Multiscale simulation of rarefied polyatomic gas flow via DIG method

TL;DR

This paper introduces a multiscale numerical method that accelerates DSMC simulations for polyatomic gases by coupling stochastic and macroscopic equations, enabling faster convergence across flow regimes.

Contribution

The novel method combines DSMC with synthetic macroscopic equations and adaptive constitutive relations to improve efficiency and applicability in simulating polyatomic gas flows.

Findings

Achieves significant speedup over standard DSMC

Effective across all flow regimes, including near-continuum

Demonstrates asymptotic-preserving properties

Abstract

A novel multiscale numerical method is developed to accelerate direct simulation Monte Carlo (DSMC) simulations for polyatomic gases with internal energy. This approach applies the general synthetic iterative scheme to stochastic simulations, removing the inherent restrictions on spatial grid size in DSMC and boosting the evolution of the particle distribution towards a steady state. Firstly, the proposed method intermittently couples the standard DSMC solver with the solution of steady-state macroscopic synthetic equations derived from the kinetic equation for polyatomic gases. These synthetic equations, encompassing accurate constitutive relations and relaxation rates, ensure applicability across the entire flow regime. Secondly, the particle distribution within the DSMC framework is adjusted to align with the solution of the macroscopic equations, significantly accelerating convergence to the steady-state solution. Finally, an adaptive treatment is implemented for the constitutive relations. Higher-order terms extracted from DSMC are applied only in rarefied regions where the local Knudsen number exceeds a predefined threshold. The fast convergence and asymptotic-preserving properties of the proposed method are demonstrated through several numerical simulations, in which it achieves remarkable speedups compared to standard DSMC, particularly in the near-continuum regime.