High Order Finite Element Discretization of the Compressible Euler and Navier-Stokes Equations

Abstract

We present a high order accurate streamline-upwind/Petrov-Galerkin (SUPG) algorithm for the solution of the compressible Euler and Navier-Stokes equations. The flow equations are written in terms of entropy variables which result in symmetric flux Jacobian matrices and a dimensionally consistent Finite Element discretization. We show that solutions derived from quadratic element approximation are of superior quality next to their linear element counterparts. We demonstrate this through numerical solutions of both classical test cases as well as examples more practical in nature.