Open Access

Shuli Yang

• In this paper, two classes of second order accurate high resolution schemes are presented on regular triangular meshes for initial value problem of two dimensional conservation laws. The first class are called Runge-Kutta-FVM MmB (locally Maximum- minimum Bounds preserving) schemes, which are first discretized by (FVM) finite volume method in space direction and modifying numerical fluxes, and then by Runge-Kutta methods in time direction; The second class, constructed by Taylor expansion in time, and then by FVM methods and making modifications to fluxes, are called Taylor- FVM MmB schemes. MmB properties of both schemes are proved for 2-D scalar conservation law. Numerical results are given for Riemann problems of 2-D scalar conservation law and 2-D gas dynamics systems and some comparisons are made between the two classes of the schemes. Key words and phrases: MmB schemes, 2-D, conservation laws, gas dynamics systems, Runge-Kutta-FVM, Taylor-FVM.