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Extended Finite Elements Method for Fluid-Structure Interaction with an Immersed Thick Non-linear Structure

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Mathematical and Numerical Modeling of the Cardiovascular System and Applications

Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 16))

Abstract

We consider an Extended Finite Element method to solve fluid-structure interaction problems in the case of an immersed thick structure described by non-linear finite elasticity. This method, that belongs to the family of the Cut Finite Element methods, allows to consider unfitted meshes for the fluid and solid domains by maintaining the fluid mesh fixed in time as the solid moves. We review the state of the art about the numerical methods for fluid-structure interaction problems and we present an overview of the Cut Finite Element methods. We describe the numerical discretization proposed here to handle the case of a thick immersed structure with size comparable or smaller than the fluid mesh element size in the case of non-linear finite elasticity. Finally, we present some three-dimensional numerical results of the proposed method.

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Acknowledgements

The authors gratefully acknowledge the financial support of the Italian MIUR by the grant PRIN12, number 201289A4LX, “Mathematical and numerical models of the cardiovascular system, and their clinical applications”. C. Vergara has been partially supported by the H2020-MSCA-ITN-2017, EU project 765374 “ROMSOC—Reduced Order Modelling, Simulation and Optimization of Coupled systems”.

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  1. MOX, Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Christian Vergara & Stefano Zonca

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  1. Christian Vergara
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  2. Stefano Zonca
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Correspondence to Stefano Zonca .

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Editors and Affiliations

  1. Department of Mathematics “F. Casorati”, University of Pavia, Pavia, Italy

    Daniele Boffi

  2. Department of Mathematics “F. Casorati”, University of Pavia, Pavia, Italy

    Luca F. Pavarino

  3. SISSA mathLab, Mathematics Area, International School for Advanced Studies, Trieste, Italy

    Gianluigi Rozza

  4. Department of Mathematics, University of Milan, Milano, Italy

    Simone Scacchi

  5. Department of Mathematics, Politecnico di Milano, Milano, Italy

    Christian Vergara

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Vergara, C., Zonca, S. (2018). Extended Finite Elements Method for Fluid-Structure Interaction with an Immersed Thick Non-linear Structure. In: Boffi, D., Pavarino, L., Rozza, G., Scacchi, S., Vergara, C. (eds) Mathematical and Numerical Modeling of the Cardiovascular System and Applications. SEMA SIMAI Springer Series, vol 16. Springer, Cham. https://doi.org/10.1007/978-3-319-96649-6_9

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