Practical deviational particle method for variance reduction in polyatomic gas DSMC simulations

TL;DR

This paper introduces a practical deviational particle method combined with the Larsen-Borgnakke model for efficient variance reduction in polyatomic gas DSMC simulations, significantly decreasing statistical errors and computational costs.

Contribution

It extends the deviational particle method to polyatomic gases by integrating the LB model, enabling accurate and efficient simulations with reduced variance.

Findings

Variance reduced to about 5% of DSMC

Effective for a broad range of non-equilibrium flows

Combines LVDSMC with inelastic collision modeling

Abstract

The direct simulation Monte Carlo (DSMC) method is a widely used stochastic particle approach to solving the Boltzmann equation. However, its computational cost remains a major drawback, which can be attributed to statistical errors when handling flows with low Mach numbers. Thus, many studies have focused on variance reduction to reduce the computational cost. One approach is the deviational particle (DP) method, which focuses solely on modeling deviations from the equilibrium state. The DP method has been implemented in the low-variance deviational simulation Monte Carlo (LVDSMC) method, which has proven effective for monatomic gas simulations but faces limitations when extended to polyatomic gases. In this study, we present a practical DP method for polyatomic gas simulations that combines the LVDSMC method with the Larsen-Borgnakke (LB) model, which introduces a group reduction algorithm for the inelastic collision process. Numerical experiments demonstrated that the proposed method efficiently and accurately simulates flows across a relatively broad range of non-equilibrium values. Remarkably, the variance was reduced to about 5% that of the DSMC method.