Numerical schemes for a multi-species BGK model with velocity-dependent collision frequency

Jeffrey Haack; Cory D. Hauck; Christian F. Klingenberg; Marlies Pirner; Sandra Warnecke

doi:10.1016/j.jcp.2022.111729

Numerical schemes for a multi-species BGK model with velocity-dependent collision frequency

Jeffrey Haack, Cory D. Hauck, Christian F. Klingenberg, Marlies Pirner, Sandra Warnecke

Multiscale Methods

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We consider a kinetic description of multi-species gas mixture modeled with Bhatnagar-Gross-Krook (BGK) collision operators, in which the collision frequency varies not only in time and space but also with the microscopic velocity. In this model, the Maxwellians typically used in standard BGK operators are replaced by a generalization of such target functions, which are defined by a variational procedure [20]. In this paper we present a numerical method for simulating this model, which uses an Implicit-Explicit (IMEX) scheme to minimize a certain potential function, mimicking the Lagrange functional that appears in the theoretical derivation. We show that theoretical properties such as conservation of mass, total momentum and total energy as well as positivity of the distribution functions are preserved by the numerical method, and illustrate its usefulness and effectiveness with numerical examples.

Original language	English
Article number	111729
Journal	Journal of Computational Physics
Volume	473
DOIs	https://doi.org/10.1016/j.jcp.2022.111729
State	Published - Jan 15 2023

Funding

We thank Bruno Després and Michael Murillo for helpful discussions. We acknowledge support for covering travel costs for Christian Klingenberg and Sandra Warnecke by the Bayerische Forschungsallianz (grant no. BaylntAn UWUE 2019-29). The work of Jeff Haack was supported by the U.S. 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). LA-UR-22-20147. 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). Marlies Pirner was supported by the Alexander von Humboldt Foundation (grant AvH F.-L.) and the German Science Foundation DFG (grant no. PI 1501/2-1). We acknowledge support for covering travel costs for Christian Klingenberg and Sandra Warnecke by the Bayerische Forschungsallianz (grant no. BaylntAn UWUE 2019-29 ). Marlies Pirner was supported by the Alexander von Humboldt Foundation (grant AvH F.-L. ) and the German Science Foundation DFG (grant no. PI 1501/2-1 ). 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 U.S. 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 ). LA-UR-22-20147 .

Funders	Funder number
DOE Public Access Plan
German Science Foundation DFG	PI 1501/2-1
United States Government
U.S. Department of Energy
Alexander von Humboldt-Stiftung	AvH F.-L
National Nuclear Security Administration	89233218CNA000001, LA-UR-22-20147
Advanced Scientific Computing Research	De-AC05-00OR22725
Los Alamos National Laboratory
Bayerische Forschungsallianz	BaylntAn UWUE 2019-29

Keywords

BGK model
Entropy minimization
Kinetic model
Multi-fluid mixture
Plasma physics
Velocity-dependent collision frequency

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10.1016/j.jcp.2022.111729

Cite this

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title = "Numerical schemes for a multi-species BGK model with velocity-dependent collision frequency",

abstract = "We consider a kinetic description of multi-species gas mixture modeled with Bhatnagar-Gross-Krook (BGK) collision operators, in which the collision frequency varies not only in time and space but also with the microscopic velocity. In this model, the Maxwellians typically used in standard BGK operators are replaced by a generalization of such target functions, which are defined by a variational procedure [20]. In this paper we present a numerical method for simulating this model, which uses an Implicit-Explicit (IMEX) scheme to minimize a certain potential function, mimicking the Lagrange functional that appears in the theoretical derivation. We show that theoretical properties such as conservation of mass, total momentum and total energy as well as positivity of the distribution functions are preserved by the numerical method, and illustrate its usefulness and effectiveness with numerical examples.",

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AU - Haack, Jeffrey

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AU - Warnecke, Sandra

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AB - We consider a kinetic description of multi-species gas mixture modeled with Bhatnagar-Gross-Krook (BGK) collision operators, in which the collision frequency varies not only in time and space but also with the microscopic velocity. In this model, the Maxwellians typically used in standard BGK operators are replaced by a generalization of such target functions, which are defined by a variational procedure [20]. In this paper we present a numerical method for simulating this model, which uses an Implicit-Explicit (IMEX) scheme to minimize a certain potential function, mimicking the Lagrange functional that appears in the theoretical derivation. We show that theoretical properties such as conservation of mass, total momentum and total energy as well as positivity of the distribution functions are preserved by the numerical method, and illustrate its usefulness and effectiveness with numerical examples.

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Numerical schemes for a multi-species BGK model with velocity-dependent collision frequency

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