Fundamental solutions to the regularised 13-moment equations: efficient computation of three-dimensional kinetic effects
Fundamental solutions to the regularised 13-moment equations: efficient computation of three-dimensional kinetic effects
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DOI：
10.1017/jfm.2017.763
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发表时间：
2017-11
影响因子：
3.7
通讯作者：
Rory Claydon;Abhay Shrestha;A. Rana;J. Sprittles;D. Lockerby
中科院分区：
文献类型：
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作者：
Rory Claydon;Abhay Shrestha;A. Rana;J. Sprittles;D. Lockerby
对于稀薄气体动力学的正则化13矩系统(R13)，对于小的偏离平衡，得到了基本解(格林函数)；这些解显示了与指数衰减项相关的努森层的存在，这在低阶系统的解(例如，Navier-Stokes-Fourier方程)中是不存在的。将这些新的基本解结合到基于基本解方法(MFS)的数值框架中，可以以极低的计算代价高效地计算三维气体微细流动。R13-MFS方法准确地恢复了定常球体周围低速流动的解析解和热球的换热(已推导出新的解析解)，捕捉到了低阶解中缺失的非平衡流动现象。为了证明这种新方法的潜力，计算了动力学效应对接近固体微粒之间流体动力相互作用的影响。最后，根据本文所采取的初步步骤，概述了今后的工作方案。
Fundamental solutions (Green’s functions) are derived for the regularised 13-moment system (R13) of rarefied gas dynamics, for small departures from equilibrium; these solutions show the presence of Knudsen layers, associated with exponential decay terms, that do not feature in the solution of lower-order systems (e.g. the Navier–Stokes–Fourier equations). Incorporation of these new fundamental solutions into a numerical framework based on the method of fundamental solutions (MFS) allows for efficient computation of three-dimensional gas microflows at remarkably low computational cost. The R13-MFS approach accurately recovers analytic solutions for low-speed flow around a stationary sphere and heat transfer from a hot sphere (for which a new analytic solution has been derived), capturing non-equilibrium flow phenomena missing from lower-order solutions. To demonstrate the potential of the new approach, the influence of kinetic effects on the hydrodynamic interaction between approaching solid microparticles is calculated. Finally, a programme of future work based on the initial steps taken in this article is outlined.