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arXiv · 2411.19076

Crank-Nicolson BGK Integrator for Multi-Scale Particle-Based Kinetic Simulations

Marcel Pfeiffer·Félix Garmirian·Tobias Ott
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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.

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Marcel Pfeiffer, Félix Garmirian, Tobias Ott. 2024-11-28. Crank-Nicolson BGK Integrator for Multi-Scale Particle-Based Kinetic Simulations. https://arxiv.org/abs/2411.19076

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