Scalable simulation of realistic volume fraction red blood cell flows through vascular networks

Abstract

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.

Highly accurate special quadrature methods for Stokesian particle suspensions in confined geometries

“…It has been applied to surfactant-covered drops 46 and vesicles 47 in three-dimensional Stokes flow. The extrapolatory method used by Lu et al 2 falls into the same category. Other types of methods are based on regularizing the kernel and adding corrections, [48][49][50][51] density interpolation techniques, 52 coordinate rotations and a subtraction method, 53 asymptotic approximations, 54 analytical expressions available only for spheres 55 or floating partitions of unity.…”

“…The disturbance flow is written as where  ( ) is as in (8), and the double layer density q must be determined through the boundary conditions. Note that u d as given by ( 11) decays as x → ∞, and by the superposition principle it satisfies (1)- (2). Also note that completion sources are placed inside the particles since the flow is external to the particles, but not inside the walls since the flow is internal to the walls (for details we refer to Pozrikidis [8, sec.…”

Codimensional Incremental Potential Contact

“…For comparisons we are able to directly test Minimal Separation (MinSep) CCD [Harmon et al 2011;Lu et al 2019] by applying it within the conservative CCD strategy from IPC [Li et al 2020a]. Here minimal separation is set to 𝑠𝑑 cur with current scaling factor 𝑠 and distance 𝑑 cur .…”

Highly accurate special quadrature methods for Stokesian particle suspensions in confined geometries

“…It has been applied to surfactant-covered drops [50] and vesicles [35] in three-dimensional Stokes ow. The extrapolatory method used in [34] falls into the same category. Other types of methods are based on regularizing the kernel and adding corrections [5,53,6,54], density interpolation techniques [40], coordinate rotations and a subtraction method [10], asymptotic approximations [11], analytical expressions available only for spheres [12] or oating partitions of unity [9,61,23].…”

“…Microhydrodynamics is the study of uid ow at low Reynolds numbers, also known as Stokes ow or creeping ow. Applications are found in biology, for example in the swimming of microorganisms [20] and in blood ow [34], as well as in the eld of micro uidics, which concerns the design and construction of miniaturized uid devices [51]. Suspensions of rigid particles in Stokes ow are important both in various applications and in fundamental uid mechanics [46,16,36,19].…”