Peculiar velocity based upwind method for inviscid compressible flows

Abstract

A new upwind Boltzmann scheme termed Peculiar Velocity based Upwind (PVU) method is developed for solving Euler equations. Upwinding is done based on peculiar velocity of Kinetic Theory of Gases. This new method is more efficient and physically more meaningful than its predecessor, the Kinetic Flux Vector Splitting (KFVS) method. The PVU method is applied to some standard test problems. The results demonstrate the soundness of the new idea.

The motivation for this work came from the idea of improving the Kinetic Flux Vector Splitting (KFVS) method [1] which was demonstrated to be very robust by its application to a wide variety of 2-D and 3-D problems using structured and unstructured meshes [2,3,4,5]. In the KFVS method upwinding is done based on whether molecular velocity is greater or less than zero. Here, a new upwind Boltzmann scheme, in which upwinding is done based on peculiar velocity, which is the relative velocity of the molecule with respect to the fluid, is presented. The upwind method for Euler equations is obtained by taking moments of the upwind scheme applied to the Boltzmann equation of Kinetic Theory of Gases.