A dual graph-norm refinement indicator for finite volume approximations of the Euler equations

Abstract

We generalise and apply a refinement indicator of the type originally designed by Mackenzie, Suli and Warnecke in [15] and [16] for linear Friedrichs systems to the Euler equations of inviscid, compressible fluid flow. The Euler equations are symmetrized by means of entropy variables and locally linearized about a constant state to obtain a symmetric hyperbolic system to which an a posteriori error analysis of the type introduced in [15] can be applied. We discuss the details of the implementation of the refinement indicator into the DLR-\(\tau\)-Code which is based on a finite volume method of box type on an unstructured grid and present numerical results.