INFLUENCE OF PENALIZATION AND BOUNDARY TREATMENT ON THE STABILITY AND ACCURACY OF HIGH-ORDER DISCONTINUOUS GALERKIN SCHEMES FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS

Abstract

A high-order interior penalty discontinuous Galerkin method for the compressible Navier–Stokes equations is introduced, which is a modification of the scheme given by Hartmann and Houston. In this paper we investigate the influence of penalization and boundary treatment on accuracy. By observing eigenvalues and condition numbers, a lower bound for the penalization term μ was found, whereas convergence studies depict reasonable upper bounds and a linear dependence on the critical time step size. By investigating conservation properties we demonstrate that different boundary treatments influence the accuracy by several orders of magnitude, and propose reasonable strategies to improve conservation properties.