boundary conditions and to finite elements. We first show that a direct generalization, as in Calgaro et al. (Appl. Numer. Math., 21, 1-40 (1997)), for the Burgers equation, would not be very efficient. We then propose a new approach where the domain of integration is decomposed in subdomains. This enables us to define localized small-scale components and we show that, in this context, there is a good separation of scales. We conclude that all the ingredients necessary for the implementation of the multilevel algorithm are present. © 1998 John Wiley & Sons, Ltd.
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    A parallel solver based on the dual Schur decomposition of general finite element matrices (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 23-46 
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    ISSN: 0271-2091
    Keywords: domain decomposition ; parallel algorithms ; finite element ; Lagrange multipliers ; projected GMRES ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A parallel solver based on domain decomposition is presented for the solution of large algebraic systems arising in the finite element discretization of mechanical problems. It is hybrid in the sense that it combines a direct factorization of the local subdomain problems with an iterative treatment of the interface system by a parallel GMRES algorithm. An important feature of the proposed solver is the use of a set of Lagrange multipliers to enforce continuity of the finite element unknowns at the interface. A projection step and a preconditioner are proposed to control the conditioning of the interface matrix.The decomposition of the finite element mesh is formulated as a graph partitioning problem. A two-step approach is used where an initial decomposition is optimized by non-deterministic heuristics to increase the quality of the decomposition.Parallel simulations of a Navier-Stokes flow problem carried out on a Convex Exemplar SPP system with 16 processors show that the use of optimized decompositions and the preconditioning step are keys to obtaining high parallel efficiencies. Typical parallel efficiencies range above 80%. © 1998 John Wiley & Sons, Ltd.
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    Large eddy simulation of temporally developing juncture flows (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 47-72 
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    ISSN: 0271-2091
    Keywords: large eddy simulation ; juncture flows ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Large eddy simulation (LES) results are reported for temporally developing solid-solid and solid-rigid-lid juncture flows. A MacCormack-type scheme that is second-order in time, and fourth-order in space for the convective terms and second-order in space for the viscous terms, is used. The simulations are obtained for a low subsonic Mach number. The subgrid-scale stresses (SGS) are modeled using the dynamic modeling procedure. The turbulent flow field generated on a flat-plate boundary layer is used to initialize the juncture flow simulations. The results of the flat-plate boundary layer simulations are validated with experimental and direct numerical simulations (DNS) data. In juncture flow simulations, the presence of an adjacent solid-wall/rigid-lid boundary altered the mean and the turbulent field, setting up gradients in the anisotropy of normal Reynolds stresses resulting in the formation of turbulence-induced secondary vortices. The relative size of these secondary vortices and the distribution of mean and turbulent quantities are in qualitative agreement with the experimental observations for the solid-solid juncture. The overall distribution of the mean and turbulence quantities showed close resemblance between the solid-solid and the solid-rigid-lid junctures; except for the absence of a second vortical region near the rigid-lid boundary. In agreement with the experimental observations, it was found that the normalized anisotropy term exhibited similarity when plotted against the distance from the boundary, regardless of the type of boundary, i.e. solid-wall or rigid-lid. The turbulent kinetic energy increased near the rigid-lid boundary. While the surface normal velocity fluctuations decreased to zero at the rigid-lid boundary, the other two velocity components showed an increase in their energy, which is also consistent with the experimental observations. © 1998 John Wiley & Sons, Ltd.
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    On initial, boundary conditions and viscosity coefficient control for Burgers' equation (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 113-128 
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    ISSN: 0271-2091
    Keywords: optimal control ; Burgers' equation ; data assimilation ; adjoint model ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In order to use the optimal control techniques in models of geophysical flow circulation, an application to a 1D advection-diffusion equation, the so-called Burgers' equation, is described. The aim of optimal control is to find the best parameters of the model which ensure the closest simulation to the observed values. In a more general case, the continuous problem and the corresponding discrete form are formulated. Three kinds of simulation are realized to validate the method. Optimal control processes by initial and boundary conditions require an implicit discretization scheme on the first time step and a decentered one for the non-linear advection term on boundaries. The robustness of the method is tested with a noised dataset and random values of the initial controls. The optimization process of the viscosity coefficient as a time- and space-dependent variable is more difficult. A numerical study of the model sensitivity is carried out. Finally, the numerical application of the simultaneous control by the initial conditions, the boundary conditions and the viscosity coefficient allows a possible influence between controls to be taken into account. These numerical experiments give methodological rules for applications to more complex situations. © 1998 John Wiley & Sons, Ltd.
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    A numerical study on flow through the spiral casing of a hydraulic turbine (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 143-156 
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    ISSN: 0271-2091
    Keywords: turbine ; spiral casing ; finite element method ; Galerkin weighted residual technique ; Gauss-Legendre quadrature ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Flow through the spiral casing of a hydraulic turbine was analyzed. Reynolds averaged Navier-Stokes equations were solved using a finite element method. The physical domain was divided into a number of hexahedral elements which are isoparametrically mapped onto standard cubic elements. Numerical integration for the unsteady momentum equation is performed over such hexahedral elements to obtain a provisional velocity field. Compliance with the mass conservation equation and determination of the pressure correction are accomplished through an iterative procedure. The velocity distribution inside the spiral casing corroborates the results available in literature. The static pressure at the midplane generally decreases from the outside wall towards the exit of the spiral casing. © 1998 John Wiley & Sons, Ltd.
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    Free-surface flow over curved surfaces: Part II: Computational model (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 201-213 
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    ISSN: 0271-2091
    Keywords: curved surface ; shallow water ; non-hydrostatic ; spillway ; finite element ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In Part I a detailed derivation of a more general shallow water equation set was developed via a perturbation analysis. A finite element computational model of these more general equations is now constructed and the model behavior is compared with conventional shallow water formulations applied to an outletworks flume. © 1998 John Wiley & Sons, Ltd.
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    Numerical and experimental investigation of turbulent flow in a rectangular duct (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 225-242 
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    ISSN: 0271-2091
    Keywords: turbulent flow ; non-linear turbulence modelling ; secondary flow ; rectangular duct ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Details of the turbulent flow in a 1:8 aspect ratio rectangular duct at a Reynolds number of approximately 5800 were investigated both numerically and experimentally. The three-dimensional mean velocity field and the normal stresses were measured at a position 50 hydraulic diameters downstream from the inlet using laser doppler velocimetry (LDV). Numerical simulations were carried out for the same flow case assuming fully developed conditions by imposing cyclic boundary conditions in the main flow direction. The numerical approach was based on the finite volume technique with a non-staggered grid arrangement and the SIMPLEC algorithm. Results have been obtained with a linear and a non-linear (Speziale) k-ε model, combined with the Lam-Bremhorst damping functions for low Reynolds numbers. The secondary flow patterns, as well as the magnitude of the main flow and overall parameters predicted by the non-linear k-ε model, show good agreement with the experimental results. However, the simulations provide less anisotropy in the normal stresses than the measurements. Also, the magnitudes of the secondary velocities close to the duct corners are underestimated. © 1998 John Wiley & Sons, Ltd.
