The Effect of Grid Skewness on Non-Unified Compact Residual Distribution Methods for Scalar Advection Diffusion Problems

Abstract

In this paper, the newly developed residual distribution (RD) method called the Flux-Difference approach is combined with the Galerkin method to solve the advectiondiffusion equation in separate (non-unified) manner. It is due to the incapability of variation grid skewness in finite volume. This Flux-Difference RD method maintains a compact stencil and the whole process of solving advection-diffusion do not require additional equations. In order to improve the order of accuracy losses by the classic RD schemes, the present scheme will be tested using non-unified manners. The numerical results show that the Flux-Difference RD method preserves second-order accuracy up to about skewness 0.4 but drops to about 1.5 orders accurate when grid skewness is 0.6.