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 sharper than existing fourth-order central schemes when solving profiles with discontinuities. Experiments on nonlinear 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.