# 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.

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### 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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