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    Computations using the preconditioning BI-CGSTAB algorithm in chemical non-equilibrium problems (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 267-291 
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    ISSN: 0271-2091
    Keywords: non-equilibrium equations ; Bi-CGSTAB method ; adaptive grid ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A robust method for solving the chemical non-equilibrium Navier-Stokes equations, including all of the species conservation and energy production equations, is developed. The algorithm is embodied in a fully coupled, implicit, large block structure. Van Leer flux splitting for inviscid terms and central differencing for viscous terms in the explicit operators are applied in the numerical algorithm. The fully-coupled system is solved implicitly and the bi-conjugate gradient stable (Bi-CGSTAB) method with a preconditioner of incomplete lower-upper (LU)-factorization (ILU) is used for solving large block structure and diagonal dominate matrix equations. The computations are performed for the hypersonic inflow over blunt bodies including half cylinder, double ellipse and blunt nose. The adaptive grid constructed by moving grid method is employed to capture the shock location. Computational results in the present study are compared with other calculated data and exhibit good agreement. Convergence histories of the mean flow variables and species equations demonstrate that the fast convergent rate can be achieved by the preconditioned Bi-CGSTAB method. © 1998 John Wiley & Sons, Ltd.
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    Efficient algebraic multigrid solvers with elementary restriction and prolongation (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 317-336 
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    ISSN: 0271-2091
    Keywords: algebraic multigrid ; elementary restriction/prolongation ; minimum residual methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An algebraic multigrid (AMG) scheme is presented for the efficient solution of large systems of coupled algebraic equations involving second-order discrete differentials. It is based on elementary (zero-order) intergrid transfer operators but exhibits convergence rates that are independent of the system bandwidth. Inconsistencies in the coarse-grid approximation are minimised using a global scaling approximation which requires no explicit geometrical information. Residual components of the error spectrum that remain poorly represented in the coarse-grid approximations are reduced by exploiting Krylof subspace methods. The scheme represents a robust, simple and cost-effective approach to the problem of slowly converging eigenmodes when low-order prolongation and restriction operators are used in multigrid algorithms. The algorithm investigated here uses a generalised conjugate residual (GCR) accelerator; it might also be described as an AMG preconditioned GCR method. It is applied to two test problems, one based on a solution of a discrete Poisson-type equation for nodal pressures in a pipe network, the other based on coupled solutions to the discrete Navier-Stokes equations for flows and pressures in a driven cavity. © 1998 John Wiley & Sons, Ltd.
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    A volume-tracking method for incompressible multifluid flows with large density variations (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 357-378 
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    ISSN: 0271-2091
    Keywords: interfacial flow ; multigrid ; surface tension ; flux-corrected transport ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical technique (FGVT) for solving the time-dependent incompressible Navier-Stokes equations in fluid flows with large density variations is presented for staggered grids. Mass conservation is based on a volume tracking method and incorporates a piecewise-linear interface reconstruction on a grid twice as fine as the velocity-pressure grid. It also uses a special flux-corrected transport algorithm for momentum advection, a multigrid algorithm for solving a pressure-correction equation and a surface tension algorithm that is robust and stable. In principle, the method conserves both mass and momentum exactly, and maintains extremely sharp fluid interfaces. Applications of the numerical method to prediction of two-dimensional bubble rise in an inclined channel and a bubble bursting through an interface are presented. © 1998 John Wiley & Sons, Ltd.
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    Numerical solution of a two-dimensional fluidized bed model (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 381-394 
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    ISSN: 0271-2091
    Keywords: fluidized bed ; hyperbolic PDEs ; Roe's method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The numerical solution of a model describing a two-dimensional fluidized bed is considered. The model takes the form of a hyperbolic system of conservation laws with source term, coupled with an elliptic equation for determining a streamfunction. Operator splitting is used to produce homogeneous one-dimensional hyperbolic systems and ordinary differential equations involving the source term. The one-dimensional hyperbolic problems are solved using Roe's method with the addition of an entropy fix. The numerical procedure is second-order in time and first-order in space. Second-order-accuracy in space is obtained using flux limiting techniques. Numerical experiments which show the development of bubbles in the bed are presented. The familiar kidney-shaped bubble, observed experimentally, is found when using the method which is second-order in space. On the same mesh, the first-order method produces bubbles which are no longer kidney-shaped. © 1998 John Wiley & Sons, Ltd.
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    Design sensitivity and finite element analysis of free surface flows with application to optimal design of casting rigging systems (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 419-442 
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    ISSN: 0271-2091
    Keywords: finite element analysis ; design sensitivity analysis ; optimization ; mold filling ; free surface ; turbulence ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A novel, fully-analytical design sensitivity formulation for transient, turbulent, free surface flows is derived and implemented in the context of finite element analysis. The time-averaged, turbulent form of the Navier-Stokes equations are solved using a mixing length model, in conjunction with the volume of fluid (VOF) method to model the free surface movement. The design derivatives of these governing equations are computed and solved to find the analytical sensitivities of the fluid position, velocity and pressure fields with respect to shape design variables. The computational efficiency produced by evaluating the sensitivities analytically is demonstrated. The design of the runner and gating system of a simple block casting is presented as an example application for using sensitivity information in design. The analytical sensitivity routine is coupled to a numerical optimizer to yield an automated method for optimal design of the casting rigging system. The results produce runner shapes which eliminate mold-gas aspiration. © 1998 John Wiley & Sons, Ltd.
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    An operator splitting algorithm for the three-dimensional advection-diffusion equation (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 461-476 
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    ISSN: 0271-2091
    Keywords: advection-diffusion equation ; operator splitting algorithm ; Holly and Preissmann scheme ; method of characteristics ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Operator splitting algorithms are frequently used for solving the advection-diffusion equation, especially to deal with advection dominated transport problems. In this paper an operator splitting algorithm for the three-dimensional advection-diffusion equation is presented. The algorithm represents a second-order-accurate adaptation of the Holly and Preissmann scheme for three-dimensional problems. The governing equation is split into an advection equation and a diffusion equation, and they are solved by a backward method of characteristics and a finite element method, respectively. The Hermite interpolation function is used for interpolation of concentration in the advection step. The spatial gradients of concentration in the Hermite interpolation are obtained by solving equations for concentration gradients in the advection step. To make the composite algorithm efficient, only three equations for first-order concentration derivatives are solved in the diffusion step of computation. The higher-order spatial concentration gradients, necessary to advance the solution in a computational cycle, are obtained by numerical differentiations based on the available information. The simulation characteristics and accuracy of the proposed algorithm are demonstrated by several advection dominated transport problems. © 1998 John Wiley & Sons, Ltd.
