Skip to main content
Article thumbnail
Location of Repository

Self-Consistent Effective Equations Modeling Blood Flow in Medium-to-Large Compliant Arteries

By Sunčica Čanić, Daniele Lamponi, Andro Mikelić and Josip Tambača

Abstract

Abstract. We study the flow of an incompressible viscous fluid through a long tube with compliant walls. The flow is governed by a given time dependent pressure head difference. The Navier-Stokes equations for an incompressible viscous fluid are used to model the flow, and the Navier equations for a curved, linearly elastic membrane to model the wall. Employing the asymptotic techniques typically used in thin domains, we derive a set of effective equations that hold in medium-to-large compliant vessels for laminar flow regimes. The main novelty is the derivation of the effective equations that do not assume any ad hoc closure, typically assumed in the derivation of one-dimensional models. Using ideas from homogenization theory for porous media flows, we obtain a closed system of effective equations that are of Biot type with memory. Memory accounts for the wave-like phenomena in the problem. Although the equations are two-dimensional, their simple structure enables a design of a numerical algorithm that has complexity of a one-dimensional solver. Our numerical simulations show that our model captures two-dimensional effects that cannot be captured using standard one-dimensional methods. Key words. Blood flow, compliant arteries, fluid-structure interaction, effective equations. AMS subject classifications. 35Q30, 74K15, 76D27 1. Introduction. I

Year: 2005
OAI identifier: oai:CiteSeerX.psu:10.1.1.135.8012
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://math.uh.edu/~canic/pape... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.