SOME IMPLEMENTATIONAL ISSUES OF CONVECTION SCHEMES FOR FINITE-VOLUME FORMULATIONS

Abstract Two higher-order upwind schemes—second-order upwind and QUICK—are examined in terms of their interpretation, implementations, as well as performance for a recirculating flow in a lid-driven cavity, in the context of a control-volume formulation using the SIMPLE algorithm. The present formulation of these schemes is based on a unified framework wherein the first-order upwind scheme is chosen as the basis, with the remaining terms being assigned to the source term. The performance of these schemes is contrasted with the first-order upwind and second-order central difference schemes. Also addressed in this study is the issue of boundary treatment associated with these higher-order upwind schemes. Two different boundary treatments—one that uses a two-point scheme consistently within a given control volume at the boundary, and the other that maintains consistency of flux across the interior face between the adjacent control volumes—are formulated and evaluated.

[1]  Robert L. Lee,et al.  Don''t suppress the wiggles|they''re telling you something! Computers and Fluids , 1981 .

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

[3]  W. Shyy,et al.  Second-order upwind and central difference schemes for recirculating flow computation , 1992 .

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

[5]  P. Tucker,et al.  MULTIGRID SOLUTION OF UNSTEADY NAVIER-STOKES EQUATIONS USING A PRESSURE METHOD , 1990 .

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

[7]  Toshiyuki Hayase,et al.  A consistently formulated QUICK scheme for fast and stable convergence using finite-volume iterative calculation procedures , 1992 .

[8]  W. Shyy A Note on Assessing Finite Difference Procedures for Large Peclet/Reynolds Number Flow Calculation , 1984 .

[9]  U. Ghia,et al.  High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method , 1982 .

[10]  S. Patankar Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[11]  R. F. Warming,et al.  Upwind Second-Order Difference Schemes and Applications in Aerodynamic Flows , 1976 .

[12]  S. P. Vanka,et al.  Study of second order upwind differencing in a recirculating flow , 1985 .

[13]  B. Launder,et al.  A comparison of hybrid and quadratic-upstream differencing in high Reynolds number elliptic flows , 1981 .

[14]  Wei Shyy,et al.  A study of finite difference approximations to steady-state, convection-dominated flow problems , 1985 .