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

  • Christian Vergara
  • Stefano ZoncaEmail author
Part of the SEMA SIMAI Springer Series book series (SEMA SIMAI, volume 16)


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.



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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Authors and Affiliations

  1. 1.MOX, Dipartimento di Matematica, Politecnico di MilanoMilanoItaly

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