Dynamic adaptive moving mesh finite-volume method for the blood flow and coagulation modeling.

Abstract

In this work, we develop numerical methods for the solution of blood flow and coagulation on dynamic adaptive moving meshes. We consider the blood flow as a flow of incompressible Newtonian fluid governed by the Navier-Stokes equations. The blood coagulation is introduced through the additional Darcy term, with a permeability coefficient dependent on reactions. To this end, we introduce moving mesh collocated finite-volume methods for the Navier-Stokes equations, advection-diffusion equations, and a method for the stiff cascade of reactions. A monolithic nonlinear system is solved to advance the solution in time. The finite volume method for the Navier-Stokes equations features collocated arrangement of pressure and velocity unknowns and a coupled momentum and mass flux. The method is conservative and inf-sup stable despite the saddle point nature of the system. It is verified on a series of analytical problems and applied to the blood flow problem in the deforming domain of the right ventricle, reconstructed from a time series of computed tomography scans. At last, we demonstrate the ability to model the coagulation process in deforming microfluidic capillaries.