A high-order Monte Carlo algorithm for the direct simulation of Boltzmann equation

A high-order algorithm of the direct simulation Monte Carlo (DSMC) method, H-DSMC, has been developed to simulate rarefied flow regimes. The mth order Taylor series expansion has been employed to obtain a more generalized form of the time discretization for the collision part of Boltzmann equation. In the purposed algorithm, the higher order collision terms are introduced as well as higher order terms in the time step of the probabilistic coefficients. These newly implemented higher order terms improve the accuracy and efficiency of the solution and enhance the convergence rate quite significantly. Comparison between results of the classic DSMC method and the H-DSMC method shows the promising performance of the introduced technique.