A finite element solver and energy stable coupling for 3D and 1D fluid models

TL;DR

This paper introduces a finite element solver with energy-stable coupling for 3D-1D incompressible flow models, enhancing stability and accuracy for complex cardiovascular simulations.

Contribution

It develops a novel coupling method with energy stability for 3D-1D flow models, applicable to realistic cardiovascular scenarios.

Findings

The solver ensures energy stability in 3D-1D coupling.

Demonstrated accurate blood flow simulation over an IVC filter.

Analyzed solver performance with state-of-the-art linear algebraic methods.

Abstract

The paper develops a solver based on a conforming finite element method for a 3D--1D coupled incompressible flow problem. New coupling conditions are introduced to ensure a suitable bound for the cumulative energy of the model. We study the stability and accuracy of the discretization method, and the performance of some state-of-the-art linear algebraic solvers for such flow configurations. Motivated by the simulation of the flow over inferior vena cava (IVC) filter, we consider the coupling of a 1D fluid model and a 3D fluid model posed in a domain with anisotropic inclusions. The relevance of our approach to realistic cardiovascular simulations is demonstrated by computing a blood flow over a model IVC filter.