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An XFEM/DG Approach for Fluid-Structure Interaction Problems with Contact

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Abstract

In this work, we address the problem of fluid-structure interaction (FSI) with moving structures that may come into contact. We propose a penalization contact algorithm implemented in an unfitted numerical framework designed to treat large displacements. In the proposed method, the fluid mesh is fixed and the structure meshes are superimposed to it without any constraint on the conformity. Thanks to the Extended Finite Element Method (XFEM), we can treat discontinuities of the fluid solution on the mesh elements intersecting the structure. The coupling conditions at the fluid-structure interface are enforced via a discontinuous Galerkin mortaring technique, which is a penalization method that ensures the consistency of the scheme with the underlining problem. Concerning the contact problem, we consider a frictionless contact model in a master/slave approach. By considering the coupled FSI-contact problem, we perform some numerical tests to assess the sensitivity of the proposed method with respect to the discretization and contact parameters and we show some examples in the case of contact between a flexible body and a rigid wall and between two deformable structures.

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Authors and Affiliations

  1. Dipartimento di Matematica, Modellistica e calcolo scientifico (MOX), Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy

    Luca Formaggia, Federico Gatti & Stefano Zonca

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  1. Luca Formaggia
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  2. Federico Gatti
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  3. Stefano Zonca
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Correspondence to Luca Formaggia.

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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”. S. Zonca has been supported by “GNCS-INdAM”.

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Formaggia, L., Gatti, F. & Zonca, S. An XFEM/DG Approach for Fluid-Structure Interaction Problems with Contact. Appl Math 66, 183–211 (2021). https://doi.org/10.21136/AM.2021.0310-19

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