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  • Articles  (50)
  • Navier-Stokes equations  (32)
  • Navier-Stokes  (18)
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  • 1995-1999  (50)
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  • Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics  (50)
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  • 1
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    A composite multigrid method for calculating unsteady incompressible flows in geometrically complex domains (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 20 (1995), S. 341-361 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; unsteady ; composite multigrid ; incompressible ; non-staggered grid ; semi-implicit ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A time-accurate, finite volume method for solving the three-dimensional, incompressible Navier-Stokes equations on a composite grid with arbitrary subgrid overlapping is presented. The governing equations are written in a non-orthogonal curvilinear co-ordinate system and are discretized on a non-staggered grid. A semi-implicit, fractional step method with approximate factorization is employed for time advancement. Multigrid combined with intergrid iteration is used to solve the pressure Poisson equation. Inter-grid communication is facilitated by an iterative boundary velocity scheme which ensures that the governing equations are well-posed on each subdomain. Mass conservation on each subdomain is preserved by using a mass imbalance correction scheme which is secondorder-accurate. Three test cases are used to demonstrate the method's consistency, accuracy and efficiency.
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    URL: http://dx.doi.org/10.1002/fld.1650200502
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  • 2
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    Integral transform solution of developing laminar duct flow in Navier-Stokes formulationExtended version of a paper presented at the 8th International Conference on Numerical Methods in Laminar and Turbulent Flow, Swansea, U.K., July 1993. (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 20 (1995), S. 1203-1213 
    Details
    ISSN: 0271-2091
    Keywords: integral transforms ; Navier-Stokes equations ; channel flow ; hybrid methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The generalized integral transform technique is employed in the hybrid numerical-analytical solution of the Navier-Stokes equations in streamfunction-only formulation, which govern the incompressible laminar flow of a Newtonian fluid within a parallel plate channel. Owing to the analytic nature of this approach, the outflow boundary condition for an infinite duct is handled exactly, and the error involved in considering finite duct lengths is investigated. The present error-controlled solutions are used to inspect the relative accuracy of previously reported purely numerical schemes and to compare Navier-Stokes and boundary layer formulations for various combinations of inlet conditions and Reynolds number.
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    URL: http://dx.doi.org/10.1002/fld.1650201102
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  • 3
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    A vector-parallel scheme for Navier-Stokes computations at multi-gigaflop performance rates (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 21 (1995), S. 445-466 
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    ISSN: 0271-2091
    Keywords: vector-parallel computing ; Navier-Stokes ; Runge-Kutta ; domain decompostion ; CFD ; gigaflop ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A class of vector-parallel schemes for solution of steady compressible or incompressible viscous flow is developed and performance studies carried out. The algorithms employ an artificial transient treatment that permits rapid integration to a steady state. In the present work a four-stage explicit Runge-Kutta scheme employing variable local step size is utilized for the ODE system integration. The RK-4 scheme is restructured to allow vectorization and enhance concurrency in the calculation for a streamfunction-vorticity formulation of the flow problem. The parameters of the resulting RK scheme can be selected to accelerate convergence of the RK recursion. Four main procedures are considered which permit vector-parallel solution: a Jacobi update, a hybrid of the Jacobi and Gauss-Seidel method, red-black ordering and domain decomposition. Numerical performance studies are conducted with a representative viscous incompressible flow calculation. Results indicate that a scheme involving domain decomposition with a Gauss-Seidel type of update for the RK four-stage scheme is most effective and provides performance in excess of 8 Gflops on the Cray C-90.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650210602
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  • 4
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    VALIDATION OF A NAVIER-STOKES SOLUTION ALGORITHM WITH EXPERIMENTAL VALUES IN A SUPERSONIC WAKE (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 137-148 
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    ISSN: 0271-2091
    Keywords: validation ; Navier-Stokes equations ; Taylor-Galerkin approach ; finite elements ; laser Doppler anemometry ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper describes the validation of a finite element solver for an axisymmetric compressible flow with experimental values, especially velocities measured with a laser Doppler anemometer in the near wake of a circular cylinder. The equations under consideration are the Navier-Stokes equations with turbulent terms. A time-stepping scheme for the solution of these equations can be produced by applying a forward-time Taylor series expansion including time derivatives of second order. These time derivatives are evaluated in terms of space derivatives in the Lax-Wendroff fashion. The method is based on unstructured triangular grids with a high resolution in the radial direction. In order to predict the measured turbulent intensites more exactly, a modification of the Baldwin-Lomax model is necessary.
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  • 5
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    A COMPARISON OF COUPLED AND SEGREGATED ITERATIVE SOLUTION TECHNIQUE FOR INCOMPRESSIBLE SWIRLING FLOW (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 353-373 
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    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; finite differences ; unsymmetric linear systems ; Krylov subspace methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In many popular solution algorithms for the incompressible Navier-Stoke equations the coupling between the momentum equations is neglected when the linearized momentum equations are solved to update the velocities. This is known to lead to poor convergence in highly swirling flows where coupling between the radial and tangential momentum equations is strong. Here we propose a coupled solution algorithm in which the linearized momentum and continuity equations are solved simultaneously. Comparisons between the new method and the well-known SIMPLEC method are presented.
