Volume 30, Issue 5
On the Five-Moment Maximum Entropy System of One-Dimensional Boltzmann Equation

Weiming Li, Yuwei Fan & Lingchao Zheng

Commun. Comput. Phys., 30 (2021), pp. 1390-1426.

Published online: 2021-10

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  • Abstract

The maximum entropy moment system extends the Euler equation to nonequilibrium gas flows by considering higher order moments such as the heat flux. This paper presents a systematic study of the maximum entropy moment system of Boltzmann equation. We consider a hypothetical one-dimensional gas and study a five-moment model. A numerical algorithm for solving the optimization problem is developed to produce the maximum entropy distribution function from known moments, and the asymptotic behaviour of the system around the singular region known as the Junk’s line, as well as that near the boundary of the realizability domain is analyzed. Furthermore, we study the properties of the system numerically, including the behaviour of the system around the Maxwellian and within the interior of the realizability domain, and properties of its characteristic fields. Our studies show the higher order entropy-based moment models to differ significantly from the Euler equations. Much of this difference comes from the singularity near the Junk’s line, which would be removed if a truncation of the velocity domain is employed.

  • Keywords

Maximum entropy method, five-moment system, characteristic structure, Boltzmann equation.

  • AMS Subject Headings

76P05, 82B40, 82D05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-30-1390, author = {Li , Weiming and Fan , Yuwei and Zheng , Lingchao}, title = {On the Five-Moment Maximum Entropy System of One-Dimensional Boltzmann Equation}, journal = {Communications in Computational Physics}, year = {2021}, volume = {30}, number = {5}, pages = {1390--1426}, abstract = {

The maximum entropy moment system extends the Euler equation to nonequilibrium gas flows by considering higher order moments such as the heat flux. This paper presents a systematic study of the maximum entropy moment system of Boltzmann equation. We consider a hypothetical one-dimensional gas and study a five-moment model. A numerical algorithm for solving the optimization problem is developed to produce the maximum entropy distribution function from known moments, and the asymptotic behaviour of the system around the singular region known as the Junk’s line, as well as that near the boundary of the realizability domain is analyzed. Furthermore, we study the properties of the system numerically, including the behaviour of the system around the Maxwellian and within the interior of the realizability domain, and properties of its characteristic fields. Our studies show the higher order entropy-based moment models to differ significantly from the Euler equations. Much of this difference comes from the singularity near the Junk’s line, which would be removed if a truncation of the velocity domain is employed.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0236}, url = {http://global-sci.org/intro/article_detail/cicp/19934.html} }
TY - JOUR T1 - On the Five-Moment Maximum Entropy System of One-Dimensional Boltzmann Equation AU - Li , Weiming AU - Fan , Yuwei AU - Zheng , Lingchao JO - Communications in Computational Physics VL - 5 SP - 1390 EP - 1426 PY - 2021 DA - 2021/10 SN - 30 DO - http://doi.org/10.4208/cicp.OA-2020-0236 UR - https://global-sci.org/intro/article_detail/cicp/19934.html KW - Maximum entropy method, five-moment system, characteristic structure, Boltzmann equation. AB -

The maximum entropy moment system extends the Euler equation to nonequilibrium gas flows by considering higher order moments such as the heat flux. This paper presents a systematic study of the maximum entropy moment system of Boltzmann equation. We consider a hypothetical one-dimensional gas and study a five-moment model. A numerical algorithm for solving the optimization problem is developed to produce the maximum entropy distribution function from known moments, and the asymptotic behaviour of the system around the singular region known as the Junk’s line, as well as that near the boundary of the realizability domain is analyzed. Furthermore, we study the properties of the system numerically, including the behaviour of the system around the Maxwellian and within the interior of the realizability domain, and properties of its characteristic fields. Our studies show the higher order entropy-based moment models to differ significantly from the Euler equations. Much of this difference comes from the singularity near the Junk’s line, which would be removed if a truncation of the velocity domain is employed.

Weiming Li, Yuwei Fan & Lingchao Zheng. (2021). On the Five-Moment Maximum Entropy System of One-Dimensional Boltzmann Equation. Communications in Computational Physics. 30 (5). 1390-1426. doi:10.4208/cicp.OA-2020-0236
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