Speaker: Denis Zorin (NYU / Courant)

Title: Simulation of 3D particulate Stokesian suspensions

Abstract: I will present a comprehensive scalable method for simulation of dense suspensions of deformable and rigid particles in 3D Stokesian fluid, based on an integral equation formulation. The main algorithmic and software components include an accurate, adaptive high-order spatial discretization of boundaries and particles, parallel FMM-based integral equation solver, "hedgehog"-type evaluation of nearly singular integrals and continuous collision handling with space-time volume constraints. The latter are the key to ensuring interference-free configuration by introducing explicit contact constraints into the system. While such constraints are unnecessary in principle as contact is prevented by fluid forces in this formulation, in the discrete form of the problem, they make it possible to eliminate catastrophic loss of accuracy for close surfaces. We obtain a significant increase in stable step size for efficient explicit time-stepping, and a reduction in the number of spatial discretization points adequate for stability. Combining this set of geometric and numerical techniques, we can simulate a high-density flow robustly, yet without incurring excessive computational cost of implicit methods. All components of our software are implemented with distributed memory parallelization scaling up to thousands of cores.