A shallow water with variable pressure model for blood flow simulation

Olivier  Delestre; Arthur R.  Ghigo; José-Maria  Fullana; Pierre-Yves  Lagrée

doi:10.3934/nhm.2016.11.69

Article Contents

2016, Volume 11, Issue 1: 69-87. Doi: 10.3934/nhm.2016.11.69

This issue Previous Article Biological and industrial models motivating nonlocal conservation laws: A review of analytic and numerical results Next Article Boundary value problem for a phase transition model

A shallow water with variable pressure model for blood flow simulation

1.
Laboratoire J.A. Dieudonné, UMR CNRS 7351 & Polytech Nice Sophia, Université de Nice - Sophia Antipolis, Parc Valrose, 06108 Nice cedex 02
2.
Sorbonne Universités, CNRS and UPMC Université Paris 06, UMR 7190, Institut Jean Le Rond d'Alembert - 4, place Jussieu, Boîte 162, 75005 Paris

Received: April 2015

Revised: September 2015

Published: March 2016

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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 and nonphysical velocities.

Keywords:

Mathematics Subject Classification: Primary: 35L65, 35Q35, 35Q92, 65M08; Secondary: 76M12, 92C10.

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