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    Non-reflecting boundary conditions applicable to general purpose CFD simulators (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 523-540 
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    ISSN: 0271-2091
    Keywords: non-reflecting boundary conditions ; numerical simulation ; compression wave ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In simulations of propagating blast waves the effects of artificial reflections at open boundaries can seriously degrade the accuracy of the computations. In this paper, a boundary condition based on a local approximation by a plane traveling wave is presented. The method yields small artificial reflections at open boundaries. The derivation and the theory behind these so-called plane-wave boundary conditions are presented. The method is conceptually simple and is easy to implement in two and three dimensions. These non-reflecting boundary conditions are employed in the three-dimensional computational fluid dynamics (CFD) solver FLACS, capable of simulating gas explosions and blast-wave propagation in complex geometries. Several examples involving propagating waves in one and two dimensions, shock tube and an example of a simulation of a propagating blast wave generated by an explosion in a compressor module are shown. The numerical simulations show that artificial reflections due to the boundary conditions employed are negligible. © 1998 John Wiley & Sons, Ltd.
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    The fundamental solution method for incompressible Navier-Stokes equations (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 565-568 
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    ISSN: 0271-2091
    Keywords: fundamental solution method ; integral equation method ; Navier-Stokes equations ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A complete boundary integral formulation for incompressible Navier-Stokes equations with time discretization by operator splitting is developed using the fundamental solutions of the Helmholtz operator equation with different order. The numerical results for the lift and the drag hysteresis associated with a NACA0012 aerofoil oscillating in pitch show good agreement with available experimental data. © 1998 John Wiley & Sons, Ltd.
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    VOLUME-TRACKING METHODS FOR INTERFACIAL FLOW CALCULATIONS (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 671-691 
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    ISSN: 0271-2091
    Keywords: volume tracking ; interfacial flow ; flux-corrected transport ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new algorithm for volume tracking which is based on the concept of flux-corrected transport (FCT) is introduced. It is applicable to incompressible 2D flow simulations on finite volume and difference meshes. The method requires no explicit interface reconstruction, is direction-split and can be extended to 3D and orthogonal curvilinear meshes in a straightforward manner. A comparison of the new scheme against well-known existing 2D finite volume techniques is undertaken. A series of progressively more difficult advection tests is used to test the accuracy of each scheme and it is seen that simple advection tests are inadequate indicators of the performance of volume-tracking methods. A straightforward methodology is presented that allows more rigorous estimates to be made of the error in volume advection and coupled volume and momentum advection in real flow situations. The volume advection schemes are put to a final test in the case of Rayleigh-Taylor instability. © 1997 by CSIRO.
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    NUMERICAL MODELLING OF THREE-DIMENSIONAL FLY-ASH FLOW IN POWER UTILITY BOILERS (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 787-806 
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    ISSN: 0271-2091
    Keywords: three-dimensional ; two-phase flow ; Eulerian modelling ; RNG k-∊ turbulence model ; particle-wall collision ; power utility boilers ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A two-fluid Eulerian model in combination with a particle-wall collision model and generalized Eulerian boundary conditions for the particulate phase is employed to predict complex three- dimensional fly-ash flows which often cause severe erosion to boiler tubes located in power utility boilers. Mean momentum and mass conservation equations are solved for each phase using a finite volume scheme with two-way coupling and a modified renormalization group (RNG)-based k -∊ turbulence model. Comparison of predicted particle concentration with measured data is made and excellent agreement is obtained. The detailed character of the particulate velocity field and concentration just downstream of the 180° bend shows a marked dependence on the Stokes number not previously reported. © 1997 by John Wiley & Sons, Ltd.
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    HIGH-ORDER BEM FORMULATIONS FOR STRONGLY NON-LINEAR PROBLEMS GOVERNED BY QUITE GENERAL NON-LINEAR DIFFERENTIAL OPERATORS. PART 2: SOME 2D EXAMPLES (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 863-873 
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    ISSN: 0271-2091
    Keywords: general BEM ; general non-linear differential operator ; homotopy ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper the general BEM proposed previously by Liao is applied to solve some 2D strongly non-linear differential equations, even including those whose governing equations and boundary conditions do not contain any linear terms. It is shown that the proposed general BEM is really valid for general non-linear problems, so that it can be applied to solve high-dimensional, strongly non-linear problems in engineering. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 863-873, 1997.
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    PEGASE: A NAVIER-STOKES SOLVER FOR DIRECT NUMERICAL SIMULATION OF INCOMPRESSIBLE FLOWS (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 833-861 
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    ISSN: 0271-2091
    Keywords: Navier-Stokes ; incompressible ; unsteady ; finite difference ; finite element ; non-staggered grid ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A hybrid conservative finite difference/finite element scheme is proposed for the solution of the unsteady incompressible Navier-Stokes equations. Using velocity-pressure variables on a non-staggeredgrid system, the solution is obtained with a projection method basedon the resolution of a pressure Poisson equation.The new proposed scheme is derived from the finite element spatial discretization using the Galerkin method with piecewise bilinear polynomial basis functions defined on quadrilateral elements. It is applied to the pressure gradient term and to the non-linear convection term as in the so-called group finite element method. It ensures strong coupling between spatial directions, inhibiting the development of oscillations during long-term computations, as demonstrated by the validation studies.Two- and three-dimensional unsteady separated flows with open boundaries have been simulated with the proposed method using Cartesian uniform mesh grids. Several examples of calculations on the backward-facing step configuration are reported and the results obtained are compared with those given by other methods. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 833-861, 1997.
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    IMPLEMENTATION OF VORTEX FILAMENT METHODS ON PARALLEL MACHINES WITH DISTRIBUTED ADAPTIVE DATA STRUCTURE (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 939-951 
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    ISSN: 0271-2091
    Keywords: vortex filament method ; parallel machines ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper addressed the implementation of vortex filament methods on parallel machines with distributed memory to simulate a three-dimensionally evolving jet. Vortical structure developments due to Kelvin-Helmholtz instability of the axially perturbed jet are also examined. The implementation is conducted in a single-programme multiple-data (SPMD) environment and the parallelism is focused on issues of data distribution, efficient support of parallel I/O and overlapping of communications with computations. In addition, since the number of segment markers in a filament is dynamically growing according to the requirement of numerical accuracy, a novel packet-oriented data structure is proposed not only to partition filament segment markers among distributed processors but also to support dynamical load balancing at run time. This work is the first to apply packet-oriented structures to implement a parallel vortex filament method. Experimental results indicate performance improvement from 1·5 to 2·6 times over static schemes on nCUBE2, DEC Alpha and IBM SP2 by incorporating the proposed scheme with packet-oriented structures. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 939-951, 1997.
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    SOME VALIDATION OF STANDARD, MODIFIED AND NON-LINEAR k-ε TURBULENCE MODELS (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 965-986 
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    ISSN: 0271-2091
    Keywords: turbulence models ; k-ε ; non-linear k-ε ; finite element method ; validation ; FEAT ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Standard, modified and non-linear k-ε: turbulence models are validated against three axisymmetric flow problems - flow through a pipe expansion, flow through a pipe constriction and an impinging jet problem - to underpin knowledge about the solution quality obtained from two-equation turbulence models. The extended models improve the prediction of turbulence as a flow approaches a stagnation point and the non-linear model allows for the prediction of anisotropic turbulence. Significantly different values for the non-linear model coefficients are proposed in comparison with values found in the literature. Nevertheless, current turbulence models are still unable to accurately predict the spreading rate of shear layers. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids, 24: 965-986, 1997.
