Improved shock-capturing of Jameson's scheme for the Euler equations

Abstract

It is known that Jameson's scheme is a pseudo-second-order-accurate scheme for solving discrete conservation laws. The scheme contains a non-linear artificial dissipative flux which is designed to capture shocks. In this paper, it is shown that the, shock-capturing of Jameson's scheme for the Euler equations can be improved by replacing the Lax-Friedrichs' type of dissipative flux with Roe's dissipative flux. This replacement is at a moderate expense of the calculation time