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  • Articles  (295)
  • Numerical Methods and Modeling  (293)
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  • 1995-1999  (295)
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  • Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics  (295)
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  • Articles  (295)
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Meccanica 34 (1999), S. 199-229 
    ISSN: 1572-9648
    Keywords: Aerodynamics ; Kutta condition ; Edge singularities ; Boundary integral equations ; Fluid dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract This review paper presents a unified formulation of the Kutta condition for steady and unsteady flows, implemented by removing all unbounded velocity singularities (of power‐law and logarithmic type) at the trailing edge, and including nonlinear wakes and thick swept‐back wings. A suitable boundary integral approach is adopted and the uniqueness issue is discussed for several wing configurations of interest in aerodynamics. Sommario. Si presenta una formulazione unificata della condizione di Kutta per flussi stazionari e non stazionari, ottenuta imponendo la limitatezza della velocità al bordo d'uscita, e valida nel caso nonlineare anche per ali a freccia. Si utilizza un opportuno approccio integrale al contorno e si discute il problema dell'unicità per svariate configurazioni alari di interesse nelle applicazioni.
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    The international journal of advanced manufacturing technology 14 (1998), S. 894-900 
    ISSN: 1433-3015
    Keywords: Aerodynamics ; Concurrent engineering ; Manufacturing costs ; Optimisation ; Statistical models ; Tolerances
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A component of the direct operating cost of aircraft is that associated with the manufacturing cost. This affects depreciation, interest, insurance and maintenance charges. By relaxing the requirements for aerodynamic surface smoothness the manufacturing cost can be reduced at the expense of an increase in drag and corresponding fuel costs. This work is part of a study to examine this multidisciplinary problem. Only isolated turbofan nacelles are considered. The costs associated with assigning different tolerance levels to the feature dimensions on nacelles are assessed. A statistical procedure is employed to estimate the cost-tolerance relationship for eleven features involving gaps, steps, surface profile and fastener flushness. This procedure requires actual manufacturing and cost source data. A knowledge of the cost-tolerance relationships is useful in a concurrent engineering context. It will allow aerodynamicists to optimise surface smoothness in consultation with production engineers, thus achieving the best compromise between cost and drag.
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 217-247 
    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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  • 4
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 369-401 
    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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  • 5
    Electronic Resource
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 403-442 
    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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  • 6
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 443-457 
    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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  • 7
    Electronic Resource
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 557-579 
    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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  • 8
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 501-517 
    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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  • 9
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 627-635 
    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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  • 10
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 677-696 
    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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  • 11
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 697-712 
    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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  • 12
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 751-769 
    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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  • 13
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 771-789 
    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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  • 14
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 725-747 
    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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  • 15
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 811-835 
    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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  • 16
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 887-905 
    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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  • 17
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 927-957 
    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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  • 18
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 1003-1022 
    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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  • 19
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 1217-1237 
    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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  • 20
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    International Journal for Numerical Methods in Fluids 27 (1998), S. 13-32 
    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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  • 21
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    International Journal for Numerical Methods in Fluids 27 (1998), S. 41-55 
    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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  • 22
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    International Journal for Numerical Methods in Fluids 27 (1998), S. 241-258 
    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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  • 23
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 23-46 
    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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  • 24
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 47-72 
    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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  • 25
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 113-128 
    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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  • 26
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 143-156 
    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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  • 27
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 201-213 
    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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  • 28
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 225-242 
    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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  • 29
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 267-291 
    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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  • 30
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 317-336 
    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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  • 31
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 357-378 
    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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  • 32
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 381-394 
    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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  • 33
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 419-442 
    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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  • 34
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 461-476 
    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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  • 35
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 523-540 
    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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  • 36
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 565-568 
    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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  • 37
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 859-881 
    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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    International Journal for Numerical Methods in Fluids 28 (1998), S. 917-943 
    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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  • 39
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 983-1007 
    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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  • 40
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 1033-1052 
    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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    International Journal for Numerical Methods in Fluids 28 (1998), S. 1053-1071 
    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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  • 42
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 1093-1108 
    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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  • 43
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 1139-1158 
    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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    International Journal for Numerical Methods in Fluids 28 (1998), S. 1159-1181 
    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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  • 45
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 1241-1261 
    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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  • 46
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 1281-1302 
    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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  • 47
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 1303-1324 
    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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  • 48
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 1371-1387 
    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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  • 49
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 1421-1440 
    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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  • 50
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 1441-1479 
    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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    International Journal for Numerical Methods in Fluids 26 (1998), S. 17-37 
    ISSN: 0271-2091
    Keywords: incompressible Navier-Stokes ; parallel finite element method ; Galerkin approximation ; 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 semi-explicit iterative finite element computational procedure for modelling unsteady incompressible fluid flows is presented. During the procedure, element flux vectors are calculated in parallel and then assembled into global flux vectors. Equilibrium iterations which introduce some ‘local implicitness’ are performed at each time step. The number of equilibrium iterations is governed by an implicitness parameter. The present technique retains the advantages of purely explicit schemes, namely (i) the parallel speed-up is equal to the number of parallel processors if the small communication overhead associated with purely explicit schemes is ignored and (ii) the computation time as well as the core memory required is linearly proportional to the number of elements. The incompressibility condition is imposed by using the artificial compressibility technique. A pressure-averaging technique which allows the use of equal-order interpolations for both velocity and pressure, this simplifying the formulation, is employed. Using a standard Galerkin approximation, three benchmark steady and unsteady problems are solved to demonstrate the accuracy of the procedure. In all calculations the Reynolds number is less than 500. At these Reynolds numbers it was found that the physical dissipation is sufficient to stabilize the convective term with no need for additional upwind-type dissipation. © 1998 John Wiley & Sons, Ltd.