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    Finite element computations for unsteady fluid and elastic membrane interaction problems (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 1091-1110 
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    ISSN: 0271-2091
    Keywords: elastohydrodynamics ; fluid-membrane interactions ; moving boundary problems ; deformable spatial domain/space-time (DSD/ST) finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The interaction between the hydrodynamic forces of a flow field and the elastic forces of adjacent deformable boundaries is described by elastohydrodynamics, a coupled fluid-elastic membrane problem. Direct numerical solution of the unsteady, highly non-linear equations requires that the dynamic evolution of both the flow field and the domain shape be determined as part of the solution, since neither is known a priori. This paper describes a numerical algorithm based on the deformable spatial domain space-time (DSD/ST) finite element method for the unsteady motion of an incompressible, viscous fluid with elastic membrane interaction. The unsteady Navier-Stoke and elastic membrane equations are solved separately using an iterative procedure by the GMRES technique with an incomplete lower-upper (ILU) decomposition at every time instant. One-dimensional, two-dimensional and deformable domain model problems are used to demonstrate the capabilities and accuracy of the present algorithm. Both steady state and transient problems are studied. © 1997 John Wiley & Sons, Ltd.
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    A linear theory for Ekman's boundary layer according to a triple deck (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 1211-1223 
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    ISSN: 0271-2091
    Keywords: Ekman's boundary layer ; triple deck ; non-homogeneity ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The problem of the interaction between Ekman's classical boundary layer and that induced by a thermally non-homogeneous site shows that the latter is strongly linked to the order of magnitude of the horizontal scale of the site.Our purpose is the analysis of the local interaction equations (Boussinesq equations) starting from a triple-deck model. This analysis yields a system of quasi-linear equations for the viscous lower deck. The linear theory of this system shows that the thermal non-homogeneity has a significant influence on the Ekman boundary layer flow owing to the interactive nature of the triple-deck structure. The numerical solution of the quasi-linear system confirms to a large extent this influence. The numerical results are given in graph form. © 1997 John Wiley & Sons, Ltd.
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    Localization of Hopf bifurcations in fluid flow problems (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 1185-1210 
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    ISSN: 0271-2091
    Keywords: Hopf bifurcation ; hydrodynamic stability ; Navier-Stokes equations ; eigenproblem ; direct simulation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper is concerned with the precise localization of Hopf bifurcations in various fluid flow problems. This is when a stationary solution loses stability and often becomes periodic in time. The difficulty is to determine the critical Reynolds number where a pair of eigenvalues of the Jacobian matrix crosses the imaginary axis. This requires the computation of the eigenvalues (or at least some of them) of a large matrix resulting from the discretization of the incompressible Navier-Stokes equations. We thus present a method allowing the computation of the smallest eigenvalues, from which we can extract the one with the smallest real part. From the imaginary part of the critical eigenvalue we can deduce the fundamental frequency of the time-periodic solution. These computations are then confirmed by direct simulation of the time-dependent Navier-Stokes equations. © 1997 John Wiley & Sons, Ltd.
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    Parallel overlapping scheme for viscous incompressible flows (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 1341-1352 
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    ISSN: 0271-2091
    Keywords: parallel ; overlapping ; FEM/FDM ; Navier-Stokes ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A 3D parallel overlapping scheme for viscous incompressible flow problems is presented that combines the finite element method, which is best suited for analysing flow in any arbitrarily shaped flow geometry, with the finite difference method, which is advantageous in terms of both computing time and computer storage. A modified ABMAC method is used as the solution algorithm, to which a sophisticated time integration scheme proposed by the present authors has been applied. Parallelization is based on the domain decomposition method. The RGB (recursive graph bisection) algorithm is used for the decomposition of the FEM mesh and simple slice decomposition is used for the FDM mesh. Some estimates of the parallel performance of FEM, FDM and overlapping computations are presented. © 1997 John Wiley & Sons, Ltd.
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    Parallel finite element computation of missile aerodynamics (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 1417-1432 
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    ISSN: 0271-2091
    Keywords: parallel computing methods ; compressible flows ; missile aerodynamics ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A flow simulation tool, developed by the authors at the Army HPC Research Center, for compressible flows governed by the Navier-Stokes equations is used to study missile aerodynamics at supersonic speeds, high angles of attack and for large Reynolds numbers. The goal of this study is the evaluation of this Navier-Stokes computational technique for the prediction of separated flow fields around high-length-to-diameter (L/D) bodies. In particular, this paper addresses two issues: (i) turbulence modelling with a finite element computational technique and (ii) efficient performance of the computational technique on two different multiprocessor mainframes, the Thinking Machines CM-5 and CRAY T3D. The paper first provides a discussion of the Navier-Stokes computational technique and the algorithm issues for achieving efficient performance on the CM-5 and T3D. Next, comparisons are shown between the computation and experiment for supersonic ramp flow to evaluate the suitability of the turbulence model. Following that, results of the computations for missile flow fields are shown for laminar and turbulent viscous effects. © 1997 John Wiley & Sons, Ltd.
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    ANALYSIS AND IMPLEMENTATION OF THE GAS-KINETIC BGK SCHEME FOR COMPUTATIONAL GAS DYNAMICS (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 21-49 
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    ISSN: 0271-2091
    Keywords: gas evolution model ; gas-kinetic BGK schemes ; entropy condition ; gas-kinetic Lax-Wendroff flux ; kinetic flux vector splitting ; local extremum diminishing ; advection equations ; non-linear hyperbolic systems ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Gas-kinetic schemes based on the BGK model are proposed as an alternative evolution model which can cure some of the limitations of current Riemann solvers. To analyse the schemes, simple advection equations are reconstructed and solved using the gas-kinetic BGK model. Results for gas-dynamic application are also presented. The final flux function derived in this model is a combination of a gas-kinetic Lax- Wendroff flux of viscous advection equations and kinetic flux vector splitting. These two basic schemes are coupled through a non-linear gas evolution process and it is found that this process always satisfies the entropy condition. Within the framework of the LED (local extremum diminishing) principle that local maxima should not increase and local minima should not decrease in interpolating physical quantities, several standard limiters are adopted to obtain initial interpolations so as to get higher-order BGK schemes. Comparisons for well-known test cases indicate that the gas-kinetic BGK scheme is a promising approach in the design of numerical schemes for hyperbolic conservation laws. © 1997 by John Wiley & Sons, Ltd.
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    Viscous flow with large fluid-fluid interface displacement (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 859-881 
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    ISSN: 0271-2091
    Keywords: 3D ; finite elements ; arbitrary Lagrange-Euler ; fluid-fluid interfaces ; annulus ; displacement ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The arbitrary Lagrange-Euler (ALE) kinematic description has been implemented in a 3D transient finite element program to simulate multiple fluid flows with fluid-fluid interface or surface displacements. The description of fluid interfaces includes variable interfacial tension, and the formulation is useful in the simulation of low and intermediate Reynolds number viscous flow. The displacement of two immiscible Newtonian fluids in a vertical (concentric and eccentric) annulus and a (vertical and inclined) tube is simulated. © 1998 John Wiley & Sons, Ltd.
