Variance reduction for FokkerPlanck based particle Monte Carlo schemes
Recently, FokkerPlanck based particle Monte Carlo schemes have been proposed and evaluated for simulations of rarefied gas flows [1], [2]and[3]. In this paper, the variance reduction for particle Monte Carlo simulations based on the FokkerPlanck model is considered. First, deviational based schemes were derived and reviewed, and it is shown that these deviational methods are not appropriate for practical FokkerPlanck based rarefied gas flow simulations. This is due to the fact that the deviational schemes considered in this study lead either to instabilities in the case of two-weight methods or to large statistical errors if the direct sampling method is applied. Motivated by this conclusion, we developed a novel scheme based on correlated stochastic processes. The main idea here is to synthesize an additional stochastic process with a known solution, which is simultaneously solved together with the main one. By correlating the two processes, the statistical errors can dramatically be reduced; especially for low Mach numbers. To assess the methods, homogeneous relaxation, planar Couette and lid-driven cavity flows were considered. For these test cases, it could be demonstrated that variance reduction based on parallel processes is very robust and effective.
variance reduction rarefied gas flow fokkerplanck equation dsmc