Particle laden Stokes flows are present in many practical problems of interest involving sedimentation, emulsions etc. These are usually solved using boundary integral methods; however solving surface integral equations with weakly singular kernels (as is the case here) using numerical quadratures is still an active area of research. In this project, we focus on a simplified situation, where all the particles are rotationally symmetric. We are trying to come up with fast, scalable solvers that can handle a large number of particles.
Resolving particle collisions is one of the major challenges in numerical simulation of real life phenomena, as they give rise to non-smooth dynamics. There are two major school of methods for handling problems with contacts; the first envelopes the bodies with a so called ‘soft layer’, which does not allow the particles to ever really touch each other. In the second, the interactions are resolved via complimentary models. This is the model we focus on in this project. We are currently trying to come up with better numerical methods for solving these problems.