Mathematical and numerical modelling of fluid flow in elastic tubes

Bänsch E, Goncharova O, Koop A, Kröner D (2008)

Publication Type: Book chapter / Article in edited volumes

Publication year: 2008

Publisher: Springer

Edited Volumes: Computational Science and High Performance Computing III

Series: Notes on Numerical Fluid Mechanics and Multidisciplinary Design

Book Volume: 101

Pages Range: 102-121

DOI: 10.1007/978-3-540-69010-8_9

Abstract

The study of fluid flow inside compliant vessels, which are deformed under an action of the fluid, is important due to many biochemical and biomedical applications, e.g. the flows in blood vessels.

The mathematical problem consists of the 3D Navier-Stokes equations for incompressible fluids coupled with the differential equations, which describe the displacements of the vessel wall (or elastic structure). We study the fluid flow in a tube with different types of boundaries: inflow boundary, outflow boundary and elastic wall and prescribe different boundary conditions of Dirichlet- and Neumann types on these boundaries. The velocity of the fluid on the elastic wall is given by the deformation velocity of the wall.

In this publication we present the mathematical modelling for the elastic structures based on the shell theory, the simplifications for cylinder-type shells, the simplifications for arbitrary shells under special assumptions, the mathematical model of the coupled problem and some numerical results for the pressure-drop problem with cylindrical elastic structure.

Authors with CRIS profile

Eberhard Bänsch Lehrstuhl für Angewandte Mathematik (Wissenschaftliches Rechnen)

Involved external institutions

Albert-Ludwigs-Universität Freiburg DE Germany (DE)

How to cite

APA:

Bänsch, E., Goncharova, O., Koop, A., & Kröner, D. (2008). Mathematical and numerical modelling of fluid flow in elastic tubes. In Egon Krause, Yurii I. Shokin, Michael Resch, Nina Shokina (Eds.), Computational Science and High Performance Computing III. (pp. 102-121). Springer.

MLA:

Bänsch, Eberhard, et al. "Mathematical and numerical modelling of fluid flow in elastic tubes." Computational Science and High Performance Computing III. Ed. Egon Krause, Yurii I. Shokin, Michael Resch, Nina Shokina, Springer, 2008. 102-121.

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