Repeated Richardson extrapolation to reduce the field discretization error in computational fluid dynamics

Abstract

ABSTRACTThe aim of this study is to extend the use of repeated Richardson extrapolation to one-dimensional (1D) and two-dimensional (2D) fields in computational fluid dynamics (CFD). The following two methods are tested: completed Richardson extrapolation (CRE), a method that has been used previously in the literature, and full Richardson extrapolation (FRE), a new method developed in this study. The Poisson’s, advection–diffusion, Laplace’s, and Burgers’ equations are solved using the finite difference method. The CRE and FRE methods were found to significantly reduce the discretization error of the numerical solutions for all nodes of the grid.