Parallel Domain Decomposition Methods For Simulating Blood Flows In Three-Dimensional Compliant Arteries
Numerical simulation of blood flows in compliant arteries is becoming an useful tool in studying the sophisticated hemodynamics in the human circulation system. Accurate modeling is important in prediction and treatment of artery diseases. In this thesis, we propose and study a parallel domain decomposition method for solving the corresponding fluid-structure interaction problem in three-dimensional space, with emphasis on the strong coupling between fluid and structure and on the parallel scalability of the solution algorithm.
We model the fluid-structure interaction by using a monolithically coupled system of linear elasticity equations for the arterial walls and incompressible Navier-Stokes equations for the blood. The fluid equations are derived in an arbitrary Lagrangian-Eulerian framework to address the complicated moving boundaries and keep track of the coupling on the interface. A finite element method based on the unstructured mesh is introduced and validated for discretizing the problem in space, and a fully implicit scheme is used for the temporal discretization.
For solving the nonlinear systems arising from the fully coupled discretization, we develop a class of Newton-Krylov-Schwarz algorithms. The investigation focuses on the parallel efficiency of the fully implicit solution algorithm, as well as the performance of one-level and two-level additive Schwarz preconditioners used in accelerating the convergence of the Newton-Krylov algorithm. Simulations based on some patient-specific pulmonary artery geometries are performed on a large scale supercomputer. Our algorithm is shown to have excellent parallel scalability with over three thousand processors and for problems with millions of unknowns, and is also robust with respect to several important physical parameters including the fluid density, the structure density, the Reynolds number, and the Poisson ratio.