Speaker
Anna Broms, Imperial College London
Abstract
The Stokes mobility and resistance problems for rigid particles in viscous fluids arise in a wide range of natural and industrial settings. I will discuss a method of fundamental solutions (MFS) that retains key advantages of boundary integral methods (BIMs), including spectral accuracy and reduced degrees of freedom. Unlike BIMs, however, it requires no special quadrature for singular integrands, since source and collocation points reside on different surfaces. For rigid bodies, the flow is represented using interior fundamental solutions (Stokeslets) whose strengths are determined by a least-squares collocation on the particle surfaces. With a suitable preconditioner, this can be solved iteratively as a square system amenable to fast summation techniques such as the fast multipole method.
A persistent difficulty for any method is the simulation of particles moving in near-contact, where discretizations become severely ill-conditioned and lubrication scales demand excessive global resolution. To address both issues, we introduce a two-body preconditioning strategy that augments the MFS with contact-adapted image constructions. For each near-touching pair, a local fine-scale boundary value problem is solved and compressed into a small set of equivalent coarse sources that couple to the global system. The scheme restores accuracy even for close-to-touching configurations, and numerical experiments show rapid GMRES convergence with robust performance in densely packed suspensions.
Joint work with Alex Barnett and Anna-Karin Tornberg.