A robust numerical method for the R13 equations of rarefied gas dynamics: Application to lid driven cavity
A robust numerical method for the R13 equations of rarefied gas dynamics: Application to lid driven cavity
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DOI：
10.1016/j.jcp.2012.11.023
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发表时间：
2013-03-01
影响因子：
4.1
通讯作者：
Struchtrup, Henning
中科院分区：
文献类型：
--
作者：
Rana, Anirudh;Torrilhon, Manuel;Struchtrup, Henning
本文提出了一种计算正则化13矩（R13）稀薄气体动力学方程稳态解的有限差分格式。该方案允许快速求解具有速度滑移和温度跳变边界条件的2D和3D边界值问题。该方案适用于Knudsen数大于0.7的盖驱动空腔问题。结果与昂贵的稀薄气体动力学求解方法（如积分矩法（IMM）和直接模拟蒙特卡罗（DSMC）方法）的结果相比较。对于这个边值问题，R13方程比经典的Navier-Stokes-Fourier方程得到了更好的结果，因为它们给出了中等克努森数下克努森边界层的近似描述。基于R13的数值解在计算上是经济的，可以被认为是中等克努森数下复杂工业问题的可靠的替代数学模型。(C) 2012爱思唯尔公司版权所有。
In this work we present a finite difference scheme to compute steady state solutions of the regularized 13 moment (R13) equations of rarefied gas dynamics. The scheme allows fast solutions for 2D and 3D boundary value problems (BVPs) with velocity slip and temperature jump boundary conditions. The scheme is applied to the lid driven cavity problem for Knudsen numbers up to 0.7. The results compare well with those obtained from more costly solvers for rarefied gas dynamics, such as the Integro Moment Method (IMM) and the Direct Simulation Monte Carlo (DSMC) method. The R13 equations yield better results than the classical Navier-Stokes-Fourier equations for this boundary value problem, since they give an approximate description of Knudsen boundary layers at moderate Knudsen numbers. The R13 based numerical solutions are computationally economical and may be considered as a reliable alternative mathematical model for complex industrial problems at moderate Knudsen numbers. (C) 2012 Elsevier Inc. All rights reserved.