从粒子系统到BGK方程

Ensaios Matemáticos Pub Date : 2023-01-27 DOI:10.21711/217504322023/em385

P. Buttà, M. Pulvirenti, S. Simonella

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引用次数: 0

摘要

(理论物理。Rev. 94 (1954)， 511-525]， P.L. Bhatnagar, E.P. Gross和M. Krook引入了一个动力学方程(BGK方程)，在克努森数比波尔兹曼方程适用的尺度小的物理情况下有效，但不足以使用流体动力学方程。在本文中，我们考虑了Bird直接模拟蒙特卡罗方法(DSMC)的随机粒子系统(非均匀Kac模型)，并对缩放变量进行了调整，从而产生了动力学和/或流体动力学描述。虽然BGK方程不能从纯标度中得到，但它确实可以从动力学的简单修改中得到。这是对《物理学》中一些论点的数学解释。Rev. 94(1954)， 511-525]，补充了[Arch。配给。动力机械。[j] .中国农业科学，2014(5)，389 - 389。遗传代数。模型16(2023)，269-293]。

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From particle systems to the BGK equation

In [Phys. Rev. 94 (1954), 511-525], P.L. Bhatnagar, E.P. Gross and M. Krook introduced a kinetic equation (the BGK equation), effective in physical situations where the Knudsen number is small compared to the scales where Boltzmann's equation can be applied, but not enough for using hydrodynamic equations. In this paper, we consider the stochastic particle system (inhomogeneous Kac model) underlying Bird's direct simulation Monte Carlo method (DSMC), with tuning of the scaled variables yielding kinetic and/or hydrodynamic descriptions. Although the BGK equation cannot be obtained from pure scaling, it does follow from a simple modification of the dynamics. This is proposed as a mathematical interpretation of some arguments in [Phys. Rev. 94 (1954), 511-525], complementing previous results in [Arch. Ration. Mech. Anal. 240 (2021), 785-808] and [Kinet. Relat. Models 16 (2023), 269-293].

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Ensaios Matemáticos

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