Shock capturing scheme based on two-shock approximation to Riemann problem

Riemann problem is a building block of modern high resolution shock capturing schemes. The exact solution of Riemann problem can not be written in close form. Certain iteration procedures are needed to get the explicit solution. Therefore, numerical schemes based on exact Riemann solver are computationally very expensive. In order to improve the computational efficiency, a shock capturing scheme to the original Riemann problem is proposed based on the two shock approximation procedure. In the scheme, all waves in the structure of Riemann problem solution are treated as shock waves. This method keeps non linear feature for Riemann problem, and the entropy does not decrease. Numerical tests indicate that the proposed scheme is efficient and of high resolution to shocks and contact discontinuities.