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An Immersed Boundary Method Based on the L 2-Projection Approach

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Book cover Domain Decomposition Methods in Science and Engineering XXIV (DD 2017)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 125))

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Abstract

In this paper we present a framework for Fluid-Structure Interaction simulations. Taking inspiration from the Immersed Boundary technique introduced by Peskin (J Comput Phys 10(2):252–271, 1972) we employ the finite element method for discretizing the equations of the solid structure and the finite difference method for discretizing the fluid flow. The two discretizations are coupled by using a volume based L 2-projection approach to transfer elastic forces and velocities between the fluid and the solid domain. We present results for a Fluid–Structure Interaction benchmark which describes self-induced oscillating deformations of an elastic beam in a flow channel.

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References

  1. D. Boffi et al., On the hyper-elastic formulation of the immersed boundary method. Comput. Methods Appl. Mech. Eng. 197(25), 2210–2231 (2008)

    Article  MathSciNet  Google Scholar 

  2. D. Devendran, C.S. Peskin, An immersed boundary energy-based method for incompressible viscoelasticity. J. Comput. Phys. 231(14), 4613–4642 (2012)

    Article  MathSciNet  Google Scholar 

  3. K. Fackeldey et al., Coupling molecular dynamics and continua with weak constraints. Multiscale Model. Simul. 9(4), 1459–1494 (2011)

    Article  MathSciNet  Google Scholar 

  4. A.J. Gil et al., The immersed structural potential method for haemodynamic applications. J. Comput. Phys. 229(22), 8613–8641 (2010)

    Article  MathSciNet  Google Scholar 

  5. B.E. Griffith, X. Luo, Hybrid finite difference/finite element version of the immersed boundary method. Int. J. Numer. Methods Eng., 1–26 (2012, submitted in revised form). https://doi.org/10.1002/nme

  6. B.E. Griffith, X. Luo, Hybrid finite difference/finite element immersed boundary method. Int. J. Numer. Methods Biomed. Eng. 33(12), e2888 (2017)

    Google Scholar 

  7. R. Henniger, D. Obrist, L. Kleiser, High-order accurate iterative solution of the Navier-Stokes equations for incompressible flows. Proc. Appl. Math. Mech. 7(1), 4100009–4100010 (2007)

    Article  Google Scholar 

  8. C. Hesch et al., A mortar approach for fluid-structure interaction problems: immersed strategies for deformable and rigid bodies. Comput. Methods Appl. Mech. Eng. 278, 853–882 (2014)

    Article  MathSciNet  Google Scholar 

  9. R. Krause, P. Zulian, A parallel approach to the variational transfer of discrete fields between arbitrarily distributed unstructured finite element meshes. SIAM J. Sci. Comput. 38(3), C307–C333 (2016)

    Article  MathSciNet  Google Scholar 

  10. W.K. Liu et al., Immersed finite element method and its applications to biological systems. Comput. Methods Appl. Mech. Eng. 195(13), 1722–1749 (2006)

    Article  MathSciNet  Google Scholar 

  11. M.G.C. Nestola et al., Three-band decomposition analysis in multiscale FSI models of abdominal aortic aneurysms. Int. J. Mod. Phys. C 27(02), 1650017 (2016)

    Google Scholar 

  12. C.S. Peskin, Flow patterns around heart valves: a numerical method. J. Comput. Phys. 10(2), 252–271 (1972)

    Article  MathSciNet  Google Scholar 

  13. S. Turek, J. Hron, Proposal for numerical benchmarking of fluid-structure interaction between an elastic object and laminar incompressible flow, in Fluid-Structure Interaction (Springer, Berlin, 2006), pp. 371–385

    MATH  Google Scholar 

  14. S. Turek et al., Numerical benchmarking of fluid-structure interaction: a comparison of different discretization and solution approaches, in Fluid Structure Interaction II (Springer, Berlin, 2011), pp. 413–424

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Computational Science, Center for Computational Medicine in Cardiology (CCMC), Università della Svizzera italiana, Lugano, Switzerland

    Maria Giuseppina Chiara Nestola

  2. ARTORG Center for Biomedical Engineering Research, University of Bern, Bern, Switzerland

    Barna Becsek, Hadi Zolfaghari & Dominik Obrist

  3. Institute of Computational Science, CCMC, Università della Svizzera italiana, Lugano, Switzerland

    Patrick Zulian & Rolf Krause

Authors
  1. Maria Giuseppina Chiara Nestola
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  2. Barna Becsek
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  3. Hadi Zolfaghari
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  4. Patrick Zulian
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  5. Dominik Obrist
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  6. Rolf Krause
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Corresponding authors

Correspondence to Maria Giuseppina Chiara Nestola , Barna Becsek , Hadi Zolfaghari , Patrick Zulian , Dominik Obrist or Rolf Krause .

Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Petter E. Bjørstad

  2. Department of Mathematics, Louisana State University, Baton Rouge, LA, USA

    Susanne C. Brenner

  3. Laboratoire Analyse, Géométrie et Applications, Université Paris 13, Villetaneuse, France

    Lawrence Halpern

  4. Department of Applied Mathematics, Kyung Hee University, Yongin, Korea (Republic of)

    Hyea Hyun Kim

  5. FB Mathematik und Informatik, Freie Universität Berlin, Berlin, Germany

    Ralf Kornhuber

  6. Western Norway University of Applied Sciences, Bergen, Norway

    Talal Rahman

  7. Courant Institute of Mathematical Sciences, New York University, New York, NY, USA

    Olof B. Widlund

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Nestola, M.G.C., Becsek, B., Zolfaghari, H., Zulian, P., Obrist, D., Krause, R. (2018). An Immersed Boundary Method Based on the L 2-Projection Approach. In: Bjørstad, P., et al. Domain Decomposition Methods in Science and Engineering XXIV . DD 2017. Lecture Notes in Computational Science and Engineering, vol 125. Springer, Cham. https://doi.org/10.1007/978-3-319-93873-8_46

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