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Hemodynamical Flows pp 333–378Cite as

Numerics of Fluid-Structure Interaction

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Part of the book series: Oberwolfach Seminars ((OWS,volume 37))

Abstract

This chapter describes numerical methods for simulating the interaction of viscous liquids with rigid or elastic bodies.

General examples of fluid-solid/structure interaction (FSI) problems are flow transporting rigid or elastic particles (particulate flow), flow around elastic structures (airplanes, submarines) and flow in elastic structures (hemodynamics, transport of fluids in closed containers). In all these settings the dilemma in modeling the coupled dynamics is that the fluid model is normally based on an Eulerian perspective in contrast to the usual Lagrangian formulation of the solid model. This makes the setup of a common variational description difficult. However, such a variational formulation of FSI is needed as the basis of a consistent Galerkin discretization with a posteriori error control and mesh adaptation, as well as the solution of optimal control problems based on the Euler-Lagrange approach.

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  1. Institute of Applied Mathematics, University of Heidelberg, Im Neuenheier Feld 293/294, D-69120, Heidelberg, Germany

    Sebastian Bönisch, Thomas Dunne & Rolf Rannacher

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  1. Sebastian Bönisch
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  2. Thomas Dunne
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Bönisch, S., Dunne, T., Rannacher, R. (2008). Numerics of Fluid-Structure Interaction. In: Hemodynamical Flows. Oberwolfach Seminars, vol 37. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7806-6_5

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