An efficient direct simulation Monte Carlo method for low Mach number noncontinuum gas flows based on the Bhatnagar-Gross-Krook model

摘要

The direct simulation Monte Carlo (DSMC) method is the preferred approach for simulating rarefied gas flows in complex geometries. However, the standard DSMC method becomes inefficient in the limit M=U < c >-> 0 when the thermal velocity fluctuations which scale with the speed of sound < c > are much larger than characteristic ensemble-averaged flow speed U. In this paper, we propose a modified DSMC algorithm which simulates the linearized Bhatnagar-Gross-Krook (BGK) approximation to the Boltzmann equation. The particles in this method are uniformly distributed in space and have a rest-state, equilibrium Maxwellian velocity distribution. The deviations from the equilibrium state are captured by weightings, indicating that each particle represents a noninteger expectation for finding gas molecules with the simulation particle's velocity in the spatial cell where it is found. The BGK approximation makes the implementation of such a method simple and efficient because the BGK collision rule can be implemented by adjusting particle weightings without the need to create new particles during the simulation. The method can be incorporated into existing DSMC simulation programs with minimal changes. We apply the new algorithm to two test problems-pressure-driven flow through a nanochannel and flow around an isolated sphere. Results obtained with the new method are in excellent agreement with previous theories and simulations.