A class of high order TVD schemes for systems of conservation laws

Abstract

The purpose of this paper is to develop improved finite difference schemes. We firstly propose to use the fourth order TVD flux presented in [21] as the building block in ENO schemes for scalar problems. A way to extend this scheme and the scheme [20] to general systems of nonlinear hyperbolic conservation laws, in one and two dimensions, is discussed in details. A semi-discrete version of the two schemes are presented. The performance of the schemes is assessed by solving test problems for the Euler equations of gas dynamics in one and two dimensions. We use exact solutions and other results to validate the results.