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  • 52
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 125-143 
    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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    International Journal for Numerical Methods in Fluids 26 (1998), S. 199-215 
    ISSN: 0271-2091
    Keywords: air-conditioning unit ; k-∊ model ; Reynolds stress 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: Details are given of a study to obtain experimental data in an idealized environment for the purpose of evaluating the corresponding computational predictions and which supplement parallel measurements made in actual packaged air-conditioning units. The system consisted of a purpose-built low-speed wind tunnel with a working section constructed to reproduce particular features of the real units. In the experiment, both the mean velocity profiles and turbulence properties of the flow are obtained from triple-hot-wire anemometry measurements. A numerical model, based on finite volume methodology, was used to obtain the solution of the Reynolds-averaged Navier-Stokes equations for incompressible isothermal flow. The Reynolds stress terms in the equations are calculated using the standard k-∊ model and second-moment closure (Reynolds stress) models. The accuracy of the two models was evaluated against the experimental measurements made 10 mm downstream of a baffle. The results show that the standard k-∊ model gave the better agreement except in regions of strong recirculation. © 1997 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 251-280 
    ISSN: 0271-2091
    Keywords: turbulence modelling ; eddy viscosity ; second-moment closure ; tidal flows ; 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: This paper employs one-point, linear eddy viscosity and differential second-moment (DSM) turbulence closures to predict the turbulent characteristics of both rectilinear and circular tidal flows. The numerical scheme is based on a finite volume approach applied to a non-staggered grid such that all flow variables are stored at one and the same set of nodes. Numerical stability is maintained through the implementation of apparent viscosities and source term linearization, which are essential if eddy viscosity terms are absent. A stable algorithm is devised for the Reynolds stresses which includes a non-linear velocity smoothing in order to stabilise the numerical scheme during flow reversal and relaminarization. Favourable agreement with the experimental rectilinear tidal data of Schröder (Tech. Rep. GK55 87/E/16, GKSS-Forshungszentrum Geesthacht, 1983) and McClean (Turbulence and Sediment Transport Measurements in a North Sea Tidal Inlet (the Jade), Springer, New York, 1987, p. 436) is reported. Numerical calculations of circular tidal flows are also presented which were motivated by the preliminary investigations of Davies and Jones (Int. j. numer. meth. fluids,12, 17 (1991)) and Davies (Continental Shelf. Res., 11, 1313 (1991)), who employed the one-equation, k-l, eddy viscosity turbulence model to simulate rectilinear and circular tidal flows. © 1998 John Wiley & Sons, Ltd.
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  • 55
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 281-301 
    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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  • 56
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 323-343 
    ISSN: 0271-2091
    Keywords: mixed convection ; finite volume algorithm ; eccentricity ; Nusselt number ; 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 computational study is performed on two-dimensional mixed convection in an annulus between a horizontal outer cylinder and a heated, rotating, eccentric inner cylinder. The computation has been done using a non-orthogonal grid and a fully collocated finite volume procedure. Solutions are iterated to convergence through a pressure correction scheme and the convection is treated by Van Leer's MUSCL scheme. The numerical procedure adopted here can easily eliminate the ‘Numerical leakage’ phenomenon of the mixed convection problem whereby strong buoyancy and centrifugal effects are encountered in the case of a highly eccentric annulus. Numerical results have been obtained for Rayleigh number Ra ranging from 7×103 to 107, Reynolds number Re from 0 to 1200 and Prandtl number Pr from 0.01 to 7. The mixed rotation parameter σ (=Ra/PrRe2) varies from ∞ (pure natural convection) to 0.01 with various eccentricities ε. The computational results are in good agreement with previous works which show that the mixed convection heat transfer characteristics in the annulus are significantly affected by σ and ε. The results indicate that the mean Nusselt number Nu increases with increasing Ra or Pr but decreases with increasing Re. In the case of a highly eccentric annulus the conduction effect becomes predominant in the throat gap. Hence the crucial phenomenon on whereby Nu first decreases and then increases can be found with increasing eccentricity. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 459-483 
    ISSN: 0271-2091
    Keywords: SIMPLE algorithm ; PISO algorithm ; unsteady 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: Various pressure-based schemes are proposed for transient flows based on well-established SIMPLE and PISO algorithms. The schemes are applied to the solution of unsteady laminar flow around a square cylinder and steady laminar flow over a backward-facing step. The implicit treatment and the performance of the various schemes are evaluated by using benchmark solutions with a small time step. Three different second-order-accurate time derivatives based on different time levels are presented. The different time derivatives are applied to the various schemes under consideration. Overall the PISO scheme was found to predict accurate results and was robust. However, for small time step values, alternative schemes can predict accurate results for approximately half the computational cost. The choice of time derivative proved to be very significant in terms of the accuracy and robustness of a scheme. Significantly, the one-sided forward differencing scheme was the most successful used in conjunction with a strongly implicit-based algorithm. However, a greater degree of accuracy was achieved using the standard PISO algorithm with the Crank-Nicolson time derivative. Recommendations for future work are discussed.© 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 533-556 
    ISSN: 0271-2091
    Keywords: mixed finite elements ; finite volumes ; groundwater flow and transport ; biodegradation ; 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 for the simulation of flow and transport of organic compounds undergoing bacterial oxygen- and nitrate-based respiration is presented. General assumptions regarding microbial population, bacteria metabolism and effects of oxygen, nitrogen and nutrient concentration on organic substrate rate of consumption are briefly described. The numerical solution techniques for solving both the flow and the transport are presented. The saturated flow equation is discretized using a high-order mixed finite element scheme, which provides a highly accurate estimation of the velocity field. The transport equation for a sorbing porous medium is approximated using a finite volume scheme enclosing an upwind TVD shock-capturing technique for capturing concentration-unsteady steep fronts. The performance and capabilities of the present approach in a bio-remediation context are assessed by considering a set of test problems. The reliability of the numerical results concerning solution accuracy and the computational efficiency in terms of cost and memory requirements are also estimated. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 519-531 
    ISSN: 0271-2091
