  The stochastic particle method based on Bhatnagar-Gross-Krook (BGK) or
ellipsoidal statistical BGK (ESBGK) model approximates the pairwise collisions
in the Boltzmann equation using a relaxation process. Therefore, it is more
efficient to simulate gas flows at small Knudsen numbers than the counterparts
based on the original Boltzmann equation, such as the Direct Simulation Monte
Carlo (DSMC) method. However, the traditional stochastic particle BGK method
decouples the molecular motions and collisions in analogy to the DSMC method,
and hence its transport properties deviate from physical values as the time
step increases. This defect significantly affects its computational accuracy
and efficiency for the simulation of multiscale flows, especially when the
transport processes in the continuum regime is important. In the present paper,
we propose a unified stochastic particle ESBGK (USP-ESBGK) method by combining
the molecular convection and collision effects. In the continuum regime, the
proposed method can be applied using large temporal-spatial discretization and
approaches to the Navier-Stokes solutions accurately. Furthermore, it is
capable to simulate both the small scale non-equilibrium flows and large scale
continuum flows within a unified framework efficiently and accurately. The
applications of USP-ESBGK method to a variety of benchmark problems, including
Couette flow, thermal Couette flow, Poiseuille flow, Sod tube flow, cavity
flow, and flow through a slit, demonstrated that it is a promising tool to
simulate multiscale gas flows ranging from rarefied to continuum regime.
