A 3D APPROXIMATE RIEMANN SOLVER FOR THE EULER EQUATIONS USING FLUX SPLITTING SCHEMES WITH A ROBUST MULTIGRID

摘要

An explicit 3D approximate Riemann solver for the Eu-ler equations is proposed using the famous shock capturing schemes with a simple cell vertex based multigrid method. A multistage Runge-Kutta time marching scheme with a local time stepping is used to achieve fast convergence to steady state. A Roe's flux difference splitting, AUSM+, Van Leer and Steger-Warming's flux vector splitting are implemented as base Riemann solvers with a third order flux reconstruction. It is shown that the proposed Riemann solvers accurately capture the shocks as well as reduce CPU time significantly with new multigrid.