Can We Find Steady-State Solutions to Multiscale Rarefied Gas Flows Within Dozens of Iterations?
Dr. Lei Wu
University of Strathclyde (UK)

One of the central problems in the study of rarefied gas dynamics is to find the steady-state solution of the Boltzmann equation quickly. When the Knudsen number is large, the conventional iterative scheme can lead to convergence within a few iterations. However, when the Knudsen number is small, hundreds of thousands iterations are needed, and yet the ``converged'' solutions are prone to be contaminated by accumulated error and large numerical dissipation. Recently, based on the gas kinetic models, the implicit unified gas kinetic scheme (UGKS) and its variants have significantly reduced the iterations in the near-continuum flow regime, but still much higher than that of the highly rarefied gas flows. In this paper, we put forward a general synthetic iterative scheme (GSIS) to find the steady-state solutions of general rarefied gas flows within dozens of iterations at any Knudsen number. The key ingredient of our scheme is that the macroscopic equations, which are solved together with the Boltzmann equation and help to adjust the velocity distribution function, not only asymptotically preserve the Navier-Stokes limit in the framework of Chapman-Enskog expansion, but also contain Newton's law for stress and Fourier's law for heat conduction explicitly. For this reason, like the implicit UGKS, the constraint that the spatial cell size should be smaller than the mean free path of gas molecules is removed, but we do not need the complex evaluation of numerical flux at the cell interface. What's more, as the GSIS does not rely on the specific kinetic model/collision operator, it can be naturally extended to quickly find converged solutions for mixture flows and even flows involving chemical reactions. These two superior advantages are expected to accelerate the slow convergence in simulation of near-continuum flows via the direct simulation Monte Carlo method and its low-variance version.

About the Speaker

吴雷博士目前是英国斯特拉斯克莱德大学机械与航天工程系的高级讲师, 2019年入选青年千人计划项目 (南科大)。主要从事稀薄气体动力学研究, 稀薄气体动力学在航空航天、微机电系统、页岩气开发等方面有着重要应用。近年来, 吴雷博士开发了一套系统有效的快速求解玻尔兹曼方程的方法, 在非平衡气体理论建模和数值模拟方面进行了富有成效的研究工作。目前已发表SCI论文60余篇,包括Journal of Fluid Mechanics (7篇,6篇一作)、Journal of Computational Physics (8 篇,6篇一作/通讯)、Physical Review A/E (16篇,9篇一作/通讯)。作为PI主持英国工程和自然科学研究会基金一项 (37万英镑), 作为Co-PI负责沙特法赫德国王石油矿产大学-爱丁堡大学-思克莱德大学合作研究基金一项 (总计284万美元)。

2019-06-20 3:00 PM
Room: A203 Meeting Room
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