A Nitsche-Based Cut Finite Element Method for a Fluid--Structure Interaction Problem

@inproceedings{Massing2015ANC,
  title={A Nitsche-Based Cut Finite Element Method for a Fluid--Structure Interaction Problem},
  author={Andr{\'e} Massing and Mats G. Larson and Anders Logg and Marie E. Rognes},
  year={2015}
}
We present a new composite mesh finite element method for fluid-structure interaction problems. The method is based on surrounding the structure by a boundary-fitted fluid mesh that is embedded into a fixed background fluid mesh. The embedding allows for an arbitrary overlap of the fluid meshes. The coupling between the embedded and background fluid meshes is enforced using a stabilized Nitsche formulation that allows us to establish stability and optimal-order a priori error estimates. We… Expand

Figures and Tables from this paper

Extended Finite Elements Method for Fluid-Structure Interaction with an Immersed Thick Non-linear Structure
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, thatExpand
A partition of unity approach to fluid mechanics and fluid-structure interaction
TLDR
Initial results point to the potential applicability of the novel overlapping domain method to a wide range of FSI applications, enabling boundary layer refinement and large deformations without the need for re-meshing or user-defined stabilization. Expand
Numerical solution of fluid-structure interaction problems by means of a high order Discontinuous Galerkin method on polygonal grids
Abstract We consider the two-dimensional numerical approximation of the fluid-structure interaction problem over unfitted fluid and structure meshes. In particular, we consider a method where theExpand
A monolithic approach to fluid-structure interaction based on a hybrid Eulerian-ALE fluid domain decomposition involving cut elements
TLDR
To the authors' knowledge the proposed method is the only method that allows for capturing boundary layers and flow detachment via appropriate grids around largely moving and deforming bodies and is able to do this e.g. without the necessity of costly remeshing procedures. Expand
An XFEM/DG Approach for Fluid-Structure Interaction Problems with Contact
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 unfittedExpand
A Nitsche-based formulation for fluid-structure interactions with contact
We derive a Nitsche-based formulation for fluid-structure interaction (FSI) problems with contact. The approach is based on the work of Chouly and Hild (SIAM J. Numer. Anal. 51 (2013) 1295–1307) forExpand
Eulerian finite element methods for interface problems and fluid-structure interactions
In this thesis, we develop an accurate and robust numerical framework for interface problems involving moving interfaces. In particular, we are interested in the simulation of fluid-structureExpand
A cut finite element method for the Darcy problem
TLDR
This work rigorously proves the stabilized formulation based on the Nitsche formulation to be well-posed and derive a priori error estimates for the velocity and pressure fields and shows that an upper bound for the condition number of the stiffness matrix holds. Expand
To appear in Fluid-Structure Interactions . Modeling , Adaptive Discretization and Solvers
The Fully Eulerian method is a monolithic approach for fluid-structure interactions, where the two fields are coupled in a fully variational setting. The striking property of the Fully Eulerian modelExpand
A stabilized Nitsche cut finite element method for the Oseen problem
Abstract We provide the numerical analysis for a Nitsche-based cut finite element formulation for the Oseen problem, which has been originally presented for the incompressible Navier–Stokes equationsExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 66 REFERENCES
Immersed finite element method for fluid-structure interactions
In this paper, we present a detailed derivation of the numerical method, Immersed Finite Element Method (IFEM), for the solution of fluid-structure interaction problems. This method is developedExpand
The fixed‐mesh ALE approach applied to solid mechanics and fluid–structure interaction problems
In this paper we propose a method to solve Solid Mechanics and fluid–structure interaction problems using always a fixed background mesh for the spatial discretization. The main feature of the methodExpand
An eXtended Finite Element Method/Lagrange multiplier based approach for fluid-structure interaction
Abstract This paper presents a new fixed grid fluid–structure interaction scheme that can be applied to the interaction of most general structures with incompressible flow. It is based on an eXtendedExpand
A cut finite element method for a Stokes interface problem
We present a finite element method for the Stokes equations involving two immiscible incompressible fluids with different viscosities and with surface tension. The interface separating the two fluidsExpand
A Stabilized Cut Finite Element Method for the Three Field Stokes Problem
TLDR
This work proposes a Nitsche-based fictitious domain method for the three field Stokes problem in which the boundary of the domain is allowed to cross through the elements of a fixed background mesh and proves that the scheme is inf-sup stable and that it has optimal convergence properties independent of how the domain boundary intersects the mesh. Expand
An arbitrary lagrangian-eulerian finite element method for transient dynamic fluid-structure interactions
Abstract Finite element models are presented for the prediction of the non-linear response of fluid-structure systems exposed to transient dynamic loading. An arbitrary Lagrangian-EulerianExpand
A stabilized Nitsche overlapping mesh method for the Stokes problem
TLDR
A Nitsche-based formulation for a general class of stabilized finite element methods for the Stokes problem posed on a pair of overlapping, non-matching meshes is developed and it is proved that the method is stable, consistent, and optimally convergent. Expand
Nitsche's method for coupling non-matching meshes in fluid-structure vibration problems
Nitsche's method [11] is a classical method for imposing essential boundary conditions weakly. Unlike the penalty method, it is consistent with the original differential equation. The strong point ofExpand
Immersed finite element method
Abstract In this paper, the immersed finite element method (IFEM) is proposed for the solution of complex fluid and deformable structure interaction problems encountered in many physical models. InExpand
An XFEM-based embedding mesh technique for incompressible viscous flows
This paper presents a finite element embedding mesh technique to efficiently embed arbitrary fluid mesh patches into Cartesian or unstructured background fluid grids. Our motivating application forExpand
...
1
2
3
4
5
...