On the remedy against shock anomalies in kinetic schemes

Shock-capturing schemes often exhibit anomalous behaviors, such as the carbuncle phenomenon and the post-shock oscillations, especially in the hypersonic flow regime. This paper proposes a simple and effective remedy against these shock instabilities in the case of the kinetic Lax-Wendroff scheme, where the well-known classic scheme is reinforced by means of an equilibrium distribution function of gas molecules. The pathologies are significantly improved to an acceptable level for practical purposes without any considerable side-effect by locally bringing out the robustness of the equilibrium flux method from the kinetic scheme. The remedy is applied only to the preprocessing of the data at cell-edges. The performance of the fortified kinetic scheme is demonstrated in the problem of a hypersonic inviscid or viscous flow past a blunt body. Comparisons are also made with various advanced shock-capturing schemes at present.