SCS: Anna Broms (KTH): MFS for 3D Stokes particle flows

Tuesday Mar 18, 2025, 10:00 AM → 11:00 AM America/New_York

3rd floor classroom (162)

Title: An Accurate Method of Fundamental Solutions for Large and Dense Particle Systems in Stokes Flow

Abstract: The Stokes mobility and resistance problems for rigid par-
ticles in viscous fluids have broad applications in both nat-
ural processes and industrial contexts and are important in
the study of transport or diffusion processes, rheology and
nonlinear shear thickening. Hydrodynamic interactions be-
tween particles are challenging to determine, as they are
simultaneously long-ranged and expensive to resolve for
dense suspensions. The latter is caused by near-singular
lubrication forces resulting from close-to-touching bodies
in relative motion. With the aim of controlling the accu-
racy for dense suspensions with a computationally cheap
method, we present a new technique for the two prob-
lems that combines the method of fundamental solutions
(MFS) with the method of images. For rigid spheres, we
propose to represent the flow using fundamental solutions
(Stokeslets) located on interior spheres, augmented by lines
of image sources adapted to each near-contact to resolve
lubrication. Source strengths are found by a least-squares
solve at contact-adapted boundary collocation nodes. In
the talk, we also discuss efficient preconditioning. The re-
sulting well-conditioned schemes are competing with state-
of-the art solvers tailored for spherical particles in Stokes
flow, yet are compatible also with other smooth particle
shapes, and scale linearly in the number of objects. For
instance, a problem of 10,000 ellipsoids is solved to 5-digit
accuracy on a workstation in less than two hours.

Join work with Alex Barnett and Anna-Karin Tornberg.