Abstract: In calculation of multidimensional fluid mechanics problems with numerical schemes that accurately capture contact discontinuity, perturbation near shock wave may increase dramatically. This is called numerical shock instability. In this paper numerical shock instability on shallow water equations is studied. By analyzing linear stability of several numerical schemes, marginal stability of schemes are found having close relation with numerical shock instability. According to eigenvalue analysis, a hybrid method is designed to remedy nonphysical phenomenon by locally modify the original schemes. Numerical experiments show efficiency and robustness of HLLC-HLL hybrid scheme in eliminating shock instability of shallow water equations.

Key words: numerical shock instability, shallow water equations, analysis of linear stability, hybrid method