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    Three-dimensional incompressible Navier-Stokes equations on non-orthogonal staggered grids using the velocity-vorticity formulation (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 917-943 
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    ISSN: 0271-2091
    Keywords: Navier-Stokes ; incompressible flow ; velocity-vorticity formulation ; generalized curvilinear co-ordinates ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper is concerned with the numerical resolution of the incompressible Navier-Stokes equations in the velocity-vorticity form on non-orthogonal structured grids. The discretization is performed in such a way, that the discrete operators mimic the properties of the continuous ones. This allows the discrete equivalence between the primitive and velocity-vorticity formulations to be proved. This last formulation can thus be seen as a particular technique for solving the primitive equations. The difficulty associated with non-simply connected computational domains and with the implementation of the boundary conditions are discussed. One of the main drawback of the velocity-vorticity formulation, relative to the additional computational work required for solving the additional unknowns, is alleviated. Two- and three-dimensional numerical test cases validate the proposed method. © 1998 John Wiley & Sons, Ltd.
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    Simulations of 2D and 3D thermocapillary flows by a least-squares finite element method (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 983-1007 
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    ISSN: 0271-2091
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Numerical results for time-dependent 2D and 3D thermocapillary flows are presented in this work. The numerical algorithm is based on the Crank-Nicolson scheme for time integration, Newton's method for linearization, and a least-squares finite element method, together with a matrix-free Jacobi conjugate gradient technique. The main objective in this work is to demonstrate how the least-squares finite element method, together with an iterative procedure, deals with the capillary-traction boundary conditions at the free surface, which involves the coupling of velocity and temperature gradients. Mesh refinement studies were also carried out to validate the numerical results. © 1998 John Wiley & Sons, Ltd.
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    Numerical modelling of advection-dispersion equation in a stretched curvilinear grid using the QUICKEST scheme (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 1033-1052 
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    ISSN: 0271-2091
    Keywords: QUICKEST ; curvilinear grid ; advection-dispersion ; stretched grid ; suspended sediment ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A stretched version of the QUICKEST scheme for solutions of the advection-dispersion equation is presented. The scheme is accurate for large degrees of stretching, so that it can be used where large gradients are present, e.g. for the calculation of sediment in suspension close to the bed. The scheme is tested for various cases of sediment advection and dispersion in one and two dimensions. © 1998 John Wiley & Sons, Ltd.
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    Computation of internal high-speed separated flow with modified B-L and J-K models (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 1053-1071 
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    ISSN: 0271-2091
    Keywords: turbulence modeling ; internal flow ; flow separation ; shock-boundary layer interaction ; finite volume method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The existence of shock-turbulent boundary layer interactions lead to very complicated flow phenomena and pose a challenge for numerical simulation. In this paper, two turbulence models, the Baldwin-Lomax (B-L) model and the Johnson-King (J-K) model, which were originally developed for simple external flow simulation, are modified to model complex high-speed internal separated flows. The full Navier-Stokes solver used in this paper is based on a cell-centered finite volume method and multistepping time marching scheme. Both implicit residual smoothing and local time stepping techniques are incorporated to accelerate the convergence rate. To ensure the numerical stability with the present explicit scheme, a point-implicit treatment to the source term in the ordinary differential equation (ODE) of the J-K model has been developed and has proved to be very effective in modeling such a complex flow. An arc-bump channel flow case has been studied. Comparisons of computed results with experimental data show that the present solver, with the modified turbulence models, predicts the shock and the flow separation very well. The J-K model is found to predict the size of the separation bubble with a higher accuracy. © 1998 John Wiley & Sons, Ltd.
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    Symmetry techniques for the numerical solution of the 2D Euler equations at impermeable boundaries (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 1093-1108 
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    ISSN: 0271-2091
    Keywords: boundary conditions ; Euler equations ; finite volume ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The implementation of boundary conditions at rigid, fixed wall boundaries in inviscid Euler solutions by upwind, finite volume methods is considered. Some current methods are reviewed. Two new boundary condition procedures, denoted as the symmetry technique and the curvature-corrected symmetry technique are then presented. Their behaviour in relation to the problem of the subsonic flow about blunt and slender elliptic bodies is analysed. The subsonic flow inside the Stanitz elbow is then computed. The symmetry technique is proven to be as accurate as one of the current methods, second-order pressure extrapolation technique. Finally, for arbitrary curved geometries, dramatic advantages of the curvature-corrected symmetry technique over the other methods are shown. © 1998 John Wiley & Sons, Ltd.
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    A Navier-Stokes solver for complex three-dimensional turbulent flows adopting non-linear modelling of the Reynolds stresses (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 1139-1158 
    Details
    ISSN: 0271-2091
    Keywords: non-linear Reynolds stresses ; k-ε turbulence model ; higher-order convective scheme ; pressure correction ; direct sparse matrix solver ; incompressible duct flows ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A non-linear modelling of the Reynolds stresses has been incorporated into a Navier-Stokes solver for complex three-dimensional geometries. A k-ε model, adopting a modelling of the turbulent transport which is not based on the eddy viscosity, has been written in generalised co-ordinates and solved with a finite volume approach, using both a GMRES solver and a direct solver for the solution of the linear systems of equations. An additional term, quadratic in the main strain rate, has been introduced into the modelling of the Reynolds stresses to the basic Boussinesq's form; the corresponding constant has been evaluated through comparison with the experimental data. The computational procedure is implemented for the flow analysis in a 90° square section bend and the obtained results show that with the non-linear modelling a much better agreement with the measured data is obtained, both for the velocity and the pressure. The importance of the convection scheme is also discussed, showing how the effect of the non-linear correction added to the Reynolds stresses is effectively hidden by the additional numerical diffusion introduced by a low-order convection scheme as the first-order upwind scheme, thus making the use of higher order schemes necessary. © 1998 John Wiley & Sons, Ltd.
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    Transient finite element analysis of generalized Newtonian coextrusion flows in complex geometries (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 1159-1181 
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    ISSN: 0271-2091
    Keywords: coextrusion ; interfacial instability ; transient simulation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A two-dimensional transient finite element model capable of simulating problems related to two-layer polymer flows has been developed. This technique represents an effective tool which can be used to study the possibility of the onset of interfacial instability in coextrusion flows, considering melt rheology as well as the fluid-geometry interaction. A code has been developed to solve the transient problem of the flow of bi-component systems of Newtonian and generalized Newtonian fluids through parallel plates and complex geometries, such as: 2:1 abrupt expansion, 2:1 (30°) expansion, 4:1 abrupt contraction and 4:1 tapered (30°) contraction. Solutions are compared with experimental data from the literature and results provided by linear stability analysis (LSA) for the case of parallel plate flows. Numerical results are in agreement with LSA results for the parallel plate geometry cases studied. The expansion geometries tend to stabilize flows in the parallel plate section downstream of the expansion. Contractions may give rise to break-up of the interface depending on the flow conditions. © 1998 John Wiley & Sons, Ltd.
