Abstract
We derive a multi-species BGK model with velocity-dependent collision frequency for a non-reactive, multi-component gas mixture. The model is derived by minimizing a weighted entropy under the constraint that the number of particles of each species, total momentum, and total energy are conserved. We prove that this minimization problem admits a unique solution for very general collision frequencies. Moreover, we prove that the model satisfies an H-Theorem and characterize the form of equilibrium.
| Original language | English |
|---|---|
| Article number | 31 |
| Journal | Journal of Statistical Physics |
| Volume | 184 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 2021 |
Funding
Marlies Pirner is supported from the Humboldt foundation and from the Austrian Science Fund (FWF) through grant number F65. The work of Cory Hauck is sponsored by the Office of Advanced Scientific Computing Research, U.S. Department of Energy, and performed at the Oak Ridge National Laboratory, which is managed by UT-Battelle, LLC under Contract No. De-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan ( http://energy.gov/downloads/doe-public-access-plan ). The work of Jeff Haack was supported by the US Department of Energy through the Los Alamos National Laboratory. Los Alamos National Laboratory is operated by Triad National Security, LLC, for the National Nuclear Security Administration of U.S. Department of Energy (Contract No. 89233218CNA000001). Los Alamos Report LA-UR-20-21464. Christian Klingenberg acknowledges a grant by the Bayrische Forschungsallianz. Christian Klingenberg acknowledges a grant by the Bayrische Forschungsallianz. Marlies Pirner is supported from the Humboldt foundation and from the Austrian Science Fund (FWF) through grant number F65. The work of Jeff Haack was supported by the US Department of Energy through the Los Alamos National Laboratory. Los Alamos National Laboratory is operated by Triad National Security, LLC, for the National Nuclear Security Administration of U.S. Department of Energy (Contract No. 89233218CNA000001). Los Alamos Report LA-UR-20-21464. The work of Cory Hauck is sponsored by the Office of Advanced Scientific Computing Research, U.S. Department of Energy, and performed at the Oak Ridge National Laboratory, which is managed by UT-Battelle, LLC under Contract No. De-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).
Keywords
- BGK approximation
- Entropy minimization
- Kinetic model
- Multi-fluid mixture
- Plasma physics
- Velocity-dependent collision frequency