三维斯托克斯流动在扁球坐标系中的基本解及其应用

The Three-Dimensional Fundamental Solution to Stokes Flow in the Oblato Spheroidal Coordinates With Applications to Multiple Spheroid Problems

通过把Lamb基本解中的调和函数转换为扁球坐标系下的表达式 ,这项研究成功地得到了一个新的Stokes流动三维基本解· 此基本解可用于解决任意多个扁椭球处于任意位置和方向时的流动问题· 应用最小二乘法 ,三维流动问题中常遇到的收敛性差的困难在此得以完全克服· 结果表明该方法具有准确度高 ,收敛性好和计算量小的特点· 由于扁球可用于模拟从圆盘到圆球的多种物体形状 ,此基本解被用于系统地分析了各种几何因素对两个扁球所受力和力矩的影响· 为了显示此方法的通用性 。

A new three_dimensional fundamental solution to the Stokes flow was proposed by transforming the solid harmonic functions in Lamb's solution into expressions in terms of the oblate spheroidal coordinates. These fundamental solutions are advantageous in treating flows past an arbitrary number of arbitrarily positioned and oriented oblate spheroids. The least squares technique was adopted herein so that the convergence difficulties often encountered in solving three_dimensional problems were completely avoided. The examples demonstrate that present approach is highly accurate, consistently stable and computationally effecient. The oblate spheroid may be used to model a variety of particle shapes between a circular disk and a sphere. For the first time, the effect of various geometric factors on the forces and torques exerted on two oblate spheroids were systematically studied by using the proposed fundamental solutions. The generality of this approach was illustrated by two problems of three spheroids.