    Keywords: wavy channel flow ; peristaltic motion ; spectral collocation 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 numerical procedure is developed for the analysis of flow in a channel whose walls describe a travelling wave motion. Following a perturbation method, the primitive variables are expanded in a series with the wall amplitude as the perturbation parameter. The boundary conditions are applied at the mean surface of the channel and the first-order perturbation quantities are calculated using the pseudospectral collocation method. Although limited by the linear analysis, the present approach is not restricted by the Reynolds number of the flow and the wave number and frequency of the wavy-walled channel. Using the computed wall shear stresses, the positions of flow separation and reattachment are determined. The variations in velocity and pressure with frequency of excitation are also presented. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 485-495 
    ISSN: 0271-2091
    Keywords: capillarity ; free surface ; finite elements ; 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: The mathematical formulation of the dynamics of free liquid surfaces including the effects of surface tension is governed by a non-linear system of elliptic differential equations. The major difficulty of getting unique closed solutions only in trivial cases is overcome by numerical methods. This paper considers transient simulations of liquid-gas menisci in vertical capillary tubes and gaps in the presence of gravity. Therefore the CFD code FIDAP 7.52 based on the Galerkin finite element method (FEM) is used. Calculations using the free surface model are presented for a variety of contact angles and cross-sections with experimental and theoretical verification. The liquid column oscillations are compared for numerical accuracy with a mechanical mathematical model, and the sensitivity with respect to the node density is investigated. The efficiency of the numerical treatment of geometric non-trivial problems is demonstrated by a prismatic capillary. Present restrictions limiting efficient transient simulations with irregularly shaped calculational domains are stated. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 605-623 
    ISSN: 0271-2091
    Keywords: arbitrary Lagrangian-Eulerian method ; body-fitted co-ordinates ; free surface ; non-linear sloshing ; Navier-Stokes 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 numerical prediction method has been proposed to predict non-linear free surface oscillation in an arbitrarily-shaped three-dimensional container. The liquid motions are described with Navier-Stokes equations rather than Laplace equations which are derived by assuming the velocity potential. The profile of a liquid surface is precisely represented with the three-dimensional curvilinear co-ordinates which are regenerated in each computational step on the basis of the arbitrary Lagrangian-Eulerian (ALE) formulation. In the transformed space, the governing equations are discretized on a Lagrangian scheme with sufficient numerical accuracy and the boundary conditions near the liquid surface are implemented in a complete manner. In order to confirm the applicability of the present computational technique, numerical simulations are conducted for the free oscillations of viscid and inviscid liquids and for highly non-linear oscillation. In addition, non-linear sloshing motions caused by horizontal and vertical excitations and a transition from non-linear sloshing to swirling are numerically predicted in three-dimensional cylindrical containers. Conclusively, it is shown that these sloshing motions associated with high non-linearity are reasonably predicted with the present numerical technique. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 637-655 
    ISSN: 0271-2091
    Keywords: liquid flow ; energy transport ; electron-beam ; 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 analysis is made of the liquid flow and energy transport in a system to evaporate metals. The energy from an electron-beam heats an axisymmetric metal disk supported by a water-cooled platform. Metal evaporates from the surface of a hot pool of liquid which is surrounded by a shell of its own solid. Flow in the pool is strongly driven by temperature-induced buoyancy and capillary forces, and is located in the transition region between laminar and turbulent flow. The evaporation rate is strongly influenced by the locations of the free boundaries. A modified finite element method is used to calculate the steady state flow and temperature fields coupled with the interface locations. The mesh is structured with spines that stretch and pivot as the interfaces move. The discretized equations are arranged in an ‘arrow’ matrix and are solved using the Newton-Raphson method. The electron-beam power and platform contact resistance are varied for cases involving the evaporation of aluminum. The results reveal the interaction of liquid flow, heat transfer and free interfaces. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 657-676 
    ISSN: 0271-2091
    Keywords: lattice gas ; cellular automata ; wave modelling ; internal waves ; standing waves ; 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: Internal waves are modelled in two different circumstances: in a continuously stratified fluid and at the interface between two immiscible fluids. This is done using the lattice gas approach. The standard single phase model and an immiscible two-phase model are both modified to incorporate gravitational interactions. Standing internal waves are set up in both models and are seen to oscillate under the action of the gravitational interaction. The results obtained suggest that the lattice gas approach can be a useful tool in the modelling of such phenomena. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 581-603 
    ISSN: 0271-2091
    Keywords: rotating co-rotating disks ; disk drives ; laminar flow ; numerical calculations ; 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 is performed for the constant property laminar flow of air in the space between a pair of disks clamped co-axially on a central hub and co-rotating in a stationary cylindrical enclosure. Both two- and three-dimensional flow conditions are examined in relation to the interdisk spacing, H, and the disk angular velocity, Ω. Two interdisk spacings are considered, corresponding to aspect ratios Γ = 0.186 and 0.279 (with Γ = H/(R2+a-R), where R2 is the disk radius, a is the disk rim-enclosure wall clearance, and R is the hub radius). A range of rotational speeds encompassing the transition from axisymmetric two-dimensional steady flow to non-axisymmetric three-dimensional unsteady flow are considered for various values of the Reynolds number, Re (with \documentclass{article}\pagestyle{empty}\begin{document}$ Re=\Omega R_2^2/v $\end{document}, where v is the kinematic viscosity of air). Axisymmetric calculations are first performed for both aspect ratios in the range 3858≤Re≤23 150. Fully three-dimensional calculations are then performed for the configuration with Γ = 0.186 and Re = 23 150, and for the configuration with Γ = 0.279 and Re = 7715, 15 430 and 23 150. The axisymmetric calculations performed with Γ = 0.186 confirm many known features of the flow, including the transition from a steady flow to an oscillatory periodic regime. This occurs at ≈Re = 23 150 for a configuration with a/H = 0, and at ≈Re = 14 670 for one with a/H = 0.28 and a finite disk thickness (b/H = 0.2). Three-dimensional calculations performed for Γ = 0.186 with a/H = 0 and Re = 23 150 reveal a circumferentially periodic flow pattern with eight foci of intensified axial component of vorticity. The axisymmetric calculations performed with Γ = 0.279 and Re 〉 7715 yield a novel, non-unique steady solution for the velocity field that is asymmetric with respect to the interdisk mid-plane. No experimental verification of this finding exists to date, but similar situations are known to arise in the context of anomalous modes of the Taylor-Couette flow. Relaxing the axisymmetry constraint allows this flow to evolve to an oscillatory three-dimensional regime of increasing irregularity with increasing rotational speed. In this case, the number of foci of intensified axial vorticity varies with time, ranging from six at Re = 7715 to between six and eight at Re = 23 150. © 1998 John Wiley & Sons, Ltd.
