Geodesic
An XFEM/DG approach for fluid-structure interaction problems with contact
Applications of Mathematics, Tome 66 (2021) no. 2, pp. 183-211.

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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.
DOI : 10.21136/AM.2021.0310-19
Classification : 65N30, 74F10, 76M10
Keywords: fluid-structure interaction; contact; extended finite element method; discontinuous Galerkin; Nitsche's method 
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Formaggia, Luca; Gatti, Federico; Zonca, Stefano. An XFEM/DG approach for fluid-structure interaction problems with contact. Applications of Mathematics, Tome 66 (2021) no. 2, pp. 183-211. doi : 10.21136/AM.2021.0310-19. http://geodesic.mathdoc.fr/articles/10.21136/AM.2021.0310-19/

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