We present an efficient, accurate, and robust method for simulation of dense suspensions of deformable and rigid particles immersed in Stokesian fluid in two dimensions. We use a well-established boundary integral formulation for the problem as the foundation of our approach. This type of formulations, with a high-order spatial discretization and an implicit and adaptive time discretization, have been shown to be able to handle complex interactions between particles with high accuracy. Yet, for dense suspensions, very small time-steps or expensive implicit solves as well as a large number of discretization points are required to avoid non-physical contact and intersections between particles, leading to infinite forces and numerical instability.Our method maintains the accuracy of previous methods at a significantly lower cost for dense suspensions. The key idea is to ensure interference-free configuration by introducing explicit contact constraints into the system. While such constraints are unnecessary in the formulation, in the discrete form of the problem, they make it possible to eliminate catastrophic loss of accuracy by preventing contact explicitly.Introducing contact constraints results in a significant increase in stable time-step size for explicit timestepping, and a reduction in the number of points adequate for stability.

Figure 1: Simulation results for 40,960 RBCs in a complex vessel geometry. For our strong scaling experiments, we use the vessel geometry shown on the left, with inflow-outflow boundary conditions at various regions of the vessel geometry. To setup the problem, we fill the vessel with nearly-touching RBCs of different sizes. The figure above shows a setup with overall 40,960 RBCs at a volume fraction of 19%, and 40,960 polynomial patches. The full simulation video is available at https://vimeo.com/329509229. ABSTRACTHigh-resolution blood flow simulations have potential for developing better understanding biophysical phenomena at the microscale, such as vasodilation, vasoconstriction and overall vascular resistance. To this end, we present a scalable platform for the simulation of red blood cell (RBC) flows through complex capillaries by modeling the physical system as a viscous fluid with immersed deformable particles. We describe a parallel boundary integral equation solver for general elliptic partial differential equations, which we apply to Stokes flow through blood vessels. We also detail a parallel collision avoiding algorithm to ensure RBCs and the blood vessel remain contact-free. We have scaled our code on Stampede2 at the Texas Advanced Computing Center up to 34,816 cores. Our largest simulation enforces a contact-free state between four billion surface * Both authors contributed equally to this research. elements and solves for three billion degrees of freedom on one million RBCs and a blood vessel composed from two million patches.