A "well-balanced" finite volume scheme for blood flow simulation

TL;DR

This paper introduces a well-balanced finite volume scheme for simulating blood flow in arteries, ensuring the preservation of equilibrium states and avoiding spurious flows caused by simple schemes.

Contribution

It develops a novel finite volume scheme that maintains equilibrium solutions in blood flow models, addressing limitations of previous methods.

Findings

The scheme preserves static equilibrium states effectively.

It prevents spurious flows in simulations with changing artery radii.

Validation with analytical and linearized solutions confirms accuracy.

Abstract

We are interested in simulating blood flow in arteries with a one dimensional model. Thanks to recent developments in the analysis of hyperbolic system of conservation laws (in the Saint-Venant/ shallow water equations context) we will perform a simple finite volume scheme. We focus on conservation properties of this scheme which were not previously considered. To emphasize the necessity of this scheme, we present how a too simple numerical scheme may induce spurious flows when the basic static shape of the radius changes. On contrary, the proposed scheme is "well-balanced": it preserves equilibria of Q = 0. Then examples of analytical or linearized solutions with and without viscous damping are presented to validate the calculations. The influence of abrupt change of basic radius is emphasized in the case of an aneurism.