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.