Abstract
We will introduce the issue of computing the blood flow and blood coagulation process. We aim to model blood as a viscoelastic fluid.
We want to capture the platelets and chemical species margination effect by red blood cells. The blood coagulation process is taken as growth of a phase field, which depends on both rheological and biochemical conditions in the vessel.
We implement our model using FEM library deal.ii. In order to scale up to hundreds of cores we apply projection methods to solution of our coupled systems of equations.
As the most promising projection method appears to be the incremental pressure correction splitting method, which we use for the Navier-Stokes part of our equations. Nonlinear terms in the Navier-Stokes equations are treated using the fixed point iteration.
NS system is solved decoupled from the convection-diffusion-reaction transport equation for the blood coagulation species. As we are dealing with processes of different time scales, we use a specific adaptive time stepping scheme for the whole system of equations.