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  • 65
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 713-724 
    ISSN: 0271-2091
    Keywords: grid generation ; 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 simple grid generation method which adopts the uni-directional interpolation idea but only interpolates one co-ordinate between two opposite boundaries. The use of this new scheme showed that (a) it is convenient to use; and (b) compared with the built-in grid generator of certain commercial computational fluid dynamics (CFD) code, it saves time significantly. © 1998 John Wiley & Sons, Ltd.
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  • 66
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 877-885 
    ISSN: 0271-2091
    Keywords: B-spline basis ; Galerkin method ; Gauss-Newton method ; mixed formulation ; 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 mixed Galerkin technique with B-spline basis functions is presented to compute two-dimensional incompressible flow in terms of the primitive variable formulation. To circumvent the Babuska-Brezzi stability criterion, the artificial compressibility formulation of the equation of mass conservation is employed. As a result, the diagonal components of the matrix form in the governing equations are not singular. The B-spline basis is used because it is superior to other splines in providing computer solutions to fluid flow problems. One of the advantages of the B-spline basis is that it has excellent approximation properties. Numerical examples of applications of the mixed formulation are presented to demonstrate the convergence characteristics and accuracy of the present formulation. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 851-874 
    ISSN: 0271-2091
    Keywords: finite elements ; Taylor-Galerkin/pressure correction ; particle settling ; drag ; rotating and non-rotating flows ; inelastic non-Newtonian fluids ; 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: Finite element solutions are presented for the flow of Newtonian and non-Newtonian fluids around a sphere falling along the centreline of a cylindrical tube. Both rotating and stationary tube scenarios are considered. Calculations are reported for three different inelastic constitutive models that manifest shear-thinning, extension-thickening and their combination. The influence of inertia and these various forms of viscous response are examined for their influence upon the drag on the settling particle and the structure of the flow. Simulations are performed by employing a semi-implicit time marching Taylor-Galerkin/pressure-correction finite element algorithm, a fractional-staged scheme of second-order-accuracy. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 837-850 
    ISSN: 0271-2091
    Keywords: dense gas dispersion ; radiation absorption ; discrete transfer 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 numerical model is presented for the prediction of thermal radiation absorption in dense gas clouds during accidental release in the atmosphere. The model is based on the discrete transfer method (DT method) that was originally developed for modelling radiation in combustion chambers. The radiation model assumes a number of representative rays of predetermined orientation fired from each of the domain boundaries. Each ray is traced through the domain elements until reaching another boundary where it is terminated. Radiation sources are calculated for each element by performing an energy balance across each element for each ray passing through it. The energy sources recovered are fed into the finite element flow solver for every time step in the energy equation. The model proved accurate, and memory and computer time efficient. It showed that accounting for radiation effects lead to improved predictions. It also showed that in certain scenarios, radiation effects could be predominant. © 1998 John Wiley & Sons, Ltd.
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  • 69
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 907-926 
    ISSN: 0271-2091
    Keywords: Euler solvers ; finite volume ; turbomachinery ; duct flow ; 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: The numerical solutions of inviscid rotational (Euler) flows were obtained using an explicit hexahedral unstructured cell vertex finite volume method. A second-order-accurate, one-step Lax-Wendroff scheme was used to solve the unsteady governing equations discretized in conservative form. The transonic circular bump, in which the location and the strength of the captured shock are well predicted, was used as the first test case. The nozzle guide vanes of the VKI low-speed turbine facility were used to validate the Euler code in highly 3D environment. Despite the high turning and the secondary flows which develop, close agreements have been obtained with experimental and numerical results associated with these test cases. © 1998 John Wiley & Sons, Ltd.
