An XFEM/DG approach for fluid-structure interaction problems with contact

Luca Formaggia; Federico Gatti; Stefano Zonca

Applications of Mathematics (2021)

  • Volume: 66, Issue: 2, page 183-211
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Formaggia, Luca, Gatti, Federico, and Zonca, Stefano. "An XFEM/DG approach for fluid-structure interaction problems with contact." Applications of Mathematics 66.2 (2021): 183-211. <http://eudml.org/doc/297389>.

@article{Formaggia2021,
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.},
author = {Formaggia, Luca, Gatti, Federico, Zonca, Stefano},
journal = {Applications of Mathematics},
keywords = {fluid-structure interaction; contact; extended finite element method; discontinuous Galerkin; Nitsche's method},
language = {eng},
number = {2},
pages = {183-211},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An XFEM/DG approach for fluid-structure interaction problems with contact},
url = {http://eudml.org/doc/297389},
volume = {66},
year = {2021},
}

TY - JOUR
AU - Formaggia, Luca
AU - Gatti, Federico
AU - Zonca, Stefano
TI - An XFEM/DG approach for fluid-structure interaction problems with contact
JO - Applications of Mathematics
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 2
SP - 183
EP - 211
AB - 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.
LA - eng
KW - fluid-structure interaction; contact; extended finite element method; discontinuous Galerkin; Nitsche's method
UR - http://eudml.org/doc/297389
ER -

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