Estimating Grid-Induced Errors in CFD by Discrete-Error-Transport Equations

Abstract

This paper presents and evaluates a method for estimating grid-induced errors in CFD solutions that recognizes error at one location in the flow domain may not be generated there, but rather generated elsewhere and then transported there. This paper derives a system of discrete error-transport equations (DETEs) to compute the evolution of grid-induced errors in finite-volume solutions of the Euler equations for compressible flows in two dimensions. The finite-volume method to which the DETEs were derived is one which can be applied to structured or unstructured meshes with cells that can be triangular, rectangular, or other polygons. Results for a test problem involving an oblique shock wave show that if the residuals in the DETEs are modeled accurately, then the DETEs can predict grid-induced errors accurately.