Dissipation Additions to Flux-Difference Splitting

Abstract

Although the flux-difference splitting methods for solving the Euler equations are generally very robust and no explicit dissipation is required. There are situations where explicit dissipation is needed. Two cases, a slowly moving shock problem and a blunt body calculation, are discussed in this paper. The slowly moving shock problem is tested extensively by Roe's Riemann solver and a cure for Roe's Riemann solver is proposed. For the second-order scheme it is found necessary to reduce the second-order accuracy to first-order accuracy inside the shock layer. For the supersonic blunt body calculation adding dissipation in the linear waves in Roe's Riemann solver can prevent numerical instability in the subsonic pocket. The drawback of Yee's formula to cure the instability when used on viscous flow calculation is demonstrated. A better solution based on the pressure gradient is proposed.