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  • 6
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    ARTIFICIAL BOUNDARIES AND FLUX AND PRESSURE CONDITIONS FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 325-352 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; artificial boundary conditions ; flux and pressure conditions ; finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Fluid dynamical problems are often conceptualized in unbounded domains. However, most methods of numerical simulation then require a truncation of the conceptual domain to a bounded one, thereby introducing artificial boundaries. Here we analyse our experience in choosing artificial boundary conditions implicitly through the choice of variational formulations. We deal particularly with a class of problems that involve the prescription of pressure drops and/or net flux conditions.
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  • 7
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    A NON-LINEAR ADAPTED TRI-TREE MULTIGRID SOLVER FOR FINITE ELEMENT FORMULATION OF THE NAVIER-STOKES EQUATIONS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 1041-1059 
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    ISSN: 0271-2091
    Keywords: grid generation ; tri-tree ; unstructured grid ; multigrid ; finite element ; mixed formulation ; analytic integration ; adaptive solver ; Navier-Stokes equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An iterative adaptive equation multigrid solver for solving the implicit Navier-Stokes equations simultaneously with tri-tree grid generation is developed. The tri-tree grid generator builds a hierarchical grid structur e which is mapped to a finite element grid at each hierarchical level. For each hierarchical finite element multigrid the Navier-Stokes equations are solved approximately. The solution at each level is projected onto the next finer grid and used as a start vector for the iterative equation solver at the finer level. When the finest grid is reached, the equation solver is iterated until a tolerated solution is reached. The iterative multigrid equation solver is preconditioned by incomplete LU factorization with coupled node fill-in.The non-linear Navier-Stokes equations are linearized by both the Newton method and grid adaption. The efficiency and behaviour of the present adaptive method are compared with those of the previously developed iterative equation solver which is preconditioned by incomplete LU factorization with coupled node fill-in.
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  • 8
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    NUMERICAL SIMULATION OF UNSTEADY VISCOUS FLOWS USING AN IMPLICIT PROJECTION METHOD (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 897-921 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; unsteady flow ; laminar flow ; turbulent flow ; projection method ; approximate factorization technique ; Engineering ; Engineering General
    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 implicit projection method for the solution of the two-dimensional, time-dependent, incompressible Navier- Stokes equations is presented. The basic principle of this method is that the evaluation of the time evolution is split into intermediate steps. The computational method is based on the approximate factorization technique. The coupled approach is used to link the equations of motion and the turbulence model equations. The standard k-∊ turbulence model is used. The current methodology, which has been tested extensively for steady problems, is now applied for the numerical simulation of unsteady flows. Several cases were tested, such as plane or axisymmetric channels, a backward-facing step, a square cavity and an axisymmetric stenosis.
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  • 9
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    ONSET OF ASYMMETRY: FLOW PAST CIRCULAR AND ELLIPTIC CYLINDERS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 1327-1345 
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    ISSN: 0271-2091
    Keywords: unsteady flows ; incompressible viscous flows ; onset of asymmetry ; Navier-Stokes equations ; finite difference method ; bluff bodies ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A computational study of the development of two- dimensional unsteady viscous incompressible flow around a circular cylinder and elliptic cylinders is undertaken at a Reynolds number of 10,000. A higher- order upwind scheme is used to solve the Navier-Stokes equations by the finite difference method in order to study the onset of computed asymmetry around bluff bodies. For the computed cases the ellipses develop asymmetry much earlier than the circular cylinder. The receptivity of the computed flows in the presence of discrete roughness and surface vibration is studied. Finally, the role of discrete roughness in triggering asymmetry for flow past a circular cylinder is studied and compared with flow visualization experiments at Re=10,000
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  • 10
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    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 
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    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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  • 11
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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 
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    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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  • 12
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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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  • 13
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    SINGLE-LAYER FINITE ELEMENT APPROXIMATION OF 3D NAVIER-STOKES EQUATIONS WITH FREE BOUNDARIES FOR SHALLOW WATER FLOWS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 143-161 
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    ISSN: 0271-2091
    Keywords: finite element ; incompressible ; Navier-Stokes ; free surface flows ; shallow water ; Engineering ; Engineering General
    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 simulate flows in the shallow water limit, the full incompressible Navier-Stokes equations with free boundaries are solved using a single layer of finite elements. This implies a polynomial approximation of the velocity profile in the vertical direction, which in turn distorts the wave speed. This fact is verified by numerical results: the wave speed depends on the vertical discretization. When at least two layers of finite elements are used, the boundary layer at the bottom can be simulated and the correct solution for the shallow water limit is recovered. Then this algorithm is applied to the prediction of Tsunami event.
