Review of computing methods for recirculating flows

Abstract

A review is presented of the many different finite difference and finite element methods (FDM and FEM) for computing recirculating flows as exemplified by the cavity flow problem. The various methods are categorized according to whether a single integrated system or two segregated, coupled systems are obtained. The integrated schemes appear to be simplest and most efficient, mainly because they satisfy the incompressibility constraint directly in the mean and because the Newton-Raphson method can be used with them. In some cases, the FEM appears to be the most accurate and stable for the same number of unknowns. The method of upwind differencing introduces serious errors in the form of false diffusion which can only be diminished by extreme refinement of mesh sizes. This has to be checked carefully by convergence studies.