Efficiency and stability of the DSBGK method

Recently, the DSBGK method (Note: the original name DS-BGK is changed to DSBGK for simplicity) was proposed to reduce the stochastic noise in simulating rarefied gas flows at low velocity. Its total computational time is almost independent of the magnitude of deviation from equilibrium state. It was verified by the DSMC method in different benchmark problems over a wide range of Kn number. Some simulation results of the closed lid-driven cavity flow, thermal transpiration flow and the open channel flow by the DSBGK method are given here to show its efficiency and numerical stability. In closed problems, the density distribution is subject to unphysical fluctuation due to the absence of density constraint at the boundary. Thus, many simulated molecules are employed by DSBGK simulations to improve the stability and reduce the magnitude of fluctuation. This increases the memory usage remarkably but has small influence to the efficiency of DSBGK simulations. In open problems, the DSBGK simulation remains stable when using about 10 simulated molecules per cell because the fixed number densities at open boundaries eliminate the unphysical fluctuation. Small modification to the CLL reflection model is introduced to further improve the efficiency slightly.