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  • 14
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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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  • 15
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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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  • 16
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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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  • 17
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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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  • 18
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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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  • 19
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    A Eulerian/Lagrangian model to calculate the evolution of a water droplet spray (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 20 (1995), S. 135-155 
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    ISSN: 0271-2091
    Keywords: Diphasic flow ; Eulerian/Lagrangian model ; Complex geometry ; Projection method ; Navier-Stokes equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We introduce a Eulerian/Lagrangian model to compute the evolution of a spray of water droplets inside a complex geometry. To take into account the complex geometry we define a rectangular mesh and we relate each mesh node to a node function which depends on the location of the node. The time-dependent incompressible and turbulent Navier-Stokes equations are solved using a projection method. The droplets are regarded as individual entities and we use a Lagrangian approach to compute the evolution of the spray. We establish the exchange laws related to mass and heat transfer for a droplet by introducing a mass transfer coefficient and a heat transfer coefficient. The numerical results from our model are compared with those from the literature in the case of a falling droplet in the atmosphere and from experimental investigation in a wind tunnel in the case of a polydisperse spray. The comparison is fairly good. We present the computation of a water droplet spray inside a complex and realistic geometry and determine the characteristics of the spray in the vicinity of obstacles.
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    URL: http://dx.doi.org/10.1002/fld.1650200204
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  • 20
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    Simulation of 2D external viscous flows by means of a domain decomposition method using an influence matrix technique (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 20 (1995), S. 1111-1136 
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    ISSN: 0271-2091
    Keywords: domain decomposition method ; finite difference method ; vortex method ; influence matrix technique ; Navier-Stokes equations ; incompressible viscous flows ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Two-dimensional external viscous flows are numerically approximated by means of a domain decomposition method which combines a vortex method and a finite difference method. The vortex method is used in the flow region which is dominated by convective effects, whereas the finite difference method is used in the flow region where viscous diffusion effects are dominant. An influence matrix technique combined with the uniformity condition of the pressure is used to enforce the tangential velocity boundary condition. Comparisons between numerical and experimental data show that the method is well adapted for simulating two-dimensional flows.
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    URL: http://dx.doi.org/10.1002/fld.1650201002
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    Fractional step method for solution of incompressible Navier-Stokes equations on unstructured triangular meshes (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 20 (1995), S. 1273-1288 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; unstructured ; finite volume ; incompressible ; Engineering ; Engineering General
    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 implicit fractional step method for the solution of the two-dimensional, time-dependent, incompressible Navier-Stokes equations is presented. The current method was developed for use on an unstructured grid made up of triangles. The basic principles of this method are that the evaluation of the time evolution is split into intermediate steps and that for the spatial discretization of the flow equations a finite volume discretization on an unstructured triangular mesh is used. The present approach has been used to simulate viscous, laminar flows for various Reynolds numbers in test cases such as a backward-facing step, a square cavity and a channel with wavy boundaries.
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    URL: http://dx.doi.org/10.1002/fld.1650201107
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    An hp adaptive strategy for finite element approximations of the Navier-Stokes equations (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 20 (1995), S. 831-851 
    Details
    ISSN: 0271-2091
    Keywords: error estimation ; adaptivity ; hp-methods ; Navier-Stokes ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Recently, a rigorous a posteriori error estimate, based on the element residual method, for the steady-state Navier-Stokes equations has been derived. In this paper, by using this error estimate, we construct an hp adaptive strategy to minimize the total computation costs while achieving a targeted accuracy for steady incompressible viscous flow problems. The basic hp adaptive strategy is to solve the approximate problem in three consecutive stages corresponding to three different meshes, i.e. an initial mesh, an intermediate adaptive h-mesh, and a final adaptive hp mesh. Our numerical result shows that the three-step hp adaptive strategy for the incompressible flow problems indeed provides an accurate approximate solution while keeping the computational costs under control.
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    URL: http://dx.doi.org/10.1002/fld.1650200810
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    An h4 accurate vorticity-velocity formulation for calculating flow past a cylinder (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 21 (1995), S. 489-497 
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    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; vorticity-velocity formulation ; finite difference methods ; Engineering ; Engineering General
    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 solution for the two-dimensional Navier-Stokes equations for incompressible flow past a cylinder is given in which the euquation of continuity is solved by a step-by-step integration procedure at each stage of an interative process. Thus the formulation involves the solution of one first-order and one second-order equation for the velocity components, together with the vorticity transport equation. the equations are solved numerically by h4-accurate methods in the case of steady flow past a circular cylinder in the Reynolds number range 10-100. Results are in satisfactory agreement with recent h4-accurate calculations. An improved approximation to the boundary conditions at large distance is also considered.
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    URL: http://dx.doi.org/10.1002/fld.1650210604
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    On identification of flow separation and vortices in internal periodic flows (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 21 (1995), S. 323-335 
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    ISSN: 0271-2091
    Keywords: flow separation ; time-periodic, unsteady ; vortices ; incompressible ; Navier-Stokes ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: To permit simplified analysis of complex time-dependent flows, possible relationship between the near-wall flow, flow separation and vortices are studied numerically for a flow in a constricted two-dimensional channel. The pulsating incoming wave-form consists of a steady flow, followed by a half-sinus flow superimposed on the steady component. One pair of vortices is created in each cycle, one vortex near each wall. The vortices propagate downstream in the next cycles, promoting flow separation as they move. Existing flow separation criteria were not found to be uniformly valid. A relation between the near-wall flow and the vortical system exists only during the steady incoming flow phase of the cycle. It seems that local criteria of flow separation cannot be found for complex internal pulsating flow fields. However, the vorticity field can be utilized, even in complex time-periodic flows, for identifying vortices that have been formed by the roll-up of shear layers.
