A NEW FOURTH ORDER NON-OSCILLATORY SCHEME FOR CONSERVATION LAWS

A new fourth order, semi-discrete, central-upwind scheme for solving systems of hyperbolic conservation laws is introduced. The scheme is a combination of a fourth order non-oscillatory reconstruction, a semi-discrete central-upwind numerical flux, which is simple, universal and efficient. The numerical solution is advanced in time by the three-stage, third-order, TVD Runge-Kutta method. The scheme combines the simplicity of the central schemes and accuracy of the upwind schemes. The advantages of the new scheme are efficiency, it achieves high order accuracy for smooth solutions and produces nonoscillatory profiles for discontinuities and it can be used for problems with non convex fluxes. Numerical experiments which show robustness of the proposed scheme are presented.