A parallel two-level method for simulating blood flows in branching arteries with the resistive boundary condition

Computer modeling of blood flows in the arteries is an important and very challenging problem. In order to understand, computationally, the sophisticated hemodynamics in the arteries, it is essential to couple the fluid flow and the elastic wall structure effectively and specify physiologically realistic boundary conditions. The computation is expensive and the parallel scalability of the solution algorithm is a key issue of the simulation. In this paper, we introduce and study a parallel two-level Newton–Krylov–Schwarz method for simulating blood flows in compliant branching arteries by using a fully coupled system of linear elasticity equation and incompressible Navier–Stokes equations with the resistive boundary condition. We first focus on the accuracy of the resistive boundary condition by comparing it with the standard pressure type boundary condition. We then show the parallel scalability results of the two-level approach obtained on a supercomputer with a large number of processors and on problems with millions of unknowns.