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    URL: http://dx.doi.org/10.1002/fld.1650210405
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    ADAPTIVE SOLUTIONS FOR UNSTEADY LAMINAR FLOWS ON UNSTRUCTURED GRIDS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 85-101 
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    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; time-dependent, separated flow ; unstructured, adaptive, dynamic grids ; local time-stepping scheme ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An adaptive finite volume method for the simulation of time-dependent, viscous flow is presented. The Navier-Stokes equations are discretized by central schemes on unstructured grids and solved by an explicit Runge-Kutta method. The essential topics of the present study are a new concept for a local Runge-Kutta time-stepping scheme, called multisequence Runge-Kutta, which reduces the severe stability restriction in unsteady problems, a common grid generation and adaptation procedure and the application of dynamic grids for capturing moving flow structures. Results are presented for laminar, separated flow around an aerofoil with a flap.
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    THE NO-SLIP BOUNDARY CONDITION IN FINITE DIFFERENCE APPROXIMATIONS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 713-729 
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    ISSN: 0271-2091
    Keywords: finite difference ; boundary conditions ; Navier-Stokes equations ; convergence analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite difference method for the Navier-Stokes equations in vorticity -streamfunction formulation is proposed to resolve the difficulty of the lack of a vorticity boundary condition at a no-slip boundary. It is particularly suitable for flows in regions with complicated geometries. Convergence with second-order accuracy in vorticity and velocity is established. In numerical experiments the convergence rates agree with theoretical predictions. Test results for the two-dimensional driven cavity problem and for the flow in expansion and contraction channels are given.
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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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    Numerical simulations of laminar flow over a 3D backward-facing step (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 1159-1183 
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    ISSN: 0271-2091
    Keywords: backward-facing step ; laminar flow ; Navier-Stokes ; finite elements ; 3D ; 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 investigation of laminar flow over a three-dimensional backward-facing step is presented with comparisons with detailed experimental data, available in the literature, serving to validate the numerical results. The continuity constraint method, implemented via a finite element weak statement, was employed to solve the unsteady three-dimensional Navier-Stokes equations for incompressible laminar isothermal flow. Two-dimensional numerical simulations of this step geometry underestimate the experimentally determined extent of the primary separation region for Reynolds numbers Re greater than 400. It has been postulated that this disagreement between physical and computational experiments is due to the onset of three-dimensional flow near Re ≈ 400. This paper presents a full three-dimensional simulation of the step geometry for 100≤ Re≤ 800 and correctly predicts the primary reattachment lengths, thus confirming the influence of three-dimensionality. Previous numerical studies have discussed possible instability modes which could induce a sudden onset of three-dimensional flow at certain critical Reynolds numbers. The current study explores the influence of the sidewall on the development of three-dimensional flow for Re greater than 400. Of particular interest is the characterization of three-dimensional vortices in the primary separation region immediately downstream of the step. The complex interaction of a wall jet, located at the step plane near the sidewall, with the mainstream flow reveals a mechanism for the increasing penetration (with increasing Reynolds number) of three-dimensional flow structures into a region of essentially two-dimensional flow near the midplane of the channel. The character and extent of the sidewall-induced flow are investigated for 100≤Re≤ 800. © 1997 John Wiley & Sons, Ltd.
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    Numerical simulation and optimal shape for viscous flow by a fictitious domain method (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 20 (1995), S. 695-711 
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    ISSN: 0271-2091
    Keywords: fictitious domain methods ; Lagrange multipliers ; Navier-Stokes equations ; optimal shape problems ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this article we discuss the fictitious domain solution of the Navier-Stokes equations modelling unsteady incompressible viscous flow. The method is based on a Lagrange multiplier treatment of the boundary conditions to be satisfied and is particularly well suited to the treatment of no-slip boundary conditions. This approach allows the use of structured meshes and fast specialized solvers for problems on complicated geometries. Another interesting feature of the fictitious domain approach is that it allows the solution of optimal shape problems without regriding. The resulting methodology is applied to the solution of flow problems including external incompressible viscous flow modelled by the Navier-Stokes equations and then to an optimal shape problem for Stokes and Navier-Stokes flow.