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  • 70
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 977-986 
    ISSN: 0271-2091
    Keywords: elastohydrodynamic lubrication ; line contact ; Reynolds equation ; numerical solution ; control 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: This paper deals with the discretization of the one-dimensional Reynolds equation coupled with the film shape equation, that is used for the numerical solution of elastohydrodynamically lubricated contacts. The derivation of the developed discretization formula is based on the control volume approach. To reduce the discretization error caused by the upwind expression of the Couette (velocity) term, non-symmetric control volumes are used for discretization of the Reynolds equation, while for the elasticity equation the standard approach is used. A numerical method for the solution of the pressure and the film thickness profiles of elastohydrodynamically lubricated isothermal line contacts is presented. Results are presented for chosen typical parameters of a highly loaded contact. To show the formula efficiency, the convergence speed of both the presented discretization formula and a chosen comparative discretization formula (A.A. Lubrecht, Ph.D. Thesis, University of Twente, The Netherlands, 1987 and C.H. Venner, Ph.D. Thesis, University of Twente, The Netherlands, 1991) are checked. The results show that the presented formula gives better approximations of film thickness values for a given number of equidistant grid nodes. Moreover, the presented approach is probably suitable for more sophisticated cases, such as transient situations and elliptical contacts. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 959-975 
    ISSN: 0271-2091
    Keywords: grid adaption ; grid iterations ; iterative solvers ; operator splitting ; 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: Solution algorithms for solving the Navier-Stokes equations without storing equation matrices are developed. The algorithms operate on a nodal basis, where the finite element information is stored as the co-ordinates of the nodes and the nodes in each element. Temporary storage is needed, such as the search vectors, correction vectors and right hand side vectors in the conjugate gradient algorithms which are limited to one-dimensional vectors. The nodal solution algorithms consist of splitting the Navier-Stokes equations into equation systems which are solved sequencially. In the pressure split algorithm, the velocities are found from the diffusion-convection equation and the pressure is computed from these velocities. The computed velocities are then corrected with the pressure gradient. In the velocity-pressure split algorithm, a velocity approximation is first found from the diffusion equation. This velocity is corrected by solving the convection equation. The pressure is then found from these velocities. Finally, the velocities are corrected by the pressure gradient. The nodal algorithms are compared by solving the original Navier-Stokes equations. The pressure split and velocity-pressure split equation systems are solved using ILU preconditioned conjugate gradient methods where the equation matrices are stored, and by using diagonal preconditioned conjugate gradient methods without storing the equation matrices. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 1023-1038 
    ISSN: 0271-2091
    Keywords: three-state anemometry ; velocity field ; particle motion 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: An application of a new flow measurement technique is described which allows for the non-intrusive simultaneous measurement of flow velocity, density, and viscosity. The viscosity information can be used to derive the flow field temperature. The combination of the three measured variables and the perfect-gas law then leads to an estimate of the flow field thermodynamic pressure. Thus, the instantaneous state of a flow field can be completely described. Three-state anemometry (3SA), a derivative of particle image velocimetry (PIV), which uses a combination of three monodisperse sizes of styrene seeding particles is proposed. A marker seeding is chosen to follow the flow as closely as possible, while intermediate and large seeding populations provide two supplementary velocity fields, which are also dependent on fluid density and viscosity. A simplified particle motion equation, aimed at turbomachinery applications, is then solved over the whole field to provide both density and viscosity data. The three velocity fields can be separated in a number of ways. The simplest and that proposed in this paper is to dye the different populations and view the region of interest through interferometric filters. The two critical aspects needed to enable the implementation of such a technique are a suitable selection of the diameters of the particle populations, and the separation of the velocity fields. There has been extensive work on the seeding particle behaviour which allows an estimate of the suitable particle diameters to be made. A technique is described in this paper to allow the separation of particles in a range of micrometer sized velocity fields through fluorescence (separation through intensity also being possible). Some preliminary results by direct numerical simulation (DNS) of a 3SA image are also presented. The particle sizes chosen were 1 μm and 5 μm, tested on the near-wake flow past a cylinder to investigate viscosity only, assuming uniform flow density. The accuracy of the technique, derived from simulations of swirling flows, is estimated as 0.5% RMS for velocity, 2% RMS for the density and viscosity, and 4% RMS for the temperature estimate. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 1055-1084 
    ISSN: 0271-2091
    Keywords: internal tides ; shelf edge ; stratification ; turbulence energy ; baroclinic ; eddy 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 non-linear, three dimensional, baroclinic model with a range of turbulence energy submodels and algebraic models for the vertical mixing of momentum and density, is used in a cross shelf form to examine the spatial variation of vertical mixing due to the internal tide at the shelf edge off the west coast of Scotland. Particular emphasis is placed on the sensitivity of the mixing to the form of the parameterization of the subgrid scale processes. Calculations using a fine finite difference grid in the horizontal of the order of 0.6 km with 50 sigma levels in the vertical and a typical winter time stratification, show that the model can reproduce the major features of the internal tide with the range of parameterizations considered here, although there are some differences in the magnitude of both the velocity and mixing intensity of the internal tide, depending upon the parameterization of the mixing. In particular, the turbulence energy models show regions of intense mixing at the sea bed where the internal tide is generated and at the sea surface above the shelf break associated with the shear production of turbulence. These differences suggest that detailed measurements of current, internal displacement of density fields and turbulence dissipation rate may be able to assess the accuracy of the various mixing models. Calculations, however, show that the internal tide is particularly sensitive to small perturbations in the initial density field, suggesting that besides detailed measurements to validate the model, a detailed synoptic data set is required for model initialization. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 1127-1154 
    ISSN: 0271-2091
    Keywords: free surface ; transient viscous incompressible fluid ; finite element method ; VOF (volume-of-fluid) 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: The VOF method is adopted for the finite element analysis of transient fluid flow with a free surface. In particular, an adaptation technique for generating an adaptive grid is incorporated to capture a higher resolution of the free surface configuration. An adaptive grid is created through the refinement and mergence of elements. In this domain the elements in the surface region are made finer than those in the remaining regions for more efficient computation. Also, three techniques based on the VOF method are newly developed to increase the accuracy of the analysis, namely the filling pattern, advection treatment and free surface smoothing techniques. Using the proposed numerical techniques, radial flow with a point source and the collapse of a dam are analysed. The numerical results agree well with the theoretical solutions as well as with the experimental results. Through comparisons with the numerical results of several cases using different grids, the efficiency of the proposed technique is verified. © 1998 by John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 1205-1216 
    ISSN: 0271-2091
