DSMC: Fast direct simulation Monte Carlo solver for the Boltzmann equation by Multi-Chain Markov Chain and multicore programming

Abstract

Direct Simulation Monte Carlo (DSMC) solves the Boltzmann equation with large Knudsen number. The Boltzmann equation generally consists of three terms: the force term, the diffusion term and the collision term. While the first two terms of the Boltzmann equation can be discretized by numerical methods such as the finite volume method, the third term can be approximated by DSMC, and DSMC simulates the physical behaviors of gas molecules. However, because of the low sampling efficiency of Monte Carlo Simulation in DSMC, this part usually occupies large portion of computational costs to solve the Boltzmann equation. In this paper, by Markov Chain Monte Carlo (MCMC) and multicore programming, we develop Direct Simulation Multi-Chain Markov Chain Monte Carlo (DSMC3): a fast solver to calculate the numerical solution for the Boltzmann equation. Computational results show that DSMC3 is significantly faster than the conventional method DSMC.