Development of a Particle-Particle Hybrid Scheme based on ESBGK and DSMC Methods to Simulate Multi-scale Transitional Flows

Abstract

In the present work, we have developed a new particle-particle hybrid method that consists of the statistical ESBGK and DSMC method. The switching criterion between two methods is not based on macroscopic gradients, as was previously used by many other researchers. Instead, in this work, a switching criterion has been developed based on the deviation of the velocity distribution function from Maxwellian, and is based on the Kolmogorov-Smirnov (K-S) statistical test. The selection of a particular particle method in each cell in the computational domain is based on the local K-S parameter value with respect to a pre-set global switching criterion. A numerically efficient technique to compute the K-S parameter is developed from which the degree of non-equilibrium can be calculated for the whole computational domain. Two well known fluid flow problems, expanding argon flow through a nozzle and a hypersonic flow over a blunt body, have been studied. The K-S parameter is shown to demarcate the regions of non-equilibrium from the near-equilibrium regions, and the solutions obtained by the hybrid method are shown to agree well with the benchmark DSMC solutions for both of the case studies. The newly developed hybrid method is also shown to be numerically more efficient than either of the component methods.