Extended finite elements method for fluid-structure interaction with an immersed thick non-linear structure

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.