A fast integral equation method for solid particles in viscous flow using quadrature by expansion

TL;DR

This paper introduces a fast, accurate boundary integral method using quadrature by expansion and spectral Ewald summation for simulating viscous flow around many rigid particles, enabling efficient large-scale particle system analysis.

Contribution

It presents a novel combination of QBX and spectral Ewald methods for rapid, high-accuracy simulations of spheroids in periodic Stokes flow, optimized for large particle systems.

Findings

Achieves M log M computational complexity for particle interactions.

Provides high-accuracy evaluation of layer potentials on and off particle surfaces.

Enables efficient simulation of large particle systems in viscous flow.

Abstract

Boundary integral methods are advantageous when simulating viscous flow around rigid particles, due to the reduction in number of unknowns and straightforward handling of the geometry. In this work we present a fast and accurate framework for simulating spheroids in periodic Stokes flow, which is based on the completed double layer boundary integral formulation. The framework implements a new method known as quadrature by expansion (QBX), which uses surrogate local expansions of the layer potential to evaluate it to very high accuracy both on and off the particle surfaces. This quadrature method is accelerated through a newly developed precomputation scheme. The long range interactions are computed using the spectral Ewald (SE) fast summation method, which after integration with QBX allows the resulting system to be solved in M log M time, where M is the number of particles. This framework is suitable for simulations of large particle systems, and can be used for studying e.g. porous media models.