两个非同心旋转圆柱间粘性流动的基本流及其数值解  

The Basic Flow of Viscous Fluid Between Two Eccentric Rotating Cylinders and Numerical Solution

作　　者：张引娣[1,2] 李开泰[2] 

机构地区：[1]长安大学理学院,西安710064 [2]西安交通大学理学院,西安710049

出　　处：《工程数学学报》2009年第4期637-647,共11页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10571142;10771167)

摘　　要：在修正双极坐标系下,本文对薄流层中的Navier-Stokes方程应用渐近分析方法和张量分析工具,得到两个非同心旋转圆柱之间粘性流体流动的基本流所满足的方程。这一基本流由两部分组成,一部分是以角速度ω旋转的同心圆柱所产生的基本流,而另一部分是带有高阶小参数的扰动流动。把扰动项用三角函数展开得到一满足非齐次边界条件的常微分方程组。在此基础上,我们得到了基本流的数值求解方法,并给出数值算例。Under the modified bipolar coordinate system, by applying the asymptotic analysis method and tensor analysis, we obtained the equations satisfied by the basic flow between two eccentric rotating cylinders. This basic flow consists of two parts. The first one is the basic flow between two concentric rotating cylinders with an angular velocity w, The second one is a disturbed flow with small parameter e of higher order. After expanding the later as the Fourier function, we derived a system of ODE with non-homogeneous boundary condition, Furthermore, we gave a numerical method for the basic flow and showed some numerical examples.

关 键 词：修正双极坐标系 张量分析 渐近分析方法 Navier—Stokes方程 

分 类 号：O242.21[理学—计算数学]