Highly accurate special quadrature methods for Stokesian particle suspensions in confined geometries,International Journal for Numerical Methods in Fluids

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Highly accurate special quadrature methods for Stokesian particle suspensions in confined geometries
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-02-22 , DOI: 10.1002/fld.4970
Joar Bagge ₁ , Anna‐Karin Tornberg ₁

Affiliation

Boundary integral methods are highly suited for problems with complicated geometries, but require special quadrature methods to accurately compute the singular and nearly singular layer potentials that appear in them. This article presents a boundary integral method that can be used to study the motion of rigid particles in three-dimensional periodic Stokes flow with confining walls. A centerpiece of our method is the highly accurate special quadrature method, which is based on a combination of upsampled quadrature and quadrature by expansion, accelerated using a precomputation scheme. The method is demonstrated for rodlike and spheroidal particles, with the confining geometry given by a pipe or a pair of flat walls. A parameter selection strategy for the special quadrature method is presented and tested. Periodic interactions are computed using the spectral Ewald fast summation method, which allows our method to run in

O (n \log n)

time for n grid points in the primary cell, assuming the number of geometrical objects grows while the grid point concentration is kept fixed.

中文翻译：

用于受限几何形状中斯托克斯粒子悬浮液的高精度特殊正交方法

边界积分方法非常适合处理复杂几何的问题，但需要特殊的正交方法来准确计算出现在其中的奇异和近奇异层势。本文提出了一种边界积分方法，可用于研究具有围壁的三维周期性 Stokes 流中刚性粒子的运动。我们方法的核心是高精度的特殊正交方法，它基于上采样正交和扩展正交的组合，使用预计算方案加速。该方法针对棒状和球状颗粒进行了演示，其限制几何形状由管道或一对平壁给出。提出并测试了特殊正交方法的参数选择策略。