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    A bore-capturing finite volume method for open-channel flows (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 1241-1261 
    Details
    ISSN: 0271-2091
    Keywords: shallow water equations ; finite volume ; open channel ; hydraulic jump ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A high-resolution finite volume hydrodynamic solver is presented for open-channel flows based on the 2D shallow water equations. This Godunov-type upwind scheme uses an efficient Harten-Lax-van Leer (HLL) approximate Riemann solver capable of capturing bore waves and simulating supercritical flows. Second-order accuracy is achieved by means of MUSCL reconstruction in conjunction with a Hancock two-stage scheme for the time integration. By using a finite volume approach, the computational grid can be irregular which allows for easy boundary fitting. The method can be applied directly to model 1D flows in an open channel with a rectangular cross-section without the need to modify the scheme. Such a modification is normally required for solving the 1D St Venant equations to take account of the variation of channel width. The numerical scheme and results of three test problems are presented in this paper. © 1998 John Wiley & Sons, Ltd.
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    Large eddy simulation of the subcritical flow past a circular cylinder: numerical and modeling aspects (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 1281-1302 
    Details
    ISSN: 0271-2091
    Keywords: large eddy simulation ; turbulent flow ; circular cylinder ; accuracy ; finite volume method ; subgrid scale model ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The turbulent flow past a circular cylinder (Re=3900) was computed by large eddy simulation (LES). The objective was not to investigate the physical phenomena of this flow in detail but to study numerical and modeling aspects which influence the quality of LES solutions. Concerning the numerical method, the most important component is the discretization of the non-linear convective fluxes. Five different schemes were investigated. Also, the influence of different grid resolutions was examined. Two aspects play an important role on the modeling side, namely the near-wall model and the subgrid scale model. Owing to the restriction to low Reynolds numbers in this study, no-slip boundary conditions were used at solid walls. Therefore, only the second aspect was taken into account. Two different subgrid scale models were applied. Additionally, LES computations without any subgrid scale modeling were carried out in order to prove the performance of the models. The results were evaluated by comparison with available experimental data. © 1998 John Wiley & Sons, Ltd.
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    Automatic grid generation of complex geometries in Cartesian co-ordinates (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 1303-1324 
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    ISSN: 0271-2091
    Keywords: grid generation ; automation ; Cartesian ; diagonal ; saw-tooth ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A method of automatic grid generation for complex boundaries in Cartesian co-ordinates is proposed in this paper. In addition to the Cartesian grid lines the diagonal segments are used for the approximations of complex geometries in Cartesian co-ordinates. A structured Cartesian grid is employed for the sake of the numerical simplicity and the potential of automatic grid generation. The automatic grid generation is achieved by this diagonal Cartesian method and the accuracy estimations of geometry approximations are given. The approximations of a few complex geometries, such as the multibody system in porous media, lake banks, grooved channels and spheres are shown and analyzed. The proposed method is verified by the numerical solutions of a rotated cavity flow. It is shown that the diagonal Cartesian method improves both the accuracy of geometry approximations and the numerical solution of a rotated cavity flow, comparing with the traditional saw-tooth method in which only Cartesian grid lines are utilized for geometry approximations. The stability and convergence of the proposed method is demonstrated. Finally, the application of the diagonal Cartesian method for the prediction of a grooved channel flow is presented. © 1998 John Wiley & Sons, Ltd.
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    Numerical prediction for laminar forced convection heat transfer in parallel-plate channels with streamwise-periodic rod disturbances (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 1371-1387 
    Details
    ISSN: 0271-2091
    Keywords: heat transfer ; duct flow ; laminar flow ; boundary conditions ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical study has been performed for the periodically fully-developed flow in two-dimensional channels with streamwise-periodic round disturbances on its two walls. To accurately describe the round disturbance boundary condition, a body fitted grid was used. The flow and heat transfer have been studied in the range of Reynolds number, Re=50-700, and Prandtl number Pr=0.71. The influences of disturbance parameters and Reynolds number on heat transfer and friction have been investigated in detail. Some of the solutions have been examined using both steady and unsteady finite difference schemes; and the same results have been obtained. The results show that different flow patterns can occur with different deployments of the disturbances. With appropriate configuration of the disturbances, the Nusselt number can reach a value four times greater than in a smooth channel at the same condition, with the penalty of a much greater pressure drop. On the other hand, if the disturbances are not deployed properly, augmentation of heat transfer cannot be acquired. © 1998 John Wiley & Sons, Ltd.
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    Parallel conjugate gradient performance for least-squares finite elements and transport problems (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 1421-1440 
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    ISSN: 0271-2091
    Keywords: parallel ; conjugate gradient ; least squares ; FEM ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this study we consider parallel conjugate gradient solution of sparse systems arising from the least-squares mixed finite element method. Of particular interest are transport problems involving convection. The least-squares approach leads to a symmetric positive system and the conjugate gradient scheme is directly applicable. The scheme is applied to both the convection-diffusion equation and to the stationary Navier-Stokes equations. Here we demonstrate parallel solution and performance studies for a representative MIMD parallel computer with hypercube architecture. © 1998 John Wiley & Sons, Ltd.
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    Simulation of gas-solid particle flows over a wide range of concentration (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 1441-1479 
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    ISSN: 0271-2091
    Keywords: gas-solid particle flow ; dilute to dense concentrations ; two-fluid model ; kinetic theory ; control-volume finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A two-fluid model of gas-solid particle flows that is valid for a wide range of the solid-phase volume concentration (dilute to dense) is presented. The governing equations of the fluid phase are obtained by volume averaging the Navier-Stokes equations for an incompressible fluid. The solid-phase macroscopic equations are derived using an approach that is based on the kinetic theory of dense gases. This approach accounts for particle-particle collisions. The model is implemented in a control-volume finite element method for simulations of the flows of interest in two-dimensional, planar or axisymmetric, domains. The chosen mathematical model and the proposed numerical method are applied to three test problems and one demonstration problem. © 1998 John Wiley & Sons, Ltd.
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    A LOCAL MESH REFINEMENT ALGORITHM APPLIED TO TURBULENT FLOW (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 519-530 
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    ISSN: 0271-2091
    Keywords: local mesh refinement ; multigrid ; finite volume ; SIMPLEC ; k-∊ ; buoyancy ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents a local mesh refinement procedure based on a discretization over internal interfaces where the averaging is performed on the coarse side. It is implemented in a multigrid environment but can optionally be used without it. The discretization for the convective terms in the velocity and the temperature equation is the QUICK scheme, while the HYBRID-UPWIND scheme is used in the turbulence equations. The turbulence model used is a two-layer k-∊ model. We have applied this formulation on a backward-facing step at Re=800 and on a three-dimensional turbulent ventilated enclosure, where we have resolved a geometrically complex inlet consisting of 84 nozzles. In both cases the concept of local mesh refinements was found to be an efficient and accurate solution strategy. © 1997 by John Wiley & Sons, Ltd.
