Distributional Monte Carlo Method with Deterministic Collision Modeling

Abstract

In our previous work, we introduced a new concept for the stochastic simulation of rarefied and nonequilibrium gas flows which we termed Distributional Monte Carlo methods. Whereas traditional Direct Simulation Monte Carlo (DSMC) methods allow each simulated particle to possess only a single velocity vector, the Distributional Monte Carlo method allows each particle’s velocity to be distributed. Intermolecular collisions over a given time step are treated not as a simple binary collision for a particle pair, but rather as a relaxation problem for the joint velocity distribution function of the total number of particles represented by the two simulated particles undergoing a collision. The current approach combines the stochastic collision selection criteria of DSMC with deterministic collision modeling using the Bhatnagar-Gross-Krook approximation. The method was applied to the Bobylev space homogeneous problem and shown to result in a variance reduction of four orders of magnitude over the Nanbu DSMC method. We propose that the development of such methods could substantially improve convergence and result in a significant variance reduction in comparison with DSMC methods.