Highly accurate special quadrature methods for Stokesian particle suspensions in confined geometries

TL;DR

This paper introduces a highly accurate boundary integral method with specialized quadrature techniques for simulating the motion of rigid particles in three-dimensional confined Stokes flow, efficiently handling complex geometries.

Contribution

The paper develops a novel boundary integral method incorporating upsampled quadrature and QBX, optimized for accurate and efficient simulation of particles in confined geometries.

Findings

Achieved high accuracy in particle motion simulations in confined geometries.

Demonstrated method's efficiency with O(n log n) computational complexity.

Validated the approach on rodlike and spheroidal particles in pipe and wall geometries.

Abstract

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 paper 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 centrepiece of our method is the highly accurate special quadrature method, which is based on a combination of upsampled quadrature and quadrature by expansion (QBX), 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 (SE) fast summation method, which allows our method to run in O(n log n) time for n grid points, assuming the number of geometrical objects grows while the grid point concentration is kept fixed.