A DIFFUSION MODEL FOR RAREFIED FLOWS IN CURVED CHANNELS
A DIFFUSION MODEL FOR RAREFIED FLOWS IN CURVED CHANNELS
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DOI：
10.1137/070690328
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发表时间：
2008-01-01
影响因子：
1.6
通讯作者：
Yoshida, H.
中科院分区：
文献类型：
--
作者：
Aoki, K.;Degond, P.;Yoshida, H.
本文在玻尔兹曼（Bhatnagar-Gross-Krook）模型的基础上，导出了二维弯曲通道中稀薄气体流动的一维对流扩散模型。流动是由沿通道壁面的温度梯度驱动的，称为热蠕变现象。该装置无需任何运动部件即可作为微泵系统使用。我们的推导是基于扩散近似的渐近技术。它给出微观（动力学）方程的宏观（流体）近似。我们还推导了曲率不连续的连接处的连接条件。利用对流扩散模型的数值近似对抽气装置进行了数值模拟，结果与全二维动力学模拟结果非常吻合。然后，它被用于在长泵装置上获得非常快速的计算，而目前的全动力学计算的计算成本对于这种情况仍然是令人望而却步的。
In this paper, we derive a one-dimensional convection-diffusion model for a rarefied gas flow in a two-dimensional curved channel on the basis of the Boltzmann (Bhatnagar-Gross-Krook) model. The flow is driven by the temperature gradient along the channel walls, which is known as the thermal creep phenomenon. This device can be used as a micropumping system without any moving part. Our derivation is based on the asymptotic technique of the diffusion approximation. It gives a macroscopic (fluid) approximation of the microscopic (kinetic) equation. We also derive the connection conditions at the junction where the curvature is not continuous. The pumping device is simulated by using a numerical approximation of our convection-diffusion model which turns out to agree very well with full two-dimensional kinetic simulations. It is then used to obtain very fast computations on long pumping devices, while the computational cost of full kinetic computations nowadays is still prohibitive for such cases.