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    A SEGREGATED SOLUTION ALGORITHM FOR INCOMPRESSIBLE FLOWS IN GENERAL CO-ORDINATES (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 515-548 
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    ISSN: 0271-2091
    Keywords: incompressible ; Navier-Stokes ; contravariant velocities ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: To analyse an incompressible Navier-Stokes flow problem in a boundary- fitted curvilinear co-ordinate system is definitely not a trivial task. In the primitive variable formulation, choices between working variables and their storage points have to be made judiciously. The present work engages contravariant velocity components and scalar pressure which stagger each other in the mesh to prevent even-odd pressure oscillations from emerging. Now that smoothness of the pressure field is attainable, the remaining task is to ensure a discrete divergence-free velocity field for an incompressible flow simulation. Aside from the flux discretizations, the indispensable metric tensors, Jacobian and Christoffel symbols in the transformed equations should be approximated with care. The guiding idea is to get the property of geometric identity pertaining to these grid-sensitive discretizations. In addition, how to maintain the revertible one-to-one equivalence at the discrete level between primitive and contravariant velocities is another theme in the present staggered formulation. A semi-implicit segregated solution algorithm felicitous for a large-scale flow simulation was utilized to solve the entire set of basic equations iteratively. Also of note is that the present segregated solution algorithm has the virtue of requiring no user-specified relaxation parameters for speeding up the satisfaction of incompressibility in an optimal sense. Three benchmark problems, including an analytic problem, were investigated to justify the capability of the present formulation in handling problems with complex geometry. The test cases considered and the results obtained herein make a useful contribution in solving problems subsuming cells with arbitrary shapes in a boundary-fitted grid system.
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    A 3D AGGLOMERATION MULTIGRID SOLVER FOR THE REYNOLDS-AVERAGED NAVIER-STOKES EQUATIONS ON UNSTRUCTURED MESHES (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 527-544 
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    ISSN: 0271-2091
    Keywords: multigrid ; unstructured ; Navier-Stokes ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An agglomeration multigrid strategy is developed and implemented for the solution of three-dimensional steady viscous flows. The method enables convergence acceleration with minimal additional memory overhead and is completely automated in that it can deal with grids of arbitrary construction. The multigrid technique is validated by comparing the delivered convergence rates with those obtained by a previously developed overset-mesh multigrid approach and by demonstrating grid-independent convergence rates for aerodynamic problems on very large grids. Prospects for further increases in multigrid efficiency for high-Reynolds-number viscous flows on highly stretched meshes are discussed.
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    NUMERICAL SIMULATION OF THE MECHANISMS GOVERNING THE ONSET OF THE BÉNARD-VON KÁRMÁN INSTABILITY (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 753-785 
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    ISSN: 0271-2091
    Keywords: numerical simulation ; spectral time discretization ; Navier-Stokes equations ; laminar flow ; shear flow ; unsteady flow ; periodic flow ; instability ; Hopf bifurcation ; non-linearity ; non-linear theory ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The onset of the Bénard-von Kármán instability consisting of the selective amplification of the linear unstable mode and yielding finally the well-known saturated state has been described many times on the basis of both numerical and experimental results in various configurations. However, neither the role of the harmonics and their coupling has been examined quantitatively, nor has the spatial structure of the instability been studied in detail. A recently developed numerical method of simulation of quasi-periodic flows makes it possible to integrate the investigation of linear and non-linear characteristics within a single numerical method. The simulation of the 2D afterbody wake presented in this paper allows us to follow the amplification of the instability over many orders of magnitude. It is shown that at all stages of its development the instability is characterized by a series of harmonics, each of them amplified with a multiple of the fundamental amplification rate during the linear regime. The amplification of harmonics results from an energy transfer from the mean flow to harmonics of increasingly higher order. Ultimately the energy losses compensate this transfer and an equilibrium, commonly called saturation of the instability, is reached. It is shown that the coupling between the fundamental harmonic and the mean flow is mainly responsible for the saturation. The convergence rate of the development of the instability into harmonics is investigated. A full description of the spatial structure of all significant harmonics both in the linear regime and at saturation is obtained. The results show that time and space characteristics of the instability can be investigated simultaneously in an efficient way. Such an approach might be particularly important in 3D wakes where the geometry has a strong influence on the behaviour of unstable flows.
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    A boundary element method for steady viscous fluid flow using penalty function formulation (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 907-929 
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    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; penalty function formulation ; boundary element method ; driven cavity 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: A new boundary element method is presented for steady incompressible flow at moderate and high Reynolds numbers. The whole domain is discretized into a number of eight-noded cells, for each of which the governing boundary integral equation is formulated exclusively in terms of velocities and tractions. The kernels used in this paper are the fundamental solutions of the linearized Navier-Stokes equations with artificial compressibility. Significant attention is given to the numerical evaluation of the integrals over quadratic boundary elements as well as over quadratic quadrilateral volume cells in order to ensure a high accuracy level at high Reynolds numbers. As an illustration, square driven cavity flows are considered for Reynolds numbers up to 1000. Numerical results demonstrate both the high convergence rate, even when using simple (direct) iterations, and the appropriate level of accuracy of the proposed method. Although the method yields a high level of accuracy in the primary vortex region, the secondary vortices are not properly resolved. © 1997 John Wiley & Sons, Ltd.
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    Computing the flow around a moving profile by numerically integrating the Navier-Stokes equations (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 125-143 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; unsteady separated flow ; laminar flow ; vorticity ; non-inertial frame ; 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 vorticity velocity formulation is proposed for the solution of the equations for viscous flow around a moving profile. A non-inertial reference frame is used and the velocities are computed from a Poincaré integral formula. The studies are directed towards the need to understand helicopter blade aerodynamics. Worked examples are given which validate the method and programme for laminar flows, at least for low Reynolds numbers. © 1998 John Wiley & Sons, Ltd.
