Solving Coupled Problems of Blood Flow and Coagulation in Moving Domains, I: Numerical Models and Simulations

We consider biophysical problems appearing in moving domains: blood flow, two-phase flow of blood with drifting clot, and coagulation process in blood flow. The corresponding mathematical models are given by the incompressible Navier–Stokes equations, the incompressible Navier–Stokes–Cahn–Hilliard equations, and the Navier–Stokes–Brinkman equations with coagulation equations for chemical kinetics and advection–diffusion of blood factors, respectively. We address blood flow problems that may attract interest of clinicians: clot-in-transit and the clot formation in blood streams. The present paper is the first in the series, where we discuss models, computational meshes, discretizations and results of simulations obtained with the fully implicit solution of aforementioned problems and pave the way for the further investigation of the algebraic solvers efficiency in the second paper of the series.