ASYMPTOTIC RELAXATION OF MOMENT EQUATIONS FOR A MULTI-SPECIES, HOMOGENEOUS BGK MODEL

Evan Habbershaw; Ryan S. Glasby; Jeffrey R. Haack; Cory D. Hauck; Steven M. Wise

doi:10.1137/23M1596314

ASYMPTOTIC RELAXATION OF MOMENT EQUATIONS FOR A MULTI-SPECIES, HOMOGENEOUS BGK MODEL

Evan Habbershaw, Ryan S. Glasby, Jeffrey R. Haack, Cory D. Hauck, Steven M. Wise

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

Abstract

Multi-species BGK models describe the dynamics of rarefied gases with constituent particles of different elements or compounds with potentially nontrivial velocity distributions. In this paper, moment equations for the bulk velocities, energies, and temperatures of a spatially homogeneous multi-species BGK model are examined. A key challenge in analyzing these equations is the fact that the collision frequencies are allowed to depend on the species temperatures, which allows for more realistic simulations of dilute gas flow. Therefore, a positive lower bound is established for the species temperatures. With this lower bound, a global existence and uniqueness of solutions to the coupled velocity-energy ODE system is established. The lower bound also enables a proof of exponential decay to a unique steady-state solution. Numerical results are presented to demonstrate how the bulk velocities and temperatures relax for large times.

Original language	English
Pages (from-to)	294-313
Number of pages	20
Journal	SIAM Journal on Applied Mathematics
Volume	85
Issue number	1
DOIs	https://doi.org/10.1137/23M1596314
State	Published - 2025

Funding

This work has been authored, in part, by UT-Battelle, LLC, under contract DEAC05-00OR22725, with the U.S. Department of Energy. The U.S. government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for U.S. government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (https://energy.gov/downloads/doe-public-access-plan). This work was supported, in part, 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 89233218CNA000001).

Keywords

kinetic theory
moment equations
multi-species BGK
rarefied gas dynamics

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AB - Multi-species BGK models describe the dynamics of rarefied gases with constituent particles of different elements or compounds with potentially nontrivial velocity distributions. In this paper, moment equations for the bulk velocities, energies, and temperatures of a spatially homogeneous multi-species BGK model are examined. A key challenge in analyzing these equations is the fact that the collision frequencies are allowed to depend on the species temperatures, which allows for more realistic simulations of dilute gas flow. Therefore, a positive lower bound is established for the species temperatures. With this lower bound, a global existence and uniqueness of solutions to the coupled velocity-energy ODE system is established. The lower bound also enables a proof of exponential decay to a unique steady-state solution. Numerical results are presented to demonstrate how the bulk velocities and temperatures relax for large times.

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ASYMPTOTIC RELAXATION OF MOMENT EQUATIONS FOR A MULTI-SPECIES, HOMOGENEOUS BGK MODEL

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