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 efficient.
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.
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Contributed by WU Wang-yi
Foundation item: the National Natural Science Foundation of China (86030028, 38970244)
Biography: ZHUANG Hong, (1965-), Professor, Ph.D.
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Hong, Z., Zong-yi, Y. & Wang-yi, W. The three-dimensional fundamental solution to Stokes flow in the oblate spheroidal coordinates with applications to multiples spheroid problems. Appl Math Mech 23, 514–534 (2002). https://doi.org/10.1007/BF02437770
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DOI: https://doi.org/10.1007/BF02437770
Key words
- Stokes flow
- fundamental solution
- three-dimension
- oblate spheroid
- multipole collocation
- least squares method
- low Reynolds number
- multiple particles