Development of a Particle–Particle Hybrid Scheme to Simulate Multiscale Transitional Flows

Abstract

In the present work, a new particle–particle hybrid method that combines the statistical ellipsoidal-statistical Bhatnagar–Gross–Krook and direct simulation Monte Carlo methods is developed. The switching criterion between the two methods is based on the deviation of the cumulative velocity distribution function from Maxwellian as measured by the Kolmogorov–Smirnov statistical test. Unlike other hybrid approaches that use switching criteria based on macroscopic properties, the selection of a particular particle method in a cell is determined by the local Kolmogorov–Smirnov parameter value with respect to a preset global switching criterion. A numerically efficient technique to compute the Kolmogorov–Smirnov parameter was developed to enable the efficient calculation of the degree of nonequilibrium. Two well-known fluid-flow problems, expanding argon flow through a nozzle and hypersonic flow over a blunt body, were studied. The Kolmogorov–Smirnov parameter is shown to demarcate the regions of nonequilibrium from the near-equilibrium regions, and the solutions obtained by the hybrid method are shown to agree well with the benchmark direct simulation Monte Carlo solutions for both case studies. The newly developed hybrid method is also shown to be numerically more efficient than either of the component methods.