Simple derivation of high-resolution schemes for compressible flows by kinetic approach

The high-resolution scheme for the compressible Navier–Stokes equations developed in Ohwada and Kobayashi [Management of discontinuous reconstruction in kinetic schemes, J. Comput. Phys. 197 (2004) 116–138] is rederived without using any special techniques of kinetic theory. The scheme is simplified and its efficiency is improved by introducing an artificial equilibrium function. High performance of the new scheme is demonstrated in the problems of double-Mach-reflection, forward-facing step, and shock-boundary-layer interaction. The detailed information for easy programming is also given.