Kinetic flux vector splitting for Euler equations

Abstract

This paper is mainly concerned with the development of a class of new upwind methods and a novel treatment of the boundary condition based on the concept of kinetic flux vector splitting (KFVS) for solving inviscid gasdynamic problems. KFVS utilizes the well-known connection that the Euler equations of motion are the moments of the Boltzmann equation whenever the velocity distribution function is a Maxwellian. After presentation of the analysis of the KFVS method in I-D in detail, it is described how KFVS can be performed in a different manner to construct various upwind methods for higher dimensions depending on the situations. Next, it is shown how the KFVS formulation together with the specular reflection model of the kinetic theory of gases at the solid boundary lead to the development of a new treatment of the flow tangency boundary condition which is robust, upwind and conservative and does not require any further assumptions or the use of fictitious grid points. Finally, the present method is tested on a wide variety of problems to demonstrate its capability in obtaining accurate and wiggle-free solutions.