Crank-Nicolson BGK Integrator for Multi-Scale Particle-Based Kinetic Simulations
Abstract
Solving the Bhatnagar-Gross-Krook (BGK) equation with a stochastic particle approach enables efficient and flexible simulations of flows in the transition regime, between continuum and free molecular flow. However, the usual first-order operator splitting between particle movement and relaxation imposes restrictions on the time step, causing the computational cost to increase with the gas density. The Crank-Nicolson stochastic particle BGK (CN-SPBGK) method is introduced here as an advanced particle-based kinetic solver designed for multi-scale gas flow simulations. This method integrates the BGK equation with second-order accuracy across all Knudsen number regimes without requiring additional parameters, while asymptotically preserving the Navier-Stokes flux in the continuum regime. Comparisons with pre-existing particle BGK methods are conducted on several test cases, with CN-SPBGK demonstrating more consistent convergence and accuracy.
Cite
@article{arxiv.2411.19076,
title = {Crank-Nicolson BGK Integrator for Multi-Scale Particle-Based Kinetic Simulations},
author = {Marcel Pfeiffer and Félix Garmirian and Tobias Ott},
journal= {arXiv preprint arXiv:2411.19076},
year = {2024}
}