A kinetic theory solution method for the Navier–Stokes equations
A kinetic theory solution method for the Navier–Stokes equations
复制标题
DOI：
10.1002/fld.1650170302
复制
发表时间：
1993-08
影响因子：
1.8
通讯作者：
M. Macrossan;R. Oliver
中科院分区：
文献类型：
--
作者：
M. Macrossan;R. Oliver
本文对Pullin和Reitz提出的基于动力学理论的欧拉方程求解方法进行了推广，为求解非定常的N-S方程提供了新的有限体积数值方法。已经采取了两种方法。在第一种方法中，平衡界面法(EIM)假定两个细胞之间的正向和反向分子通量在细胞间的界面处达到动态平衡。一旦知道了所有晶胞界面的平衡态，就可以很容易地计算出纳维-斯托克斯通量。在第二种方法中，使用标准动力学理论来计算Pullin欧拉解中出现的人工耗散项。从通量中减去这些项，再加上N-S耗散通量。新方法已经在一维定常流动和二维非定常边界层流动中进行了试验，得到了激波内部结构的解。与流动中梯度的长度尺度相比，一维解对于较大的单元尺寸具有非常高的精度，并且随着单元尺寸的减小而收敛到精确解。用EIM得到的稳态解与其他方法的结果一致，但所需的计算量大大减少。
The kinetic-theory-based solution methods for the Euler equations proposed by Pullin and Reitz are here extended to provide new finite volume numerical methods for the solution of the unsteady Navier-Stokes equations. Two approaches have been taken. In the first, the equilibrium interface method (EIM), the forward- and backward-flowing molecular fluxes between two cells are assumed to come into kinetic equilibrium at the interface between the cells. Once the resulting equilibrium states at all cell interfaces are known, the evaluation of the Navier-Stokes fluxes is straightforward. In the second method, standard kinetic theory is used to evaluate the artificial dissipation terms which appear in Pullin's Euler solver. These terms are subtracted from the fluxes and the Navier-Stokes dissipative fluxes are added in. The new methods have been tested in a 1D steady flow to yield a solution for the interior structure of a shock wave and in a 2D unsteady boundary layer flow. The 1D solutions are shown to be remarkably accurate for cell sizes large compared to the length scale of the gradients in the flow and to converge to the exact solutions as the cell size is decreased. The steady-state solutions obtained with EIM agree with those of other methods, yet require a considerably reduced computational effort.