Fast Ewald summation for Stokesian particle suspensions

SUMMARYWe present a numerical method for suspensions of spheroids of arbitrary aspect ratio, which sediment under gravity. The method is based on a periodized boundary integral formulation using the Stokes double layer potential. The resulting discrete system is solved iteratively using generalized...

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Bibliographic Details
Published in:International journal for numerical methods in fluids 2014-12, Vol.76 (10), p.669-698
Main Authors: Af Klinteberg, Ludvig, Tornberg, Anna-Karin
Format: Article
Language:English
Subjects:
Accuracy
Applied and Computational Mathematics
boundary integral
Computation
Computational fluid dynamics
Double layer
error estimation
ewald summation
Fluid flow
integral equations
Integrals
Mathematical models
microfluidics
multibody dynamics
Numerical analysis
spectral
Tillämpad matematik och beräkningsmatematik
viscous flows
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Summary:SUMMARYWe present a numerical method for suspensions of spheroids of arbitrary aspect ratio, which sediment under gravity. The method is based on a periodized boundary integral formulation using the Stokes double layer potential. The resulting discrete system is solved iteratively using generalized minimal residual accelerated by the spectral Ewald method, which reduces the computational complexity to O(NlogN), where N is the number of points used to discretize the particle surfaces. We develop predictive error estimates, which can be used to optimize the choice of parameters in the Ewald summation. Numerical tests show that the method is well conditioned and provides good accuracy when validated against reference solutions. Copyright © 2014 John Wiley & Sons, Ltd. We present a double layer boundary integral formulation for Stokes flow in periodic suspensions, together with a framework for computing the periodic sums of the formulation using fast Ewald summation. The method has O(N log N) computational complexity and provides good accuracy in validation.
ISSN:0271-2091
1097-0363
1097-0363
DOI:10.1002/fld.3953