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    NUMERICAL SIMULATION OF INCOMPRESSIBLE FLOWS WITH MOVING INTERFACES (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 615-638 
    Details
    ISSN: 0271-2091
    Keywords: finite element method ; front tracking ; incompressible two fluid system ; mold filling ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical model has been developed for the 2D simulation of free surface flows or, more generally speaking, moving interface ones. The bulk fluids on both sides of the interface are taken into account in simulating the incompressible laminar flow state. In the case of heat transfer the whole system, i.e. walls as well as possible obstacles, is considered. This model is based on finite element analysis with an Eulerian approach and an unstructured fixed mesh. A special technique to localize the interface allows its temporal evolution through this mesh. Several numerical examples are presented to demonstrate the capabilities of the model. © 1997 by John Wiley & Sons, Ltd.
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    SOLUTION OF THE ADVECTION-DIFFUSION EQUATION USING A COMBINATION OF DISCONTINUOUS AND MIXED FINITE ELEMENTS (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 595-613 
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    ISSN: 0271-2091
    Keywords: advection-diffusion equation ; discontinuous finite element method ; mixed finite element method ; solute transport in porous media ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: When transport is advection-dominated, classical numerical methods introduce excessive artificial diffusion and spurious oscillations. Special methods are required to overcome these phenomena. To solve the advection-diffusion equation, a numerical method is developed using a discontinuous finite element method for the discretization of the advective terms. At the discontinuities of the approximate solution, numerical advective fluxes are calculated using one-dimensional approximate Riemann solvers. The method is stabilized with a multidimensional slope limiter which introduces small amounts of numerical diffusion when sharp concentration fronts occur. In addition, the diffusive term is discretized using a mixed hybrid finite element method. With this approach, numerical oscillations are completely avoided for a full range of cell Peclet numbers. The combination of discontinuous and mixed finite elements can be easily applied to 2D and 3D models using various types of elements in regular and irregular meshes. Numerical tests show good agreement with 1D and 2D analytical solutions. This approach is compared at the same time with two different numerical methods, a standard mixed finite method and a finite volume approach with high-resolution upwind terms. Regular and irregular meshes are used for the numerical tests to study the mesh effects on the numerical results. Our data show that in all cases this approach performs well. © 1997 by John Wiley & Sons, Ltd.
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    NUMERICAL SIMULATION OF SHALLOW WATER WAVE PROPAGATION USING A BOUNDARY ELEMENT WAVE EQUATION MODEL (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 1-15 
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    ISSN: 0271-2091
    Keywords: shallow water equations ; boundary element method ; wave equation model ; free surface flow ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The present paper makes use of a wave equation formulation of the primitive shallow water equations to simulate one-dimensional free surface flow. A numerical formulation of the boundary element method is then developed to solve the wave continuity equation using a time-dependent fundamental solution, while an explicit finite difference scheme is used to derive velocities from the primitive momentum equation. One-dimensional free surface flows in open channels are treated and the results compared with analytical and numerical solutions. © 1997 John Wiley & Sons, Ltd.
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    BEM SOLUTION OF THE 3D INTERNAL NEUMANN PROBLEM AND A REGULARIZED FORMULATION FOR THE POTENTIAL VELOCITY GRADIENTS (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 81-100 
    Details
    ISSN: 0271-2091
    Keywords: boundary element ; velocity ; gradients ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The direct boundary element method is an excellent candidate for imposing the normal flux boundary condition in vortex simulation of the three-dimensional Navier-Stokes equations. For internal flows, the Neumann problem governing the velocity potential that imposes the correct normal flux is ill-posed and, in the discrete form, yields a singular matrix. Current approaches for removing the singularity yield unacceptable results for the velocity and its gradients. A new approach is suggested based on the introduction of a pseudo-Lagrange multiplier, which redistributes localized discretization errors - endemic to collocation techniques -  over the entire domain surface, and is shown to yield excellent results. Additionally, a regularized integral formulation for the velocity gradients is developed which reduces the order of the integrand singularity from four to two. This new formulation is necessary for the accurate evaluation of vorticity stretch, especially as the evaluation points approach the boundaries. Moreover, to guarantee second-order differentiability of the boundary potential distribution, a piecewise quadratic variation in the potential is assumed over triangular boundary elements. Two independent node-numbering systems are assigned to the potential and normal flux distribu- tions on the boundary to account for the single- and multi-valuedness of these variables, respectively. As a result, higher accuracy as well as significantly reduced memory and computational cost is achieved for the solution of the Neumann problem. © 1997 John Wiley & Sons, Ltd.
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    ADAPTIVE LINEARIZATION AND GRID ITERATIONS WITH THE TRI-TREE MULTIGRID REFINEMENT-RECOARSEMENT ALGORITHM FOR THE NAVIER-STOKES EQUATIONS (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 155-168 
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    ISSN: 0271-2091
    Keywords: tri-tree multigrid ; ILU coupled node fill-in preconditioner ; element Reynolds number ; adaptive refinements ; adaptive recoarsements ; grid iterations ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The tri-tree algorithm for refinements and recoarsements of finite element grids is explored. The refinement-recoarsement algorithm not only provides an accurate solution in certain parts of the grid but also has a major influence on the finite element equation system itself. The refinements of the grid lead to a more symmetric and linear equation matrix. The recoarsements will ensure that the grid is not finer than is necessary for preventing divergence in an iterative solution procedure. The refinement-recoarsement algorithm is a dynamic procedure and the grid is adapted to the instant solution.In the tri-tree multigrid algorithm the solution from a coarser grid is scaled relatively to the increase in velocity boundary condition for the finer grid. In order to have a good start vector for the solution of the finer grid, the global Reynolds number or velocity boundary condition should not be subject to large changes. For each grid and velocity solution the element Reynolds number is computed and used as the grid adaption indicator during the refinement-recoarsement procedure.The iterative tri-tree multigrid method includes iterations with respect to the grid. At each Reynolds number the same boundary condition s are applied and the grid is adapted to the solution iteratively until the number of unknowns and elements in the grid becomes constant. In the present paper the following properties of the tri-tree algorithm are explored: the influence of the increase in boundary velocities and the size of the grid adaption indicator on the amount of work for solving the equations, the number of linear iterations and the solution error estimate between grid levels. The present work indicates that in addition to the linear and non-linear iterations, attention should also be given to grid adaption iterations. © 1997 by John Wiley & Sons, Ltd.
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    The entrance effect of laminar flow over a backward-facing step geometry (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 633-644 
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    ISSN: 0271-2091
    Keywords: laminar flow ; entrance effect ; backward-facing step ; sudden expansion ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The study investigates the entrance effect for flow over a backward-facing step by comparing predictions that set the inlet boundary at various locations upstream of the sudden expansion. Differences are most significant in the sudden expansion region. If the geometry has an inlet channel, then shorter reattachment and separation lengths are predicted. Comparisons with experimental data indicate that better agreement is found using a long inlet channel, but only for low Reynolds numbers where the experimental error is less significant. For certain cases, predictions with a high expansion number are perturbed by the entrance effect more than low-expansion-number predictions; however, the effect is localized in the sudden expansion region. Channels with low expansion numbers always experience a greater entrance effect after some distance upstream and downstream of the sudden expansion. The boundary layer growth in the inlet channel was examined using a uniform inlet velocity profile. © 1997 John Wiley & Sons, Ltd.
