IMPROVED FINITE-DIFFERENCE SCHEME FOR THE SOLUTION OF CONVECTION-DIFFUSION PROBLEMS WITH THE SIMPLEN ALGORITHM

Abstract

An improved version of the differencing scheme used in the simplen algorithm is presented. In the original scheme, source terms are upwinded in the modeled equations. This approach is extended here by application of upwinding to the terms representing cross-stream fluxes in addition to the upwinding of the source terms. The method is then applied to three case studies involving two-dimensional, incompressible, laminar flow. Excellent agreement between these numerical solutions and the corresponding analytical/benchmark solutions is achieved. The new method is shown to be superior in accuracy compared to the original method.