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

ZHUANG Hong; YAN Zong-yi; WU Wang-yi

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Article Navigation > Applied Mathematics and Mechanics > 2002 > 23(5): 459-476

ZHUANG Hong, YAN Zong-yi, WU Wang-yi. The Three-Dimensional Fundamental Solution to Stokes Flow in the Oblato Spheroidal Coordinates With Applications to Multiple Spheroid Problems[J]. Applied Mathematics and Mechanics, 2002, 23(5): 459-476.

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

1.
Faculty of Traffic Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, P R China;
2.
Department of Civil Engineering, The University of Hong Kong, Pokfulam Road

Received Date: 2000-05-18
Rev Recd Date: 2001-10-15
Publish Date: 2002-05-15

Abstract

Abstract

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.
- Stokes flow,
- fundamental solution,
- three-dimension,
- oblate spheroid,
- multipole collocation,
- least squares method,
- low Reynolds number,
- multiple particle

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References(16)

References

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