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    A staggered control volume scheme for unstructured triangular grids (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 697-717 
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    ISSN: 0271-2091
    Keywords: control volume ; staggered grid ; unstructured mesh ; incompressible flow ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The purpose of this work is to introduce and validate a new staggered control volume method for the simulation of 2D/axisymmetric incompressible flows.   The present study introduces a numerical procedure for solving the Navier-Stokes equations using the primitive variable formulation. The proposed method is an extension of the staggered grid methodology to unstructured triangular meshes for a control volume approach which features ease of handling of irregularly shaped domains. Two alternative elements are studied: transported scalars are stored either at the sides of an element or at its vertices, while the pressure is always stored at the centre of an element. Two interpolation functions were investigated for the integration of the momentum equations: a skewed mass-weighted upwind function and a flow-oriented exponential shape function. The momentum equations are solved over the covolume of a side or of a vertex and the pressure-velocity coupling makes use of a localized linear reconstruction of the discontinuous pressure field surrounding an element in order to obtain the pressure gradient terms. The pressure equation is obtained through a discretization of the continuity equation which uses the triangular element itself as the control volume.   The method is applied to the simulation of the following test cases: backward-facing step flow, flow over a two-dimensional obstacle and flow in a pipe with sudden contraction of cross-sectional area. All numerical investigations are compared with experimental data from the literature. A grid convergence and error analysis study is also carried out for flow in a driven cavity.   Results compared favourably with experimental data and so the new control volume scheme is deemed well suited for the prediction of incompressible flows in complex geometries. © 1997 John Wiley & Sons, Ltd.
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    An adaptive finite element method for forced convection (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 803-823 
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    ISSN: 0271-2091
    Keywords: incompressible ; Navier-Stokes ; heat transfer ; adaptive FEM ; forced convection ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents an adaptive finite element method to solve forced convective heat transfer. Solutions are obtained in primitive variables using a high-order finite element approximation on unstructured grids. Two general-purpose error estimators are developed to analyse finite element solutions and to determine the characteristics of an improved mesh which is adaptively regenerated by the advancing front method. The adaptive methodology is validated on a problem with a known analytical solution. The methodology is then applied to heat transfer predictions for two cases of practical interest. Predictions of the Nusselt number compare well with measurements and constitute an improvement over previous results. © 1997 John Wiley & Sons, Ltd.
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    On the relation between the entropy balance and the numerical solutions of systems of conservation laws (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 825-845 
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    ISSN: 0271-2091
    Keywords: conservation laws ; entropy inequality ; Euler equations ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This work deals with the relation between the numerical solutions of hyperbolic systems of conservation laws and the associated entropy evolution. An analysis of the continuum problem by means of variational calculus clearly emphasizes the consequences of the adopted reconstruction procedure on the induced entropy balance. A methodology is proposed that allows for a posterior local and global spurious entropy production estimates on the basis of an additional equation representing a discrete approximation to the entropy inequality. The problem of defining a consistent approximation of the numerical entropy flux is also addressed in detail. Properly designed numerical experiments support the analysis and contribute to providing a more comprehensive evaluation of the numerical entropy dynamics. © 1997 John Wiley & Sons, Ltd.
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    AN ADAPTIVE FINITE ELEMENT SCHEME FOR HYDRAULIC FRACTURING WITH PROPPANT TRANSPORT (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 645-670 
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    ISSN: 0271-2091
    Keywords: hydraulic fracturing ; finite elements ; moving adaptive grids ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A mathematical model and adaptive finite element scheme are developed for describing the distribution of proppant in a propagating hydraulic fracture. The governing equation for proppant concentration is derived by applying the conservation law of mass to the proppant and to the proppant-laden fluid. Shah's empirical equation, which relates the proppant concentration and the indices of the non-Newtonian fluid, is used to describe the proppant-laden fluid. The proppant distribution inside a hydraulic fracture can then be obtained by solving the proppant concentration equation together with the governing equations of fluid and elasticity for a hydraulic fracturing. A novel moving grid scheme is developed that combines grid point insertion with redistribution. Four examples corresponding to different in situ stress distributions are computed to demonstrate the scheme. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 14 Ill.
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  • 99
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    VALIDATION OF NUMERICAL SHALLOW WATER MODELS FOR STRATIFIED SEICHES (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 771-786 
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    ISSN: 0271-2091
    Keywords: shallow water equations ; seiches ; stratification ; analytical solution ; validation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new analytical solution is presented for the case of a stratified seiche. This solution, especially its energetics, is useful for the validation of numerical shallow water models under stratified conditions. The utility of the analytical solution for validation is shown by using it to validate a simple finite difference numerical model. A comparison of the energetics of the numerical and analytical solutions reveals that the model results converge rapidly to the analytical solution with increasing resolution, such that a grid size of 30×30 would appear adequate for validation. In addition to properly resolving the spatial features, good temporal resolution is also necessary for validation, i.e use of a Courant number (Cr) less than one. For example, owing to the numerical dispersion of the present model, using Cr=5/4 rather than Cr =1/4 for the 50×50 grid resulted in 3·6 times larger RMS errors of model versus analytical barotropic available potential energy.This new analytical solution should be applied to a test suite of such validation tools before using such numerical models to simulate the more realistic geophysical flows encountered in lakes, bays, harbours and semi-enclosed seas under stratified conditions. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 7 Ill.
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  • 100
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    ADAPTIVE PARALLEL MULTIGRID SOLUTION OF 2D INCOMPRESSIBLE NAVIER-STOKES EQUATIONS (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 875-892 
    Details
    ISSN: 0271-2091
    Keywords: adaptive parallel multigrid method ; local refinement criteria ; incompressible Navier-Stokes equations ; hole pressure problem ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper an adaptive parallel multigrid method and an application example for the 2D incompressible Navier-Stokes equations are described. The strategy of the adaptivity in the sense of local grid refinement in the multigrid context is the multilevel adaptive technique (MLAT) suggested by Brandt. The parallelization of this method on scalable parallel systems is based on the portable communication library CLIC and the message-passing standards: PARMACS, PVM and MPI. The specific problem considered in this work is a two-dimensional hole pressure problem in which a Poiseuille channel flow is disturbed by a cavity on one side of the channel. Near geometric singularities a very fine grid is needed for obtaining an accurate solution of the pressure value. Two important issues of the efficiency of adaptive parallel multigrid algorithms, namely the data redistribution strategy and the refinement criterion, are discussed here. For approximate dynamic load balancing, new data in the adaptive steps are redistributed into distributed memories in different processors of the parallel system by block remapping. Among several refinement criteria tested in this work, the most suitable one for the specific problem is that based on finite-element residuals from the point of view of self-adaptivity and computational efficiency, since it is a kind of error indicator and can stop refinement algorithms in a natural way for a given tolerance. Comparisons between different global grids without and with local refinement have shown the advantages of the self-adaptive technique, as this can save computer memory and speed up the computing time several times without impairing the numerical accuracy. © 1997 By John Wiley & Sons, Ltd. Int. J. Numer. Methods Fluids 24, 875-892, 1997.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
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