A hybrid particle approach based on the unified stochastic particle Bhatnagar-Gross-Krook and DSMC methods

Abstract

For the simulation of multiscale gas flows, the numerical scheme should be valid and efficient in both rarefied and continuum regimes. For example, the Direct Simulation Monte Carlo (DSMC) method is not appropriate because of its huge computational cost in the continuum regime. Various kinds of hybrid methods with DSMC have been proposed to deal with this difficulty. One of them is the particle-particle hybrid method, which combines DSMC with another stochastic particle method that is based on an approximate kinetic model, such as the BGK-DSMC hybrid method. Since the same kind of computational particles is applied in the stochastic particle BGK (SPBGK) and DSMC methods, they can be implemented in a unified particle framework. Therefore, compared to the CFD-DSMC hybrid method, the BGK-DSMC hybrid method avoids difficulties caused by the amalgamation of two fundamentally different types of solvers. However, the traditional SPBGK method decouples the molecular motions and collisions in analogy to DSMC, and hence its transport properties deviate from physical values as the time step size increases. This defect significantly affects its computational accuracy and efficiency in the continuum regime. In the present paper, instead of the traditional SPBGK method, a unified stochastic particle BGK (USPBGK) method, which has second-order accuracy in time and space, is combined with DSMC. Comparing the computational performance of the USPBGK-DSMC and BGK-DSMC hybrid methods for numerical test cases of hypersonic flows past a cylinder and plume flows out of a planar micronozzle, one note that the proposed USPBGK-DSMC hybrid method can achieve higher efficiency for such multiscale gas flow simulations. In addition, an equilibrium-breakdown criterion based on the ratio of the time scales of the macroscopic flow field and molecule collision is proposed as a switching criterion for the new hybrid method. This criterion depends on the local Knudsen number and is easy to implement in a unified particle framework. © 2020 Elsevier Inc.