Skip to main content
SpringerLink
Log in
Book cover

Numerical Mathematics and Advanced Applications - ENUMATH 2013 pp 745–753Cite as

Eulerian Techniques for Fluid-Structure Interactions: Part I – Modeling and Simulation

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE,volume 103)

Abstract

This contribution is the first part of two papers on the Fully Eulerian formulation for fluid-structure interactions. We derive a monolithic variational formulation for the coupled problem in Eulerian coordinates. Further, we present the Initial Point Set method for capturing the moving interface. For the discretization of this interface problem, we introduce a modified finite element scheme that is locally fitted to the moving interface while conserving structure and connectivity of the system matrix when the interface moves. Finally, we focus on the time-discretization for this moving interface problem.

Keywords

  • Couple Problem
  • Arbitrary Lagrangian Eulerian
  • Immerse Boundary Method
  • Eulerian Formulation
  • Solid Domain

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Baiges, R. Codina, The fixed-mesh ALE approach applied to solid mechanics and fluid-structure interaction problems. Int. J. Numer. Methods Eng. 81, 1529–1557 (2010)

    MATH  MathSciNet  Google Scholar 

  2. H.-J. Bungartz, M. Schäfer (eds.), Fluid-Structure Interaction II: Modelling, Simulation, Optimisation. Lecture Notes in Computational Science and Engineering, vol. 73 (Springer, New York, 2010)

    Google Scholar 

  3. T. Dunne, An Eulerian approach to fluid-structure interaction and goal-oriented mesh refinement. Int. J. Numer. Math. Fluids. 51, 1017–1039 (2006)

    CrossRef  MATH  MathSciNet  Google Scholar 

  4. T. Dunne, R. Rannacher, T. Richter, Numerical simulation of fluid-structure interaction based on monolithic variational formulations, in Comtemporary Challenges in Mathematical Fluid Mechanics, ed. by G. Galdi, R. Rannacher (World Scientific, Singapore, 2010)

    Google Scholar 

  5. S. Frei, T. Richter, A locally modified parametric finite element method for interface problems. SIAM J. Numer. Anal. 52(5), 2315–2334 (2013)

    CrossRef  MathSciNet  Google Scholar 

  6. S. Frei, T. Richter, T. Wick, Eulerian techniques for fluid-structure interactions – part II: applications, in ENUMATH 2013 Proceedings, Lausanne. Lecture Notes in Computational Science and Engineering (Springer, 2014)

    Google Scholar 

  7. P. He, R. Qiao, A full-Eulerian solid level set method for simulation of fluid – structure interactions. Microfluid. Nanofluidics 11, 557–567 (2011)

    CrossRef  Google Scholar 

  8. A. Laadhari, R. Ruiz-Baier, A. Quarteroni, Fully Eulerian finite element approximation of a fluid-structure interaction problem in cardiac cells. Int. J. Numer. Methods Eng. 96, 712–738 (2013)

    CrossRef  MathSciNet  Google Scholar 

  9. A. Legay, J. Chessa, T. Belytschko, An Eulerian-Lagrangian method for fluid-structure interaction based on level sets. Comput. Methods Appl. Mech. Eng. 195, 2070–2087 (2006)

    CrossRef  MATH  MathSciNet  Google Scholar 

  10. U. Mayer, A. Popp, A. Gerstenberger, W. Wall, 3d fluid – structure – contact interaction based on a combined XFEM FSI and dual mortar contact approach. Comput. Mech. 46(1), 53–67 (2010)

    CrossRef  MATH  MathSciNet  Google Scholar 

  11. N. Moes, J. Dolbow, T. Belytschko, A finite element method for crack growth without remeshing. Int. J. Numer. Methods Eng. 46, 131–150 (1999)

    CrossRef  MATH  Google Scholar 

  12. C. Peskin, The immersed boundary method, in Acta Numerica 2002, vol. 1–39 (Cambridge University Press, Cambridge, 2002), pp. 1–39

    Google Scholar 

  13. T. Richter, A fully Eulerian formulation for fluid-structure interaction problems. J. Comput. Phys. 233, 227–240 (2013)

    CrossRef  MathSciNet  Google Scholar 

  14. T. Richter, T. Wick, Finite elements for fluid-structure interaction in ALE and fully Eulerian coordinates. Comput. Methods Appl. Mech. Eng. 199, 2633–2642 (2010)

    CrossRef  MATH  MathSciNet  Google Scholar 

  15. J. Sethian, Level Set Methods and Fast Marching Methods Evolving Interfaces in Computational Geometry (Cambridge University Press, Cambridge, 1999)

    MATH  Google Scholar 

  16. T. Wick, Fully Eulerian fluid-structure interaction for time-dependent problems. Comput. Methods Appl. Mech. Eng. 255, 14–26 (2013)

    CrossRef  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Heidelberg, INF 294, 69120, Heidelberg, Germany

    Stefan Frei & Thomas Richter

  2. The Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, 78712, USA

    Thomas Wick

Authors
  1. Stefan Frei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Thomas Richter
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Thomas Wick
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thomas Richter .

Editor information

Editors and Affiliations

  1. MATHICSE-ANMC, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Assyr Abdulle

  2. SB MATHICSE CMCS, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Simone Deparis

  3. SB MATHICSE ANCHP, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Daniel Kressner

  4. SB MATHICSE CSQI, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Fabio Nobile

  5. SB MATHICSE GR-PI, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Marco Picasso

Rights and permissions

Reprints and Permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Frei, S., Richter, T., Wick, T. (2015). Eulerian Techniques for Fluid-Structure Interactions: Part I – Modeling and Simulation. In: Abdulle, A., Deparis, S., Kressner, D., Nobile, F., Picasso, M. (eds) Numerical Mathematics and Advanced Applications - ENUMATH 2013. Lecture Notes in Computational Science and Engineering, vol 103. Springer, Cham. https://doi.org/10.1007/978-3-319-10705-9_74

Download citation

search

Navigation