A conservative flux‐splitting method for steady shock capturing

Abstract

AbstractA novel flux‐splitting method that can preserve the flux conservation properties for the steady shock waves is proposed in present paper. The proposed method is based on the total variation diminishing (TVD) scheme, and the dissipative flux term is constructed by the flux directly instead of conservative variables. Similar transformations are imposed on the anti‐dissipation term, which is formulated by utilizing the limiter function. Numerical experiments were performed on the one, quasi one‐ and two‐dimensional shock wave problems. The computed results show that, the steady shock waves can be accurately captured within two grid points by the proposed conservative flux‐splitting (CFS) method, and numerical oscillations are successfully eliminated near the flow discontinuities. The conservation and accuracy of present method are demonstrated by comparisons with the TVD, flux vector splitting and flux difference splitting methods.