Exponential BGK Integrator for Multi-Scale Particle-Based Kinetic Simulations

TL;DR

This paper introduces an exponential BGK integrator that enhances multi-scale particle-based kinetic simulations by improving accuracy, positivity, and computational efficiency for rarefied gas flows across various regimes.

Contribution

A novel exponential BGK integrator that is compatible with existing Monte Carlo codes, offering improved robustness and efficiency for multi-scale rarefied gas simulations.

Findings

Demonstrates accuracy across a wide range of rarefaction parameters.

Provides a robust and flexible scheme suitable for large-scale simulations.

Achieves more affordable and efficient multi-scale gas flow modeling.

Abstract

Despite the development of an extensive toolbox of multi-scale rarefied flow simulators, such simulations remain challenging due to the significant disparity of collisional and macroscopic spatio-temporal scales. Our study offers a novel and consistent numerical scheme for a coupled treatment of particles advection and collision governed by the BGK evolution, honouring positivity of the velocity distribution. Our method shares its framework, in spirit, with the unified gas kinetic class of multi-scale schemes. Yet it provides attractive features for particle-based stochastic simulations, readily implementable to existing direct simulation Monte-Carlo codes. We demonstrate accuracy and performance of the devised scheme for prototypic gas flows, over a wide-range of rarefaction parameters. Due to the resulting robustness and flexibility of the devised exponential BGK integrator, the scheme paves the way towards more affordable simulations of large- and multi-scale rarefied gas phenomena.