Well‐balanced high‐order solver for blood flow in networks of vessels with variable properties. (31st July 2013)

• Record Type: Journal Article
• Authors: Müller, Lucas O.; Toro, Eleuterio F.
• Is Part Of: International journal for numerical methods in biomedical engineering. Volume 29:Number 12(2013:Dec.)
• Page Start: 1388
• Page End: 1411
• Publication Date: 2013-07-31
• Subjects: Biomedical engineering -- Periodicals; Imaging systems in medicine -- Periodicals; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 610.28
• DOI: 10.1002/cnm.2580
• Languages: English
• ISSNs: 2040-7939

Abstract

<abstract abstract-type="main" id="cnm2580-abs-0001"> <title>ABSTRACT</title> <p>We present a well‐balanced, high‐order non‐linear numerical scheme for solving a hyperbolic system that models one‐dimensional flow in blood vessels with variable mechanical and geometrical properties along their length. Using a suitable set of test problems with exact solution, we rigorously assess the performance of the scheme. In particular, we assess the well‐balanced property and the effective order of accuracy through an empirical convergence rate study. Schemes of up to fifth order of accuracy in both space and time are implemented and assessed. The numerical methodology is then extended to realistic networks of elastic vessels and is validated against published state‐of‐the‐art numerical solutions and experimental measurements. It is envisaged that the present scheme will constitute the building block for a closed, global model for the human circulation system involving arteries, veins, capillaries and cerebrospinal fluid. Copyright © 2013 John Wiley &amp; Sons, Ltd.</p> </abstract>