On the numerical dissipation of high resolution schemes for hyperbolic conservation laws

Abstract

In recent years, a number of new shock-capturing finite difference schemes, often called high resolution schemes, have been constructed. This paper presents a comparison of these schemes in terms of their numerical dissipation, which becomes very obvious from numerical results obtained for two initial value problems of a two-dimensional advection equation. We consider TVD schemes, which are constructed to prevent the total variation of the numerical approximations from increasing, as well as UNO schemes which only guarantee that the number of local extrema does not increase.