A class of high order TVD schemes for systems of conservation laws (Q2456039)

Summary: The purpose of this paper is to develop improved finite difference schemes. We firstly propose to use the fourth order total variation diminishing (TVD) flux presented by the author [Fourth order TVD scheme for hyperbolic conservation laws, J. Numerical Algorithm (submitted)] as the building block in essentially non-oscillatory schemes for scalar problems. A way to extend this scheme and the author's scheme [C. R. Accad. Bulg. Sci. 58, No. 8, 879--888 (2005; Zbl 1085.65085)] to general systems of nonlinear hyperbolic conservation laws, in one and two dimensions, is discussed in details. Semi-discrete versions 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.