Fast Ewald summation for Stokesian particle suspensions

• 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
• ISSN: 0271-2091; 1097-0363; 1097-0363
• DOI: 10.1002/fld.3953

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.