On DSMC Calculations of Rarefied Gas Flows with Small Number of Particles in Cells

The direct simulation Monte Carlo (DSMC) analysis of two- and three-dimensional rarefied gas flows requires computational resources of very large proportions. One of the major causes for this is that, along with the multidimensional computational mesh, the standard DSMC approach also requires a large number of particles in each cell of the mesh in order to obtain sufficiently accurate results. This paper presents the development and validation of a modified simulation procedure which allows more accurate calculations with a smaller mean number of particles ($\langle N\rangle\sim1$) in the grid cells. In the new algorithm, the standard DSMC collision scheme is replaced by a two-step collision procedure based on “Bernoulli trials” scheme (or its simplified version proposed by the author), which is applied twice to the cells (or subcells) of a dual grid within a time step. The modified algorithm uses a symmetric Strang splitting scheme that improves the accuracy of the splitting scheme to $O(\tau^2)$ with respect to the time step $\tau$, making the modified DSMC method an effective numerical tool for both steady and unsteady gas flow calculations on fine multidimensional grids. The latter is particularly important for simulation of vortical and unstable rarefied gas flows. The modified simulation scheme might also be useful for DSMC calculations within the subcell areas of a multilevel computational grid.