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Volume 16, Issue 3
A Novel Construction of Distribution Function Through Second-Order Polynomial Approximation in Terms of Particle Mass, Momentum and Energy

Z. Y. Yuan, Z. Chen, C. Shu, Y. Y. Liu & Z. L. Zhang

Adv. Appl. Math. Mech., 16 (2024), pp. 738-770.

Published online: 2024-02

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  • Abstract

In this paper, we propose a new way to construct the distribution function through the second-order polynomial approximation in terms of particle mass, momentum and energy. The new construction holds three distinguished features. First, the formulations are more concise as compared with the third-order truncated Hermite polynomial expansion which yields Grad’s 13-moment distribution function; Second, all moments of the present distribution function are determined from conservation laws; Third, these moments are closely linked to the most desirable variables, such as mass, momentum and energy. Then, this new distribution function is applied to construct a new gas kinetic flux solver. Numerical validations show that the proposed method recovers the Navier-Stokes solutions in the continuum regime. In addition, it outperforms Grad’s 13-moment distribution function in the transition regime, especially in the prediction of temperature and heat flux.

  • AMS Subject Headings

82C40

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COPYRIGHT: © Global Science Press

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@Article{AAMM-16-738, author = {Yuan , Z. Y.Chen , Z.Shu , C.Liu , Y. Y. and Zhang , Z. L.}, title = {A Novel Construction of Distribution Function Through Second-Order Polynomial Approximation in Terms of Particle Mass, Momentum and Energy}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2024}, volume = {16}, number = {3}, pages = {738--770}, abstract = {

In this paper, we propose a new way to construct the distribution function through the second-order polynomial approximation in terms of particle mass, momentum and energy. The new construction holds three distinguished features. First, the formulations are more concise as compared with the third-order truncated Hermite polynomial expansion which yields Grad’s 13-moment distribution function; Second, all moments of the present distribution function are determined from conservation laws; Third, these moments are closely linked to the most desirable variables, such as mass, momentum and energy. Then, this new distribution function is applied to construct a new gas kinetic flux solver. Numerical validations show that the proposed method recovers the Navier-Stokes solutions in the continuum regime. In addition, it outperforms Grad’s 13-moment distribution function in the transition regime, especially in the prediction of temperature and heat flux.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2023-0107}, url = {http://global-sci.org/intro/article_detail/aamm/22936.html} }
TY - JOUR T1 - A Novel Construction of Distribution Function Through Second-Order Polynomial Approximation in Terms of Particle Mass, Momentum and Energy AU - Yuan , Z. Y. AU - Chen , Z. AU - Shu , C. AU - Liu , Y. Y. AU - Zhang , Z. L. JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 738 EP - 770 PY - 2024 DA - 2024/02 SN - 16 DO - http://doi.org/10.4208/aamm.OA-2023-0107 UR - https://global-sci.org/intro/article_detail/aamm/22936.html KW - Second-order truncated expansion, peculiar velocity space, compatibility conditions and moment relationships, gas kinetic flux solver, continuum regime to rarefied regime. AB -

In this paper, we propose a new way to construct the distribution function through the second-order polynomial approximation in terms of particle mass, momentum and energy. The new construction holds three distinguished features. First, the formulations are more concise as compared with the third-order truncated Hermite polynomial expansion which yields Grad’s 13-moment distribution function; Second, all moments of the present distribution function are determined from conservation laws; Third, these moments are closely linked to the most desirable variables, such as mass, momentum and energy. Then, this new distribution function is applied to construct a new gas kinetic flux solver. Numerical validations show that the proposed method recovers the Navier-Stokes solutions in the continuum regime. In addition, it outperforms Grad’s 13-moment distribution function in the transition regime, especially in the prediction of temperature and heat flux.

Yuan , Z. Y.Chen , Z.Shu , C.Liu , Y. Y. and Zhang , Z. L.. (2024). A Novel Construction of Distribution Function Through Second-Order Polynomial Approximation in Terms of Particle Mass, Momentum and Energy. Advances in Applied Mathematics and Mechanics. 16 (3). 738-770. doi:10.4208/aamm.OA-2023-0107
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