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

• Published in: International journal for numerical methods in biomedical engineering 2023-11, Vol.39 (11), p.e3731-n/a
• Main Authors: Terekhov, Kirill M., Butakov, Ivan D., Danilov, Alexander A., Vassilevski, Yuri V.
• Format: Article
• Language: English
• Subjects: adaptive mesh; Advection-diffusion equation; Blood coagulation; Blood flow; Capillaries; Cascade chemical reactions; Coagulation; collocated; Computed tomography; Deformation; Finite element method; finite volume; Finite volume method; Fluid flow; Incompressible flow; inf‐sup stability; Mathematical models; Microfluidics; moving mesh; Navier-Stokes equations; Newtonian fluids; Nonlinear systems; Numerical methods; Permeability; Permeability coefficient; Saddle points; Ventricle
• ISSN: 2040-7939; 2040-7947
• DOI: 10.1002/cnm.3731

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. We consider a cell‐centered finite‐volume method for the blood flow and coagulation problems. We extend the method to dynamic adaptive moving meshes. It allows modelling the blood flow on meshes obtained from a time series of computed tomography scans as well as virtually extending the experiment in rigid microfluidic capillaries to pulsating geometry.