FULLY DISCRETE HIGH-RESOLUTION SCHEMES FOR HYPERBOLIC CONSERVATION LAWS

The present paper is a sequel to two previous papers in which rigorous, up to fourth-order, fully discrete (FD) upwind TVD schemes have been presented. In this paper we discuss in detail the extension of these schemes to solutions of non-linear hyperbolic systems. The performance of the schemes is assessed by solving test problems for the time-dependent Euler equations of gas dynamics in one and two space dimensions. We use exact solutions and experimental data to validate the results.