Self-Consistent Effective Equations Modeling Blood Flow in Medium-to-Large Compliant Arteries
| Autor: | Josip Tambača, Daniele Lamponi, Sunčica Čanić, Andro Mikelić |
|---|---|
| Rok vydání: | 2005 |
| Předmět: |
Biot number
fluid-structure interaction incompressible Newton fluid linear elastic membrane effective model Ecological Modeling General Physics and Astronomy Geometry Laminar flow General Chemistry Mechanics Homogenization (chemistry) Computer Science Applications Euler equations Physics::Fluid Dynamics symbols.namesake Pressure-correction method Modeling and Simulation Fluid–structure interaction symbols Reynolds-averaged Navier–Stokes equations Shallow water equations Mathematics |
| Zdroj: | Multiscale Modeling & Simulation. 3:559-596 |
| ISSN: | 1540-3467 1540-3459 |
| DOI: | 10.1137/030602605 |
| Popis: | 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 {; ; ; \sl 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. |
| Databáze: | OpenAIRE |
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