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Fluid-Structure Interaction pp 110–145Cite as

Adaptive Finite Element Approximation of Fluid-Structure Interaction Based on an Eulerian Variational Formulation

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 53))

Abstract

We propose a general variational framework for the adaptive finite element approximation of fluid-structure interaction problems. The modeling is based on an Eulerian description of the (incompressible) fluid as well as the (elastic) structure dynamics. This is achieved by tracking the movement of the initial positions of all ‘material’ points. In this approach the deformation appears as a primary variable in an Eulerian framework. Our approach uses a technique which is similar to the Level Set method in so far that it also tracks initial data, in our case the set of Initial Positions, and from this determines to which ‘phase’ a point belongs. To avoid the need for reinitialization of the initial position set, we employ the harmonic continuation of the structure velocity field into the fluid domain. Based on this monolithic model of the fluid-structure interaction we apply the dual weighted residual method for goal-oriented a posteriori error estimation and mesh adaptation to fluid-structure interaction problems. Several stationary as well as nonstationary examples are presented.

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Authors and Affiliations

  1. Institute of Applied Mathematics, University of Heidelberg, INF 294/293, 69120, Heidelberg, Germany

    Thomas Dunne & Rolf Rannacher

Authors
  1. Thomas Dunne
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  2. Rolf Rannacher
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Editor information

Editors and Affiliations

  1. Technische Universität München Institut für Informatik, Boltzmannstraße 3, 85748, Garching, Germany

    Hans-Joachim Bungartz

  2. Fachgebiet Numerische Berechnungsverfahren im Maschinenbau, Technische Universität Darmstadt, Petersenstraße 30, 64287, Darmstadt, Germany

    Michael Schäfer

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Dunne, T., Rannacher, R. (2006). Adaptive Finite Element Approximation of Fluid-Structure Interaction Based on an Eulerian Variational Formulation. In: Bungartz, HJ., Schäfer, M. (eds) Fluid-Structure Interaction. Lecture Notes in Computational Science and Engineering, vol 53. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-34596-5_6

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