  We present a parallel-scalable method for simulating non-dilute suspensions
of deformable particles immersed in Stokesian fluid in three dimensions. A
critical component in these simulations is robust and accurate collision
handling. This work complements our previous work [L. Lu, A. Rahimian, and D.
Zorin. Contact-aware simulations of particulate Stokesian suspensions. Journal
of Computational Physics 347C: 160-182] by extending it to 3D and by
introducing new parallel algorithms for collision detection and handling. We
use a well-established boundary integral formulation with spectral Galerkin
method to solve the fluid flow. The key idea is to ensure an interference-free
particle configuration by introducing explicit contact constraints into the
system. While such constraints are typically unnecessary in the formulation
they make it possible to eliminate catastrophic loss of accuracy in the
discretized problem by preventing contact explicitly. The incorporation of
contact constraints results in a significant increase in stable time-step size
for locally-implicit time-stepping and a reduction in the necessary number of
discretization points for stability. Our method maintains the accuracy of
previous methods at a significantly lower cost for dense suspensions and the
time step size is independent from the volume fraction. Our method permits
simulations with high volume fractions; we report results with up to 60% volume
fraction. We demonstrated the parallel scaling of the algorithms on up to 16K
CPU cores.
