Parallel algorithms for direct blood flow simulations
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Fluid mechanics of blood can be well approximated by a mixture model of a Newtonian fluid and deformable particles representing the red blood cells. Experimental and theoretical evidence suggests that the deformation and rheology of red blood cells is similar to that of phospholipid vesicles. Vesicles and red blood cells are both area preserving closed membranes that resist bending. Beyond red blood cells, vesicles can be used to investigate the behavior of cell membranes, intracellular organelles, and viral particles. Given the importance of vesicle flows, in this thesis we focus in efficient numerical methods for such problems: we present computationally scalable algorithms for the simulation of dilute suspension of deformable vesicles in two and three dimensions. Our method is based on the boundary integral formulation of Stokes flow. We present new schemes for simulating the three-dimensional hydrodynamic interactions of large number of vesicles with viscosity contrast. The algorithms incorporate a stable time-stepping scheme, high-order spatiotemporal discretizations, spectral preconditioners, and a reparametrization scheme capable of resolving extreme mesh distortions in dynamic simulations. The associated linear systems are solved in optimal time using spectral preconditioners. The highlights of our numerical scheme are that (i) the physics of vesicles is faithfully represented by using nonlinear solid mechanics to capture the deformations of each cell, (ii) the long-range, N-body, hydrodynamic interactions between vesicles are accurately resolved using the fast multipole method (FMM), and (iii) our time stepping scheme is unconditionally stable for the flow of single and multiple vesicles with viscosity contrast and its computational cost-per-simulation-unit-time is comparable to or less than that of an explicit scheme. We report scaling of our algorithms to simulations with millions of vesicles on thousands of computational cores.