An evaluation of eight discretization schemes for two‐dimensional convection‐diffusion equations

Abstract

AbstractA comparative study of eight discretization schemes for the equations describing convection‐diffusion transport phenomena is presented. The (differencing) schemes considered are the conventional central, upwind and hybrid difference schemes,1,2 together with the quadratic upstream,3,4 quadratic upstream extended4 and quadratic upstream extended revised difference4 schemes. Also tested are the so called locally exact difference scheme5 and the power difference scheme.6 In multi‐dimensional problems errors arise from ‘false diffusion’ and function approximations. It is asserted that false diffusion is essentially a multi‐dimensional source of error. Hence errors associated with false diffusion may be investigated only via two‐ and three‐dimensional problems. The above schemes have been tested for both one‐ and two‐dimensional flows with sources, to distinguish between ‘discretization’ errors and ‘false diffusion’ errors.7 The one‐dimensional study is reported in Reference 7. For 2D flows, the quadratic upstream difference schemes are shown to be superior in accuracy to the others at all Peclet numbers, for the test cases considered. The stability of the schemes and their CPU time requirements are also discussed.