Non-oscillatory central-upwind scheme for hyperbolic conservation laws

Abstract

We introduce a new fourth order, semi-discrete, central-upwind scheme for solving systems of hyperbolic conservation laws. The scheme is a combination of a fourth order non-oscillatory reconstruction, a semi-discrete central-upwind numerical flux and the third order TVD Runge-Kutta method. Numerical results suggest that the new scheme achieves a uniformly high order accuracy for smooth solutions and produces non-oscillatory profiles for discontinuities. This is especially so for long time evolution problems. The scheme combines the simplicity of the central schemes and accuracy of the upwind schemes. The advantages of the new scheme will be fully realized when solving various examples.

Keywords:

• Central scheme
• Upwind scheme
• Runge-Kutta methods
• Non-oscillatory schemes
• Conservation laws
• Semi-discrete schemes
• Euler equations