Semi-discrete central-upwind Rankine-Hugoniot schemes for hyperbolic systems of conservation laws

Abstract

We study semi-discrete central-upwind schemes and develop a new technique that allows one to decrease the amount of numerical dissipation present in these schemes without compromising their robustness. The goal is achieved by obtaining more accurate estimates for the one-sided local speeds of propagation using the discrete Rankine-Hugoniot conditions. In the two-dimensional case, these estimates are further enhanced with the help of the numerical dissipation switch mechanism, which is automatically activated near contact discontinuities and shear layers. The resulting central-upwind Rankine-Hugoniot schemes are tested on a number of numerical examples for both the one- and two-dimensional Euler equations of gas dynamics. The obtained results clearly demonstrate the superiority of the proposed method over the existing semi-discrete central-upwind schemes.