Crank-Nicolson BGK Integrator for Multi-Scale Particle-Based Kinetic Simulations
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912136627748864 |
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| author | Pfeiffer, Marcel Garmirian, Félix Ott, Tobias |
| author_facet | Pfeiffer, Marcel Garmirian, Félix Ott, Tobias |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19076 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Crank-Nicolson BGK Integrator for Multi-Scale Particle-Based Kinetic Simulations Pfeiffer, Marcel Garmirian, Félix Ott, Tobias Fluid Dynamics Computational Physics 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. |
| title | Crank-Nicolson BGK Integrator for Multi-Scale Particle-Based Kinetic Simulations |
| topic | Fluid Dynamics Computational Physics |
| url | https://arxiv.org/abs/2411.19076 |