A composite semi-conservative scheme for hyperbolic conservation laws (Q846433)

The author uses a non-conservative form of conservation laws to construct a semi-conservative scheme which becomes conservative in the neighborhood of a discontinuity. The proposed scheme captures the shock with high accuracy but yields rarefaction shocks in the presence of a sonic point. A simple criterion is proposed to utilize the idea of the composite scheme to avoid such unphysical solution. As it is numerically demonstrated in the paper, the proposed composite scheme gives a good result when applied to various convex, or convex-concave scalar test problems.