In this paper we present a novel technique for the simulation of moving boundaries and moving rigid bodies immersed in a rarefied gas using an Eulerian-Lagrangian formulation based on least square method. The rarefied gas is simulated by solving the Bhatnagar-Gross-Krook (BGK) model for the Boltzmann equation of rarefied gas dynamics. The BGK model is solved by an Arbitrary Lagrangian-Eulerian (ALE) method, where grid-points/particles are moved with the mean velocity of the gas. The computational domain for the rarefied gas changes with time due to the motion of the boundaries. To allow a simpler handling of the interface motion we have used a meshfree method based on a least-square approximation for the reconstruction procedures required for the scheme. We have considered a one way, as well as a two-way coupling of boundaries/rigid bodies and gas flow. The numerical results are compared with analytical as well as with Direct Simulation Monte Carlo (DSMC) solutions of the Boltzmann equation. Convergence studies are performed for one-dimensional and two-dimensional test-cases. Several further test problems and applications illustrate the versatility of the approach.

中文翻译：

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具有移动边界的 Boltzmann 方程 BGK 模型的无网格任意拉格朗日-欧拉方法

在本文中，我们提出了一种使用基于最小二乘法的欧拉-拉格朗日公式来模拟浸入稀薄气体中的移动边界和移动刚体的新技术。通过求解稀薄气体动力学 Boltzmann 方程的 Bhatnagar-Gross-Krook (BGK) 模型来模拟稀薄气体。BGK 模型通过任意拉格朗日-欧拉 (ALE) 方法求解，其中网格点/粒子随气体的平均速度移动。由于边界的运动，稀薄气体的计算域随时间变化。为了更简单地处理界面运动，我们使用了一种基于最小二乘近似的无网格方法，用于该方案所需的重建程序。我们已经考虑了一种方式，以及边界/刚体和气流的双向耦合。将数值结果与玻尔兹曼方程的解析解以及直接模拟蒙特卡罗 (DSMC) 解进行比较。对一维和二维测试用例进行收敛研究。几个进一步的测试问题和应用说明了该方法的多功能性。