Discretization Error Estimation Using Error Transport Equation

Abstract

The goal of this paper is to develop a dynamic algorithm that can be used in conjunction with computational fluid dynamics (CFD) simulation codes to quantify the discretization error in a selected process variable. The focus is on fluid dynamics applications where conservation equations are solved for primitive variables using finite difference and/or control volume approach. A transport equation for the error is formulated and solved along with a localized residual estimation based on modified equation concept. Spatiotemporal evolution of the error distribution is mapped and compared to exact error for various cases. A new method is suggested for deriving the modified equation specifically aimed at using it with commercial CFD codes which use finite volume approach.