Interaction of rigid body motion and rarefied gas dynamics based on the BGK model
Interaction of rigid body motion and rarefied gas dynamics based on the BGK model
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DOI：
10.3934/mine.2020010
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
S. Tiwari;A. Klar;G. Russo
中科院分区：
文献类型：
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作者：
S. Tiwari;A. Klar;G. Russo
在本文中，我们提出了运动的刚体浸没在稀薄气体的模拟。稀薄气体通过求解Boltzmann方程的Bhatnager-Gross-Krook（BGK）模型来模拟。求解牛顿-欧拉方程来模拟刚体运动。作用在刚体上的力和力矩由周围的气体计算。显式欧拉格式用于时间积分的牛顿-欧拉方程。BGK模型通过Russo & Filbet [22]建议的半拉格朗日方法求解。由于刚体的运动，稀薄气体的计算域（以及刚体与气体域之间的界面）随时间而变化。为了允许一个更简单的处理界面运动，我们使用了无网格方法的插值过程中的半拉格朗日计划。我们已经考虑了一个单向，以及一个双向耦合的刚体和气体流动。我们使用漫反射的刚体上的边界条件，也对计算域的边界。在一个空间维度的数值结果进行了比较分析，以及与直接模拟Monte Carlo（DSMC）的Boltzmann方程的解决方案。在二维的情况下，结果与DSMC模拟的Boltzmann方程和其他研究人员所获得的结果进行了比较。几个测试问题和应用程序说明了该方法的通用性。
In this paper we present simulations of moving rigid bodies immersed in a rarefied gas. The rarefied gas is simulated by solving the Bhatnager-Gross-Krook (BGK) model for the Boltzmann equation. The Newton-Euler equations are solved to simulate the rigid body motion. The force and the torque on the rigid body is computed from the surrounded gas. An explicit Euler scheme is used for the time integration of the Newton-Euler equations. The BGK model is solved by the semi-Lagrangian method suggested by Russo & Filbet [22]. Due to the motion of the rigid body, the computational domain for the rarefied gas (and the interface between the rigid body and the gas domain) changes with respect to time. To allow a simpler handling of the interface motion we have used a meshfree method for the interpolation procedure in the semi-Lagrangian scheme. We have considered a one way, as well as a two-way coupling of rigid body and gas flow. We use diffuse reflection boundary conditions on the rigid body and also on the boundary of the computational domain. In one space dimension the numerical results are compared with analytical as well as with Direct Simulation Monte Carlo (DSMC) solutions of the Boltzmann equation. In the two-dimensional case results are compared with DSMC simulations for the Boltzmann equation and with results obtained by other researchers. Several test problems and applications illustrate the versatility of the approach.