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    Fourth-order method for solving the Navier-Stokes equations in a constricting channel (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 1119-1135 
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    ISSN: 0271-2091
    Keywords: fourth-order methods ; 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 fourth-order numerical method for solving the Navier-Stokes equations in streamfunction/vorticity formulation on a two-dimensional non-uniform orthogonal grid has been tested on the fluid flow in a constricted symmetric channel. The family of grids is generated algebraically using a conformal transformation followed by a non-uniform stretching of the mesh cells in which the shape of the channel boundary can vary from a smooth constriction to one which one possesses a very sharp but smooth corner. The generality of the grids allows the use of long channels upstream and downstream as well as having a refined grid near the sharp corner. Derivatives in the governing equations are replaced by fourth-order central differences and the vorticity is eliminated, either before or after the discretization, to form a wide difference molecule for the streamfunction. Extra boundary conditions, necessary for wide-molecule methods, are supplied by a procedure proposed by Henshaw et al. The ensuing set of non-linear equations is solved using Newton iteration. Results have been obtained for Reynolds numbers up to 250 for three constrictions, the first being smooth, the second having a moderately sharp corner and the third with a very sharp corner. Estimates of the error incurred show that the results are very accurate and substantially better than those of the corresponding second-order method. The observed order of the method has been shown to be close to four, demonstrating that the method is genuinely fourth-order. © 1997 John Wiley & Sons, Ltd.
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    An ILU smoother for the incompressible Navier-Stokes equations in general co-ordinates (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 20 (1995), S. 59-74 
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    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; Multigrid method ; Smoothing method ; ILU factorization ; General co-ordinates ; Engineering ; Engineering General
    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 the incompressible Navier-Stokes equations in general two- and three-dimensional domains using a multigrid method is considered. Because a great variety of boundary-fitted grids may occur, robustness is at a premium. Therefore a new ILU smoother called CILU (collective ILU) is described, based on r-transformations. In CILU the matrix that is factorized is block-structured, with blocks corresponding to the set of physical variables. A multigrid algorithm using CILU as smoother is investigated. The performance of the algorithm in two and three dimensions is assessed by numerical experments. The results show that CILU is a good smoother for the incompressible Navier-Stokes equations discretized on general non-orthogonal curvilinear grids.
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    Algebraic multigrid methods for the solution of the Navier-Stokes equations in complicated geometries (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 281-301 
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    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; SIMPLE algorithm ; algebraic multigrid 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: The application of standard multigrid methods for the solution of the Navier-Stokes equations in complicated domains causes problems in two ways. First, coarsening is not possible to full extent since the geometry must be resolved by the coarsest grid used. Second, for semi-implicit time-stepping schemes, robustness of the convergence rates is usually not obtained for convection-diffusion problems, especially for higher Reynolds numbers. We show that both problems can be overcome by the use of algebraic multigrid (AMG), which we apply for the solution of the pressure and momentum equations in explicit and semi-implicit time-stepping schemes. We consider the convergence rates of AMG for several model problems and demonstrate the robustiness of the proposed scheme. © 1998 John Wiley & Sons, Ltd.
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    A projection method for shallow water equations (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 27 (1998), S. 81-95 
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    ISSN: 0271-2091
    Keywords: shallow waters ; Navier-Stokes ; lagoons ; projections ; parallel computations ; 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 dynamics of shallow water has been studied and an algorithm for this dynamics has been developed. Results have been obtained with data of the Venice lagoon using a model made expressively by a semi-implicit method based on a finite element method in space. Comparison has been made between field data and the results of the simulation. Very good agreement is shown over a long period of simulation. © 1998 John Wiley & Sons, Ltd.
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    A spectral-finite difference solution of the Navier-Stokes equations in three dimensions (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 129-142 
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    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; unsteady flow ; three-dimensional channel ; finite differences ; spectral techniques ; 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 computational code for the numerical integration of the three-dimensional Navier-Stokes equations in their non-dimensional velocity-pressure formulation is presented. The system of non-linear partial differential equations governing the time-dependent flow of a viscous incompressible fluid in a channel is managed by means of a mixed spectral-finite difference method, in which different numerical techniques are applied: Fourier decomposition is used along the homogeneous directions, second-order Crank-Nicolson algorithms are employed for the spatial derivatives in the direction orthogonal to the solid walls and a fourth-order Runge-Kutta procedure is implemented for both the calculation of the convective term and the time advancement. The pressure problem, cast in the Helmholtz form, is solved with the use of a cyclic reduction procedure. No-slip boundary conditions are used at the walls of the channel and cyclic conditions are imposed at the other boundaries of the computing domain.Results are provided for different values of the Reynolds number at several time steps of integration and are compared with results obtained by other authors. © 1998 John Wiley & Sons, Ltd.
