Convergence test on ensemble-averaged direct simulation Monte Carlo modeling of laser-produced plasma

Abstract

Modeling the expansion of laser-produced plasmas (LPP) is challenging due to their hypersonic expansion rate and large density gradients. The direct simulation Monte Carlo (DSMC) method can be used to model such fluid flow but minimizing the computational error typically requires extremely fine grids for dense flows and ensemble-averaging of multiple runs. However, the computational load is high for small grid sizes and the convergence rate of ensemble-averaged quantities has not been explored yet to the best of our knowledge. Here, we test the statistical convergence of DSMC data by performing 3D monoatomic LPP simulations for multiple trials. Two plume temperatures were considered, corresponding to initial mean free paths that are comparable and much smaller than the grid size. We showed that the average values of the mean free path and kinetic energies only differ to within 5% using only 25 trials. Moreover, simulating a dense LPP using large grid sizes leads to a slower convergence but the error sufficiently reduces with ensemble averaging. This study clarifies the necessary statistical averaging for performing DSMC simulations of unsteady LPP expansion.