phmathВестник Государственного университета просвещения. Серия: Физика-МатематикаBulletin of Federal State University of Education. Series: Physics and Mathematics2949-50832949-5067Federal State University of Education10.18384/2949-5067-2025-4-150phmath-732Research ArticleФИЗИКАPHYSICSМакроскопические газодинамические приближения локальной неравновесной функции распределения молекул по скоростямMacroscopic Gas-Dynamic Approximations of the Local Nonequilibrium Molecular Velocity Distribution Functionhttps://orcid.org/0000-0001-8529-5300ТимохинМ. Ю.TimokhinM.

Максим Юрьевич Тимохин, кандидат физико-математических наук, старший научный сотрудник

физический факультет

Москва; Новосибирск

Maksim Yu. Timokhin, Cand. Sci. (Phys.-Math.), Senior Researcher

Faculty of Physics

Moscow; Novosibirsk

timokhin@physics.msu.ruhttps://orcid.org/0000-0002-9439-6573БондарьЕ. А.BondarYe.

Евгений Александрович Бондарь, кандидат физико-математическихнаук, заместитель директора по научной работе, старший научный сотрудник

физический факультет

Москва; Новосибирск

Yevgeniy A. Bondar, Cand. Sci. (Phys.-Math.), Deputy Director for Research, Senior Researcher

Faculty of Physics

Moscow; Novosibirsk

bond@itam.nsc.ruМосковский государственный университет имени М. В. Ломоносова; Институт теоретической и прикладной механики им. С. А. Христиановича Сибирского отделения Российской академии наукРоссияLomonosov Moscow State University; Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of ScienceRussian Federation202519042026045976Copyright © Тимохин М.Ю., Бондарь Е.А., 20262026Тимохин М.Ю., Бондарь Е.А.Timokhin M., Bondar Y.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.physmathmgou.ru/jour/article/view/732   Цель

   Цель. Исследование применимости классических макроскопических приближений для получения неравновесной локальной функции распределения внутри структуры сильной ударной волны.

   Процедура и методы

   Процедура и методы. В настоящей работе рассматриваются возможности аппроксимации неравновесной молекулярной функции распределения с помощью различных макроскопических моделей (уравнения Навье – Стокса – Фурье, уравнения Барнетта, оригинальные и регуляризированные 13-моментные уравнения Грэда).

   Результаты

   Результаты. Результаты восстановления локальной функции распределения по макропараметрам течения для рассматриваемых моделей сравниваются друг с другом и с эталонным решением в различных точках структуры плоской ударной волны. В качестве эталонного решения используется метод прямого статистического моделирования (ПСМ) Монте-Карло, который обеспечивает макропараметры потока, необходимые для восстановления функции распределения.

   Теоретическая значимость. Сделаны выводы, что все рассмотренные классические модели довольно плохо предсказывают функцию распределения в сверхзвуковой части структуры ударной волны, где наблюдаются сильные осцилляции и нефизичные отрицательные значения.

   Aim

   Aim. The investigation into the applicability of classical macroscopic approximations to obtain the nonequilibrium local distribution function inside the structure of a strong shock wave.

   Methodology

   Methodology. This paper examines the capability of various macroscopic models (the Navier – Stokes – Fourier equations, the Burnett equations, and the original and regularized 13-moment Grad equations) to approximate a nonequilibrium molecular velocity distribution function.

   Results

   Results. The locally reconstructed distribution functions obtained from the flow macro-parameters for the considered models are compared with each other and with a benchmark solution at different locations within the structure of a planar shock wave. The benchmark solution is provided by the Direct Simulation Monte Carlo (DSMC) method, which supplies the flow macro-parameters required for the reconstruction of the distribution function.

   Research implications

   Research implications. All considered models predict the distribution function rather poorly in the supersonic part of the shock-wave structure, where strong oscillations and nonphysical negative values are observed.

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The authors declare that there are no conflicts of interest present.