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    An improved projection scheme applied to pseudospectral methods for the incompressible Navier-Stokes equations (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 501-521 
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    ISSN: 0271-2091
    Keywords: projection scheme ; Navier-Stokes equations ; pseudospectral Chebyshev methods ; unsteady 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: An improved projection scheme is proposed and applied to pseudospectral collocation-Chebyshev approximation for the incompressible Navier-Stokes equations. It consists of introducing a correct predictor for the pressure, one which is consistent with a divergence-free velocity field at each time step. The main objective is to allow a time variation of the pressure gradient at boundaries. From different test problems, it is shown that this method, associated with a multistep second-order time scheme, provides a time accuracy of the same order as the temporal scheme used for the pressure, and also improves the prediction of the velocity slip. Moreover, it does not exhibit any numerical boundary layer mentioned as a drawback of fractional steps algorithm, and does not require the use of staggered grids for the velocity and the pressure. Its effectiveness is validated by comparison with a previous time-splitting algorithm proposed by Goda (K. Goda, J. Comput. Phys., 30, 76-95 (1979)) and implemented by Gresho (P. Gresho, Int. j. numer. methods fluids, 11, 587-620 (1990)) to finite element approximations. Steady and unsteady solutions for the regularized driven cavity and the rotating cavity submitted to throughflow are also used to assess the efficiency of this algorithm. © 1998 John Wiley & Sons, Ltd.
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    A compact fourth-order finite difference scheme for the steady incompressible Navier-Stokes equations (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 20 (1995), S. 1137-1151 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; streamfunction ; vorticity ; compact scheme ; driven cavity problem ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We note in this study that the Navier-Stokes equations, when expressed in streamfunction-vorticity form, can be approximated to fourth-order accuracy with stencils extending only over a 3 x 3 square of points. The key advantage of the new compact fourth-order scheme is that it allows direct iteration for low-to-medium Reynolds numbers. Numerical solutions are obtained for the model problem of the driven cavity and compared with solutions available in the literature. For Re ≤ 7500 point-SOR iteration is used and the convergence is fast.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650201003
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    Decay of confined, two-dimensional, spatially periodic arrays of vortices: A numerical investigation (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 21 (1995), S. 155-180 
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    ISSN: 0271-2091
    Keywords: computational fluid dynamics ; finite-difference method ; Navier-Stokes equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The disarrangement of a perturbed lattice of vortices was studied numerically. The basic state is an exponentially decaying, exact solution of the Navier-Stokes equations. Square arrays of vortices with even numbers of vortex cells along each side were perturbed and their evolution was investigated. Whether the energy in the perturbation grows somewhat before it decays or decays monotonically depends on the initial strength of the vortices of the basic state, the extent of lateral confinement and the structure of the perturbation. The critical condition for temporally local instability, i.e. the critical amplitude of the basic state that must be exceeded to allow energy transfer from the basic state to the perturbation, is discussed. In the strongly confined case of a square lattice of four vortices the appearance of enchancement of global rotation is the result of energy transfer from the basic state to a temporally local unstable mode. Energy is transferred from the basic state to larger-scaled structures (inverse cascade) only if the scales of the larger structures are inherently contained in the initial structure of the perturbation. The initial structure of the double array of vortices is not maintained except for a very special form of perturbation. The facts that large scales decay more slowly than small scales and that, when non-linearities are sufficiently strong, energy is transferred from one scale to another explain the differences in the disarrangement process for different initial strengths of the vortices of the basic state. The stronger vortices, i.e. the vortices perturbed in a manner that increases their strength, tend to dominate the weaker vortices. The pairing and subsequent merging (or capture) of vortices of like sense into larger-scale vortices are described in terms of peaks in the evolution of the square root of the palinstrophy divided by the enstrophy.
    Additional Material: 21 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650210206
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    A NUMERICAL PROCEDURE FOR PREDICTING MULTIPLE SOLUTIONS OF A SPHERICAL TAYLOR-COUETTE FLOW (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 1135-1147 
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    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; Taylor-Couette flow ; multiple solutions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new numerical procedure for predicting multiple solutions of Taylor vortices in a spherical gap is presented. The steady incompressible Navier-Stokes equations in primitive variables are solved by a finite- difference method using a matrix preconditioning technique. Routes leading to multiple flow states are designed heuristically by imposing symmetric properties. Both symmetric and asymmetric solutions can be predicted in a deterministic way. The current procedure gives very fast convergence rate to the desired flow modes. This procedure provides an alternative way of finding all possible stable steady axisymmetric flow modes.
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    AN APPROXIMATE PROJECTION SCHEME FOR INCOMPRESSIBLE FLOW USING SPECTRAL ELEMENTS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 673-688 
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    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; projection methods ; operator splitting ; spectral element methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An approximate projection scheme based on the pressure correction method is proposed to solve the Navier-Stokes equations for incompressible flow. The algorithm is applied to the continuous equations; however, there are no problems concerning the choice of boundary conditions of the pressure step. The resulting velocity and pressure are consistent with the original system. For the spatial discretization a high-order spectral element method is chosen. The high-order accuracy allows the use of a diagonal mass matrix, resulting in a very efficient algorithm. The properties of the scheme are extensively tested by means of an analytical test example. The scheme is further validated by simulating the laminar flow over a backward-facing step.