    Keywords: multigrid method ; residual transfer ; convection-diffusion 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 multigrid method is studied for the solution of a linear system resulting from the high-order nine-point discretization of the convection-diffusion equations. The residual injection operator is used as a substitute for the usual full-weighting in the multigrid process. A heuristic analysis is given to obtain a dynamic injection operator that is cost-effective for both diffusion- and convection-dominated problems. Numerical experiments are employed to test the stability and efficiency of the proposed method. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 27 (1998), S. 81-95 
    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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    International Journal for Numerical Methods in Fluids 27 (1998), S. 97-107 
    ISSN: 0271-2091
    Keywords: least-squares ; finite elements ; flow ; 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: The least-squares mixed finite element method is concisely described and supporting error estimates and computational results for linear elliptic (steady diffusion) problems are briefly summarized. The extension to the stationary Navier-Stokes problems for Newtonian, generalized Newtonian and viscoelastic fluids is then considered. Results of numerical studies are presented for the driven cavity problem and for a stick-slip problem. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 27 (1998), S. 127-138 
    ISSN: 0271-2091
    Keywords: compressible flow ; supersonic flows ; aerofoils ; Cauchy/Riemann equations ; Crocco's relation ; 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, alternative formulations of the steady Euler equations for conservation of mass, momentum and energy are adopted for the numerical simulation of compressible flows with shock waves. The total enthalpy is assumed to be constant and hence an isentropic density is calculated in terms of the velocity components. Also, the x- and y-momentum equations written in conservation form are combined to yield the tangential and normal momentum equations. For smooth flows the tangential momentum equation reduces to the entropy transport equation, while the normal momentum equation gives the vorticity in terms of the entropy gradient normal to the flow direction (Crocco's relation). Hence the velocity components can be obtained from the continuity equation and normal momentum equation (Cauchy/Riemann equations), while the entropy correction for the density is obtained from the tangential momentum equation (this correction is not needed in the isentropic flow regions). The present formulation can be easily extended to handle variable total enthalpy. Preliminary results are presented for transonic and supersonic flows over aerofoils and the entropy and vorticity effects are clearly identified. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 27 (1998), S. 159-168 
    ISSN: 0271-2091
    Keywords: finite element method ; Galerkin method ; residual free bubbles ; 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 overview of the unusual stabilized finite element method and of the standard Galerkin method enriched with residual free bubble functions is presented. For the first method a concrete model problem illustrates its application in advective-diffusive-reactive equations and for the second method it is shown how static condensation of residual free bubbles gives rise to mass lumping and selective reduced integration, which are viewed as numerical tricks and can now be derived by the standard Galerkin method without tricks. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 27 (1998), S. 139-157 
    ISSN: 0271-2091
    Keywords: hydrodynamic stability ; finite element method ; incompressible cavity flow ; Arnold'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: Numerical methods have been applied to theoretical studies of instability and transition to turbulence. In this study an analysis of the linear stability of incompressible flow is undertaken. By means of the finite element method the two-dimensional base flow is computed numerically over a range of Reynolds numbers and is perturbed with three-dimensional disturbances. The partial differential equations governing the evolution of perturbation are obtained from the non-linear Navier-Stokes equations with a slight compressibility by using linear stability and normal mode analysis. In terms of the finite element discretization a non-singular generalized eigenproblem is formulated from these equations whose solution gives the dispersion relation between complex growth rate and wave number. This study presents stability curves to identify the critical Reynolds number and critical wavelength of the neutral mode and discusses the mechanism of instability. The stability of lid-driven cavity flow is examined. Taylor-Göertler-like vortices in the cavity are obtained by means of reconstruction of three-dimensional flows. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 27 (1998), S. 169-177 
    ISSN: 0271-2091
    Keywords: wall laws ; wavy surfaces ; 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: We describe a new approach for developing new wall-laws for rough surfaces. We also give error estimates on a simple model. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 27 (1998), S. 229-239 
    ISSN: 0271-2091
    Keywords: kinetic approach ; finite element schemes ; Euler equations ; 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: Starting from the gas kinetic model, a new class of schemes for hyperbolic systems of conservation laws is presented. The flow solvers are based on the Boltzmann equations. The numerical discretization is based on the upwind cell vertex fluctuation-splitting model. The method is truly multidimensional in the sense that the splitting is independent of a particular normal direction; the geometry of the mesh does not influence the upwinding. Numerical results for inviscid flow test cases are presented to indicate the robustness and accuracy of the schemes. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 27 (1998), S. 193-206 
    ISSN: 0271-2091
    Keywords: finite element ; finite volume ; numerical dissipation ; compressible 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: We refer to as mixed element/volume (MEV) methods the application of finite element for diffusion terms and finite volume for advection terms in a flow model. The compatibility of these methods can be checked for some low-order approximations; the resulting schemes may enjoy the relative mesh-regularity-independent accuracy of finite element methods as discussed in a first section. In recent years a number of developments (by INRIA Dassault and T. Barth, among others) have produced P1-continuous schemes that involve some MUSCL/TVD unidirectional limitation; the resulting schemes are very useful but sometimes may involve much more numerical viscosity than necessary, especially for unsteady computations. In the present study, a new version is built by using a larger molecule for the intercell flux evaluation. The 1D version can be promoted to fourth- or even fifth-order spatial accuracy. The 2D version is no better than second-order-accurate; however, it involves only a sixth-order dissipation and the global accuracy is markedly improved even on irregular meshes. The above development extends the ability of the MUSCL/MEV scheme towards the accurate calculation of unsteady flows involving vortex shedding. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 157-186 
    ISSN: 0271-2091
    Keywords: advective transport ; semi-implicit ; conservative ; unconditionally stable ; 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 scalar transport method which is appropriate for simulations over a wide range of Courant number is described. Von Neumann stability and matrix invertibility are guaranteed for all Courant numbers and the method has less diffusive and dispersive error than simpler implicit methods. It is implemented for vertical scalar transport in a three-dimensional hydrodynamic model, with horizontal transport discretized explicitly. The method is applied and compared with simpler semi-implicit methods in several test cases and used for a simulation of scalar transport in an estuary. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 1-22 
    ISSN: 0271-2091
    Keywords: accretion disk ; compressible Navier-Stokes equations ; stratified flow ; operator splitting ; hydrodyamic code ; boundary layer ; 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 numerical approach based on consistent operator splitting is presented for computing compressible, highly stratified flows in astrophysics. The algorithm is particularly designed to search for steady or almost steady solutions for the time-dependent Navier-Stokes equations, describing viscous flow under the influence of a strong gravitational field. The algorithm proposed is multidimensional and works in Cartesian, cylindrical or spherical co-ordinates. It uses a second-order finite volume scheme with third-order upwinding and a second-order time discretization. An adaptive time step control and monotonic multilevel grid distribution has been incorporated to speed up convergence. This method has been incorporated into a hydrodynamical code by which, for the first time, for two-dimensional models the dynamics of the boundary layer in the accretion disk around a compact star could be computed over the whole viscous time scale. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 73-94 
