The artificial compression method for computation of shocks and contact discontinuities. 3: Self-adjusting hybrid schemes

This paper presents a new computational method for the calculation of discontinuous solutions of hyperbolic systems of conservation laws, and in particular contact discontinuities. The method consists of two stages; in the first stage a standard finite difference scheme is hybridized with a nonoscillatory first order method to allow a monotonic transition of discontinuities; in the second stage artificial compression is applied to sharpen transitions of discontinuities. This modification of a standard finite difference method results in a scheme which preserves the order of truncation error of the original method and yet yields a sharp and oscillation free transition of both shocks and contact discontinuities. The modification can be easily implemeted in existing computer codes.