On the Five-Moment Maximum Entropy System of One-Dimensional Boltzmann Equation

On the Five-Moment Maximum Entropy System of One-Dimensional Boltzmann Equation

Year:    2021

Author:    Weiming Li, Yuwei Fan, Lingchao Zheng

Communications in Computational Physics, Vol. 30 (2021), Iss. 5 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2020-0236

Communications in Computational Physics, Vol. 30 (2021), Iss. 5 : pp. 1390–1426

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    37

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

Author Details

Weiming Li

Yuwei Fan

Lingchao Zheng