    ISSN: 0271-2091
    Keywords: compressible turbulent flows ; implicit solver ; characteristics-based method ; low-Re two-equation turbulence models ; 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 unfactored method for the coupled solution of the compressible Navier-Stokes equations with two-equation turbulence models is presented. Both fluid-flow and turbulence transport equations are discretized by a characteristics-based scheme. The implicit unfactored method combines Newton subiterations and point-by-point Gauss-Seidel subrelaxation. Implicit-coupled and -decoupled strategies are compared for their efficiency in the solution of the Navier-Stokes equations in conjunction with low-Re two-equation turbulence models. Computations have been carried out for the flow over an axisymmetric bump using the k-∊ and k-ω models. Comparisons have been obtained with experimental data and other numerical solutions. The present study reveals that the implicit unfactored implementation of the two-equation turbulence models reduces the computing time and improves the robustness of the CFD code in turbulent compressible flows. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 95-112 
    ISSN: 0271-2091
    Keywords: square columns in tandem ; finite element method ; improved BTD ; 3D computation ; aerodynamic characteristics ; 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- (2D) and three-dimensional (3D) finite element analyses for flow around two square columns in tandem arrangement were performed with various column spacings and Reynolds numbers. The computed values were compared with the wind-tunnel results in terms of the aerodynamic characteristics of the leeward column. In most 2D computations, strong vortices were formed behind the windward column, irrespective of widely changed Reynolds numbers. This was different from the experimental phenomena of equivalent spacing, so that the computed time-averaged pressure coefficients were not identical to the experimental values except when the distance between the two columns was adequately wide or narrow. On the other hand, in 3D computation, distinct differences in flow structures behind the column were observed between Reynolds numbers of 103 and 104 and the pressure coefficient in the 3D analysis with Re=104 agreed well with the experimental value. Thus, the effectiveness of 3D computations and Reynolds number effects on the flow around two square columns have been confirmed. © 1998 John Wiley & Sons, Ltd.
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  • 88
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 129-142 
    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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  • 89
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 719-736 
    ISSN: 0271-2091
    Keywords: front tracking ; mesh adaptation ; 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 numerical model is developed for the simulation of moving interfaces in viscous incompressible flows. The model is based on the finite element method with a pseudo-concentration technique to track the front. Since a Eulerian approach is chosen, the interface is advected by the flow through a fixed mesh. Therefore, material discontinuity across the interface cannot be described accurately. To remedy this problem, the model has been supplemented with a local mesh adaptation technique. This latter consists in updating the mesh at each time step to the interface position, such that element boundaries lie along the front. It has been implemented for unstructured triangular finite element meshes. The outcome of this technique is that it allows an accurate treatment of material discontinuity across the interface and, if necessary, a modelling of interface phenomena such as surface tension by using specific boundary elements. For illustration, two examples are computed and presented in this paper: the broken dam problem and the Rayleigh-Taylor instability. Good agreement has been obtained in the comparison of the numerical results with theory or available experimental data. © 1998 John Wiley & Sons, Ltd.
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  • 90
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 601-616 
    ISSN: 0271-2091
    Keywords: turbulence modeling ; CFD ; finite volume method ; vortex shedding ; two-layer approach ; 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 results of numerical simulations of vortex shedding past a free-standing square cylinder at ReD=22 000, obtained with different turbulence models. Using wall functions, the standard k-ε model is compared with a modification suggested by Kato and Launder (Proc. 9th Symp. Turbulent Shear Flows, Kyoto, 10-4-1 (1993)). In addition, both versions are used in a two-layer approach, in which the flow close to the cylinder is computed with a locally more suitable one-equation turbulence model and only outside the viscous near-wall layer with the two mentioned high-Re model versions. To allow a comparison, the simulations are performed first using the same computational domain and boundary conditions as in previous investigations. Then results are presented that were obtained on a computational domain and with boundary conditions more suitable for a comparison with the experiments. © 1998 John Wiley & Sons, Ltd.
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  • 91
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 663-677 
    ISSN: 0271-2091
    Keywords: CFD ; control volume ; polar cylindrical 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: In the numerical simulation of fluid flows using a polar cylindrical grid, grid lines meet at a single point on the axis of the polar cylindrical grid system; this makes the grids around the axis degenerate from being general quadrilaterals into triangles. Therefore, a special treatment must be performed when the axis has to be included in the computational domain in order to solve a non-axisymmetrical fluid flow problem. In this paper a new numerical method has been developed to deal with the difficulty of the axis when the control volume technique is used with a non-staggered grid arrangement. Two illustrative examples of the proposed method are presented for simulating the fluid flows on the axis and all the numerical results obtained for the two examples are shown to be in good agreement with the available analytical solutions. © 1998 John Wiley & Sons, Ltd.
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  • 92
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 501-521 
    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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  • 93
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 703-718 
    ISSN: 0271-2091
    Keywords: pressure transient ; air vessel ; air entrainment ; fluid system ; 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 describes an improved numerical method and computational procedure for the implementation of typical air vessel responses and their influence on the pressure transient for unsteady flow in a pipeline system with air entrainment. The proposed numerical method and computational procedure is without the necessity of an excessive iterative procedure as required previously by the conventional approach. The effects of air in the transient fluid system with the air vessel were then studied through the improved numerical computational method. Free and dissolved gases in the transported fluid, and cavitation at vapour pressure, are included. © 1998 John Wiley & Sons, Ltd.
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  • 94
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 737-757 
    ISSN: 0271-2091
    Keywords: high-order ; compact ; finite difference ; no-slip ; no-penetration ; driven cavity ; 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 recent papers have studied fourth-order compact discretizations of the streamfunction vorticity equations. They differed primarily in how the no-slip wall boundary conditions were handled. In this paper, these different formulas are compared to one another, as well as to three newly proposed formulas. Special consideration is paid to the truncation errors; in particular, it is shown that many well-known formulations are actually more accurate by O(h) than previously reported, where h is the mesh size. These new theoretical error rates are confirmed with an analytical model problem. The different formulas are then compared with published driven cavity results, both in terms of accuracy and performance, and the newly proposed high-order Jensen formula is judged to have the marginally best combination of these properties. © 1998 John Wiley & Sons, Ltd.