    Additional Material: 6 Ill.
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    Asymptotic-Newton method for solving incompressible flows (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 861-878 
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    ISSN: 0271-2091
    Keywords: Navier-Stokes ; non-linear methods ; asymptotic-Newton 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: In this paper we present a comparative study of three non-linear schemes for solving finite element systems of Navier-Stokes incompressible flows. The first scheme is the classical Newton-Raphson linearization, the second one is the modified Newton-Raphson linearization and the last one is a new scheme called the asymptotic-Newton method. The relative efficiency of these approaches is evaluated over a large number of examples. © 1997 John Wiley & Sons, Ltd.
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    AN ARTIFICIAL BOUNDARY CONDITION FOR TWO-DIMENSIONAL INCOMPRESSIBLE VISCOUS FLOWS USING THE METHOD OF LINES (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 483-493 
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    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; Oseen equations ; method of lines ; artificial boundary condition ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We design an artificial boundary condition for the steady incompressible Navier-Stokes equations in streamfunction-vorticity formulation in a flat channel with slip boundary conditions on the wall. The new boundary condition is derived from the Oseen equations and the method of lines. A numerical experiment for the non-linear Navier-Stokes equations is presented. The artificial boundary condition is compared with Dirichlet and Neumann boundary conditions for the flow past a rectangular cylinder in a flat channel. The numerical results show that our boundary condition is more accurate.
    Additional Material: 2 Ill.
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    Adaptive hybrid (prismatic-tetrahedral) grids for incompressible flows (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 1085-1105 
    Details
    ISSN: 0271-2091
    Keywords: adaptive ; hybrid grids ; incompressible ; Navier-Stokes ; finite volume ; pressure correction ; 3-D ; 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: Hybrid grids consisting of prisms and tetrahedra are employed for the solution of the 3-D Navier-Stokes equations of incompressible flow. A pressure correction scheme is employed with a finite volume-finite element spatial discretization. The traditional staggered grid formulation has been substituted with a collocated mesh approach which uses fourth-order artificial dissipation. The hybrid grid is refined adaptively in local regions of appreciable flow variations. The scheme operations are performed on an edge-wise basis which unifies treatment of both types of grid elements. The adaptive method is employed for incompressible flows in both single and multiply-connected domains. © 1998 John Wiley & Sons, Ltd.
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    Method of finite difference solutions to the transient bubbly air-water flows (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 1155-1180 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; averaged volume transport equations ; void wave propagation speed ; interfacial effects ; two-phase flow ; finite difference 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 one-dimensional, time-dependent, isothermal, incompressible, Newtonian fluid, two-phase volume averaging model was developed to study momentum interaction effects in vertical ducts with bubble flow regime. For the evaluation of averaged description, potential inviscid flow around bubbles was considered in order to get closure relationships. The linear dynamic analysis is based on the eigenvalue technique, determining the domain of the hyperbolic behavior and the void fraction wave velocity, which are compared with previous models and experimental data. The solution to the partial differential equations is based on the finite difference technique implicit scheme. These schemes serve to demonstrate the numerical solution procedure. The numerical results are compared with analytical solution and experimental data for void fraction wave propagation. The importance of the surface tension effect in the behavior of the phases in transient conditions is shown. © 1998 John Wiley & Sons, Ltd.
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    AN ADAPTIVE FINITE ELEMENT METHOD FOR A TWO-EQUATION TURBULENCE MODEL IN WALL-BOUNDED FLOWS (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 101-120 
    Details
    ISSN: 0271-2091
    Keywords: incompressible ; Navier-Stokes ; adaptive FEM ; turbulencek-∊ 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: This paper presents an adaptive finite element method for solving incompressible turbulent flows using a k-∊ model of turbulence. Solutions are obtained in primitive variables using a highly accurate quadratic finite element on unstructured grids. A projection error estimator is presented that takes into account the relative importance of the errors in velocity, pressure and turbulence variables. The efficiency and convergence rate of the methodology are evaluated by solving problems with known analytical solutions. The method is then applied to turbulent flow over a backward-facing step and predictions are compared with experimental measurements. © 1997 John Wiley & Sons, Ltd.
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    Orthogonal grid generation for Navier-Stokes computations (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 215-224 
    Details
    ISSN: 0271-2091
    Keywords: orthogonal grids ; hyperbolic grid generation ; Navier-Stokes equations ; higher-order 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: Body conforming orthogonal grids were generated using a fast hyperbolic method for aerofoils, and were used to solve the Navier-Stokes equation in the generalized orthogonal system for the first time for time accurate simulation of incompressible flow. For grid generation, the Beltrami equation and the definition equation for the orthogonality are solved using a finite difference method. The grids generated around aerofoils by this method have better orthogonality than the results published by earlier investigators. The Navier-Stokes equation at Reynolds numbers of 3000 and 35 000 for NACA 0012 and NACA 0015 respectively, have been solved as an application. The obtained results match quite well with the corresponding experimental results. © 1998 John Wiley & Sons, Ltd.
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