A Navier-Stokes asymptotic preserving Direct Simulation Monte Carlo method for multi-species gas flows

TL;DR

This paper presents a novel asymptotic-preserving Monte Carlo method for multi-species gas flows that accurately captures both continuum and rarefied regimes by decomposing collision operators and preserving Navier-Stokes asymptotics.

Contribution

It introduces a new APMC method that decomposes collision operators into macro and micro parts, achieving second-order accuracy and ease of application to complex multi-species flows.

Findings

Preserves Navier-Stokes asymptotics in fluid limit.

Maintains accuracy in kinetic limit.

Applicable to multi-species flows with complex collisions.

Abstract

This paper introduces a new asymptotic-preserving Monte Carlo (APMC) method for simulating multi-species gas flows. This method decomposes the collision operator of the traditional APMC methods into macro and micro collision parts: the macro collision part corresponds to the first-order Chapman-Enskog (CE) expansion, solved with a second-order scheme; In contrast, the micro collision part represents the reminder of high-order nonequilibrium terms, calculated following the traditional APMC methods. As a result, this new APMC method preserves Navier-Stokes asymptotics and second-order accuracy in the fluid limit, while maintaining the advantage of the traditional APMC methods in the kinetic limit. Therefore, it is suitable for multi-species gas flows that span multiple scales due to superior resolution and accuracy in both continuum and rarefied flow regimes. Moreover, directly constructed based on the DSMC collision solver, this new APMC method circumvents the complexities of modeling and computing kinetic models. This feature makes it easily applicable to multi-species gas flows with intricate collision models and more than two species. Finally, a coupling scheme with DSMC has been developed to extend the applicability of this new APMC method to multi-species gas flows with disparate masses.