A new fourth-order non-oscillatory central scheme for hyperbolic conservation laws

We propose a new fourth-order non-oscillatory central scheme for computing approximate solutions of hyperbolic conservation laws. A piecewise cubic polynomial is used for the spatial reconstruction and for the numerical derivatives we choose genuinely fourth-order accurate non-oscillatory approximations. The solution is advanced in time using natural continuous extension of Runge–Kutta methods. Numerical tests on both scalar and gas dynamics problems confirm that the new scheme is non-oscillatory and yields sharp results when solving profiles with discontinuities. Experiments on non-linear Burgers' equation indicate that our scheme is superior to existing fourth-order central schemes in the sense that the total variation of the computed solutions are closer to the total variation of the exact solution.