A class of the relaxation schemes for two-dimensional Euler systems of gas dynamics

Abstract

In the computation of approximate solutions to hyperbolic conservation laws, relaxation schemes have proven to be very useful. In this paper we present a new higher order relaxation scheme based on higher order nonoscillatory central space discretization and higher order time discretization without use of Riemann solvers. Numerical experiments with 2D Euler systems of gas dynamics are presented to demonstrate the remarkable accuracy of the relaxation scheme. © 2002 Springer-Verlag Berlin Heidelberg.