Comparison of Relaxation Methods for the Euler Equations.

Abstract

The performance of four relaxation methods for the compressible Euler equations is examined. The Euler equations are cast into the Euler implicit delta form. Four spatial discretization methods, the central difference (CD), total variation diminishing of Yee and Harten (TVD), flux difference splitting of Roe (FDS) and flux vector splitting of Van Leer (FVS), are applied to the spatial derivatives of the right-hand side. Flux splitting Gauss Seidel (FSGS), approximate flux splitting Gauss Seidel (AFSGS-I and AFSGS-II), and lower-upper symmetric Gauss Seidel (LU-SGS) methods are tested for the solution of the implicit equations. Numerical results are presented for a two-dimensional flow about a circular arc bump. Compatibility and efficiency of the numerical solutions are analyzed for all combinations between relaxation methods and spatial discretization methods. Steady-state solutions are independent of the relaxation methods. The AFSGS-II method gives the best efficiency for all spatial discretization methods.