Calculations of Riemann Problems for 2-D Scalar Conservation Laws by Second Order Accurate MmB Scheme

Abstract

Numerical solutions of Riemann problems for 2-D scalar conservation law are given by a second order accurate MmB (local Meximum-minimum Bounds preserving) scheme which is non-splitting. The numerical computations show that the scheme has high resolution and non-oscillatory properties. The results are completely in accordance with the theoretical solutions and all cases are distinguished efficiently.