A shallow water with variable pressure model for blood flow simulation

TL;DR

This paper introduces a finite volume method with hydrostatic reconstruction for simulating blood flow in arteries with variable properties, demonstrating improved accuracy and stability over simpler schemes.

Contribution

The study develops and validates a novel numerical approach for blood flow modeling that handles variable artery properties effectively.

Findings

Hydrostatic reconstruction reduces spurious oscillations.

Method accurately captures effects of variable stiffness and cross-section.

Validated against literature examples.

Abstract

We performed numerical simulations of blood flow in arteries with a variable stiffness and cross-section at rest using a finite volume method coupled with a hydrostatic reconstruction of the variables at the interface of each mesh cell. The method was then validated on examples taken from the literature. Asymptotic solutions were computed to highlight the effect of the viscous and viscoelastic source terms. Finally, the blood flow was computed in an artery where the cross-section at rest and the stiffness were varying. In each test case, the hydrostatic reconstruction showed good results where other simpler schemes did not, generating spurious oscillations andnonphysical velocities.