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  • 95
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 815-840 
    ISSN: 0271-2091
    Keywords: boundary element method ; three-dimensional mixing flow ; Newtonian fluid ; viscoelastic ; 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 boundary element method (BEM) is implemented for the simulation of three-dimensional transient flows of typical relevance to mixing. Creeping Newtonian and viscoelastic fluids of the Maxwell type are examined. A boundary-only formulation in the time domain is proposed for linear viscoelastic flows. Special emphasis is placed on cavity flows involving simple- and multiple-connected moving domains. The BEM becomes particularly suited in multiple-connected flows, where part of the boundary (stirrer or rotor) is moving, and the remaining outer part (cavity or barrel) is at rest. In this case, conventional methods, such as the finite element method (FEM), generally require remeshing or mesh refinement of the three-dimensional fluid volume as the flow evolves and the domain of computation changes with time. The BEM is shown to be much easier to implement since the kinematics of the elements bounding the fluid is known (imposed). It is found that, for simple cavity flow induced by a rotating vane at constant angular velocity, the tractions at the vane tip and cavity face exhibit non-linear periodic dynamical behavior with time for fluids obeying linear constitutive equations. © 1998 John Wiley & Sons, Ltd.
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  • 96
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 887-902 
    ISSN: 0271-2091
    Keywords: potential flow ; free surface ; spectral method ; surface gravity waves ; dip formation ; 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 efficient numerical method for unsteady free surface motions, with simple geometries, has been devised. Under the potential flow assumption, the governing equation of free surface flows becomes a Laplace equation, which is treated here by means of a series expansions of the velocity potential. The free surface is represented with a height function. The present method is applied to surface gravity waves to test the stability and accuracy of the method. To show the versatility of the method, a model for a dip formation is considered. © 1998 John Wiley & Sons, Ltd.
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  • 97
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 903-915 
    ISSN: 0271-2091
    Keywords: finite elements ; incompressible flow ; drag coefficient ; heat transfer ; numerical modelling ; solid sphere ; 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 reports numerical simulation of the flow past a heated/cooled sphere. A Galerkin finite element method is used to solve the 3D incompressible Boussinesq equations in primitive variable form. Numerical simulations of flow around the sphere for a range of Grashof numbers and moderate Reynolds numbers, were conducted. The drag coefficient for adiabatic flow shows good agreement with standard correlations over the range of the Reynolds numbers investigated. It is shown that the drag can vary considerably with heating of the sphere and that computational fluid dynamics methods can be used to derive constitutive laws for macroscopic momentum and heat exchange in multiphase flow. © 1998 John Wiley & Sons, Ltd.
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  • 98
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 945-960 
    ISSN: 0271-2091
    Keywords: variational acceleration method ; composite grids ; local refinement ; 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 shows that the well-known variational acceleration method described by Wachspress (E. Wachspress, Iterative Solution of Elliptic Systems and Applications to the Neutron Diffusion Equations of Reactor Physics, Prentice-Hall, Englewood Cliffs, NJ, 1966) and later generalized to multilevels (known as the additive correction multigrid method (B.R Huthchinson and G.D. Raithby, Numer. Heat Transf., 9, 511-537 (1986))) is similar to the FAC method of McCormick and Thomas (S.F McCormick and J.W. Thomas, Math. Comput., 46, 439-456 (1986)) and related multilevel methods. The performance of the method is demonstrated for some simple model problems using local refinement and suggestions for improving the performance of the method are given. © 1998 John Wiley & Sons, Ltd.
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  • 99
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 961-981 
    ISSN: 0271-2091
    Keywords: numerical methods ; boundary element method ; shear flow ; hydrodynamics ; spheroids ; hair bundles ; 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 indirect boundary element method was used to study the hydrodynamics of longitudinal shear flow and cross flow with a longitudinal rate of shear over prolate and oblate hemispheroidal protuberances projecting from a plane wall. Analytic techniques such as Fourier analysis, spheroidal co-ordinates, and the method of images were used to make the numerical methods more efficient. A novel method for computing the hydrodynamic torque was used - instead of directly calculating the torque from the weightings of the Green's functions (a method that is only valid when the weightings have physical significance) the hydrodynamic torque was computed indirectly using a Green's function for torque that derived here. As a test of this method, the present scheme was applied to determine the hydrodynamic torque of full spheroids, where exact solutions are known, and excellent results were obtained. Our results for hemispheroids projecting from plane walls were, except for extremely wide oblate hemispheroids, within a factor of two of those of full spheroids. Our results also agreed with those of previous study of oblate hemispheroidal protuberances. © 1998 John Wiley & Sons, Ltd.
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  • 100
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 1013-1031 
    ISSN: 0271-2091
    Keywords: advected grid ; mixing layer ; spatial development ; 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 advected grid explicit (AGE) method for direct numerical simulation of ‘incompressible’ turbulent shear flows is presented. The Navier-Stokes equations are used for momentum in a velocity-pressure formulation. Mass continuity and an equation of state link pressure with density (which is not assumed identically constant). Time advancement is entirely explicit, and spatial representation is localized (e.g. finite difference) and centred. Magnitudes of non-linear terms are reduced on advected grid(s), and numerical instabilities are efficiently reduced by ‘targeted diffusion’. Computation time scales directly on the number of grid points (virtual memory issues aside), and is very short for a DNS method. A spatially developing two-stream mixing layer was simulated as an example, reaching a vorticity thickness Reynolds number 〉20 000. Comparison with experimental results from self-similar mixing layers is satisfactory in terms of growth rate and Reynolds stress profiles. Turbulent vortical structures are visualized by means of pressure surfaces. © 1998 John Wiley & Sons, Ltd.
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