A Kinetic theory-based wave / particle flux-splitting scheme for the euler equations

A new upwind scheme, designated the Kinetic Wave / Particle Split (KWPS) scheme, is developed by combining the strengths of two existing schemes to create a new highly efficient and accurate algorithm. Similar to the Kinetic Flux Vector Split (KFVS) scheme, the KWPS scheme is derived from the Boltzmann equation of kinetic theory built on the knowledge that the discretized Euler equations are obtained as moments of the discretized Boltzmann equation when the local velocity distribution is Maxwellian. However, before taking moments in the KWPS formulation, the molecular velocity term is split into convective and thermal velocity components as is done in the Wave / Particle Split (WPS) approach. The resulting KWPS algorithm provides the same accuracy as the baseline KFVS algorithm but is an order of magnitude more efficient.