Highly accurate special quadrature methods for Stokesian particle suspensions in confined geometries
arXiv:2005.12614 · doi:10.1002/fld.4970
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.
arXiv comment46 pages, 41 figures
References in corpus (23)
- An Immersed Boundary Method with Direct Forcing for the Simulation of Particulate Flows
- How to mesh up Ewald sums (I): A theoretical and numerical comparison of various particle mesh routines
- Quadrature by Expansion: A New Method for the Evaluation of Layer Potentials
- Spectral Ewald Acceleration of Stokesian Dynamics for polydisperse suspensions
- A fast integral equation method for solid particles in viscous flow using quadrature by expansion
- Fast algorithms for Quadrature by Expansion I: Globally valid expansions
- A highly accurate boundary integral equation method for surfactant-laden drops in 3D
- An accurate integral equation method for simulating multi-phase Stokes flow
- Fast Ewald summation for free-space Stokes potentials
- A Fast Algorithm for Quadrature by Expansion in Three Dimensions
- A Simple Method for Computing Singular or Nearly Singular Integrals on Closed Surfaces
- Adaptive quadrature by expansion for layer potential evaluation in two dimensions
- A local target specific quadrature by expansion method for evaluation of layer potentials in 3D
- Boundary integral equation analysis for suspension of spheres in Stokes flow
- Estimation of quadrature errors in layer potential evaluation using quadrature by expansion
- Hydrodynamic Irreversibility in Particle Suspensions with Non-Uniform Strain
- Harmonic density interpolation methods for high-order evaluation of Laplace layer potentials in 2D and 3D
- A Fast Algorithm with Error Bounds for Quadrature by Expansion
- Regularized Single and Double Layer Integrals in 3D Stokes Flow
- Optimization of Fast Algorithms for Global Quadrature by Expansion Using Target-Specific Expansions
- Scalable Simulation of Realistic Volume Fraction Red Blood Cell Flows through Vascular Networks
- Simulation and validation of surfactant-laden drops in two-dimensional Stokes flow
- Fast Ewald summation for Green's functions of Stokes flow in a half-space