On the higher-order bounded discretization schemes for finite volume computations of incompressible flows

Abstract In recent years, three higher-order non-oscillatory schemes, SMART, SHARP and HLPA, have been proposed for the simulation of steady incompressible flows. This paper presents a comparison of these schemes in terms of their numerical accuracy, computational cost and algorithmic simplicity. The comparison is made on the basis of applications to three test problems, one linear and two non-linear, all involving a simultaneous presence of convective dominance and flow-to-grid skewness. Computed results show that the three schemes yield similar solutions which are nearly as good as those obtained with the QUICK scheme but without the physically unrealistic oscillations of the latter. However, there is a marked variation in their computational costs, especially in the case of fine grids.

[1]  P. Gaskell,et al.  Curvature‐compensated convective transport: SMART, A new boundedness‐ preserving transport algorithm , 1988 .

[2]  Richard S. Varga,et al.  Application of Oscillation Matrices to Diffusion-Convection Equations , 1966 .

[3]  J. Zhu,et al.  A local oscillation-damping algorithm for higher-order convection schemes , 1988 .

[4]  B. P. Leonard,et al.  A stable and accurate convective modelling procedure based on quadratic upstream interpolation , 1990 .

[5]  W. Rodi,et al.  Finite volume methods for two-dimensional incompressible flows with complex boundaries , 1989 .

[6]  J. Z. Zhu,et al.  Computation of axisymmetric confined jets in a diffuser , 1992 .

[7]  G. D. Raithby,et al.  Skew upstream differencing schemes for problems involving fluid flow , 1976 .

[8]  A. D. Gosman,et al.  Numerical Prediction of Turbulent Flow over Surface-Mounted Ribs , 1985 .

[9]  H. L. Stone.  ITERATIVE SOLUTION OF IMPLICIT APPROXIMATIONS OF MULTIDIMENSIONAL PARTIAL DIFFERENTIAL EQUATIONS , 1968 .

[10]  B. Launder,et al.  The numerical computation of turbulent flows , 1990 .

[11]  A. G. Hutton,et al.  THE NUMERICAL TREATMENT OF ADVECTION: A PERFORMANCE COMPARISON OF CURRENT METHODS , 1982 .

[12]  Wolfgang Rodi,et al.  Calculation of Annular and Twin Parallel Jets Using Various Discretization Schemes and Turbulence-Model Variations , 1981 .

[13]  G. Binder,et al.  Confined Jets in a Diverging Duct , 1983 .

[14]  C. Rhie,et al.  A numerical study of the turbulent flow past an isolated airfoil with trailing edge separation , 1982 .

[15]  B. P. Leonard,et al.  Simple high-accuracy resolution program for convective modelling of discontinuities , 1988 .

[16]  S. G. Rubin,et al.  A diagonally dominant second-order accurate implicit scheme , 1974 .

[17]  J. Zhu.  A low-diffusive and oscillation-free convection scheme , 1991 .

[18]  Michael A. Leschziner,et al.  Discretization of nonlinear convection processes: A broad-range comparison of four schemes , 1985 .

[19]  D. Spalding,et al.  A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows , 1972 .

[20]  C. Rhie,et al.  Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation , 1983 .