A numerical scheme for a multi-scale model of thrombus in arteries

TL;DR

This paper develops a numerical scheme for a multi-scale model of thrombus formation in arteries, incorporating fluid-structure interaction and elastic properties of blood flow, with theoretical analysis of stability and well-posedness.

Contribution

It introduces a novel implicit Euler discretization for a complex multi-scale thrombus model, providing theoretical guarantees of stability and local well-posedness.

Findings

Derivation of a priori estimates for the scheme

Proof of local well-posedness using Faedo-Galerkin method

Establishment of stability conditions for the numerical method

Abstract

In this article, the time-discretization of the fluid structure interaction model in the three-dimensional boundary domain is taken into account, which explains the mechanical interaction between the blood flow and the Hookean elasticity. The interface between the two phases is given by a soft transition layer and spreads to the finite thickness. On the implicit Euler scheme for this discretization, We derive a variety of priori estimates and then use the Faedo-Galerkin method to prove the local well-poseedness results.