MmB schemes on regular triangular meshes for 2-D conservation laws.
| SC 92-17 | Shuli Yang
MmB schemes on regular triangular meshes for 2-D conservation laws. | |
Abstract: 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.
Keywords: MmB schemes,
2-D,
conservation laws,
gas dynamics systems,
Runge-Kutta-FVM,
Taylor-FVM