Estimating Grid-Induced Errors in Navier-Stokes Solutions by Euler 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. These DETEs are then used to estimate grid-induced errors of Navier-Stokes solutions obtained by using the Fluent code on the basis that error transport is mostly by convection and not by diffusion. Results for a test problem involving compressible low Mach number flow over an iced airfoil show that if the residuals in the DETEs are modeled accurately, then the DETEs can predict grid-induced errors accurately.