The development of a Riemann solver for the steady supersonic Euler equations

An improved version (HLLC) of the Harten, Lax, van Leer Riemann solver (HLL) for the steady supersonic Euler equations is presented. Unlike the HLL, the HLLC version admits the presence of the slip line in the structure of the solution. This leads to enhanced resolution of computed slip lines by Godunov type methods. We assess the HLLC solver in the context of the first order Godunov method and the second order weighted average flux method (WAF). It is shown that the improvement embodied in the HLLC solver over the HLL solver is virtually equivalent to incorporating the exact Riemann solver.