A monolithic approach to fluid‐structure interaction based on a hybrid Eulerian‐ALE fluid domain decomposition involving cut elements

Schott, Benedikt; Ager, Christoph; Wall, Wolfgang A.

doi:10.1002/nme.6047

Cited by 25 publications

(20 citation statements)

References 51 publications

(205 reference statements)

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“…This renders such approaches highly attractive, eg, for interactions of solids with turbulent incompressible flows, in which capturing boundary layer effects in the vicinity of solids is a crucial task. For a detailed presentation including numerical examples of Approach 5, hybrid Eulerian-ALE within a monolithic framework, the reader is referred to the work of Schott et al 58 This overview of a number of novel approaches indicates high flexibility when incorporating non-interface-fitted meshes to the overall discretization concept for FSI. Depending on the FSI problem configuration, the expected structural deformation, and the need to account for topological changes or to even support contact or detachment processes of solids, the proposed Approaches 1-5 can exploit their capabilities in different situations.…”

Section: Approach 3 (Unfitted-ale: Unfitted Moving Fluid Mesh Technimentioning

confidence: 99%

Monolithic cut finite element–based approaches for fluid‐structure interaction

Schott

Ager

Wall

2019

Numerical Meth Engineering

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Summary Cut finite element method–based approaches toward challenging fluid‐structure interaction (FSI) are proposed. The different considered methods combine the advantages of competing novel Eulerian (fixed grid) and established arbitrary Lagrangian‐Eulerian (moving mesh) finite element formulations for the fluid. The objective is to highlight the benefit of using cut finite element techniques for moving‐domain problems and to demonstrate their high potential with regard to simplified mesh generation, treatment of large structural motions in surrounding flows, capturing boundary layers, their ability to deal with topological changes in the fluid phase, and their general straightforward extensibility to other coupled multiphysics problems. In addition to a pure fixed‐grid FSI method, advanced fluid‐domain decomposition techniques are also considered, leading to highly flexible discretization methods for the FSI problem. All stabilized formulations include Nitsche‐based weak coupling of the phases supported by the ghost penalty technique for the flow field. For the resulting systems, monolithic solution strategies are presented. Various two‐ and three‐dimensional FSI cases of different complexity levels validate the methods and demonstrate their capabilities and limitations in different situations.

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Section: Approach 3 (Unfitted-ale: Unfitted Moving Fluid Mesh Technimentioning

confidence: 99%

Monolithic cut finite element–based approaches for fluid‐structure interaction

Schott

Ager

Wall

2019

Numerical Meth Engineering

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“…A strong effect is expected to arise especially from the discontinuous viscous fluid stress on the interface between single fluid elements. This issue can be resolved by an increase of the resolution of the computational fluid mesh close to the interface Γ FP or a hybrid approach as presented in [30,48].…”

Section: Computed Results and Discussionmentioning

confidence: 99%

“…This includes fluid pressure and deformation dependent varying porosity and therefore provides an insight into the modeling potential of the poroelastic formulation. The requirement for a sufficiently resolved fixed grid fluid domain close to the interface or a hybrid approach as presented in [30,48] is highlighted by oscillations of the relative velocity in the poroelastic domain. Nevertheless, the large interface motion and deformation of the permeable structure for this problem configuration shows the advantages of the applied poroelastic formulation and the CutFEM approach.…”

Section: Resultsmentioning

confidence: 99%

“…Development of the CutFEM, as it will be applied to fluid equations, started by analyses on the Poisson equation [19], the Stokes equation [20,21], and finally, including advection, the Oseen equation [22,23]. It has been successfully applied to various applications including two-phase flow [24][25][26] and fluid-structure interaction [27][28][29][30]. Herein, a weak imposition of the interface constraint through Nitsche-based methods and the stabilization of "cut" elements by a so-called Ghost-Penalty stabilization [31] are the predominant approaches.…”

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confidence: 99%

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A Nitsche-based cut finite element method for the coupling of incompressible fluid flow with poroelasticity

Ager

Schott

Winter

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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The focus of this contribution is the numerical treatment of interface coupled problems concerning the interaction of incompressible fluid flow and permeable, elastic structures. The main emphasis is on extending the range of applicability of available formulations on especially three aspects. These aspects are the incorporation of a more general poroelasticity formulation, the use of the cut finite element method (CutFEM) to allow for large interface motion and topological changes of the fluid domain, and the application of a novel Nitsche-based approach to incorporate the Beavers-Joseph (-Saffmann) tangential interface condition. This last aspect allows one to extend the practicable range of applicability of the proposed formulation down to very low porosities and permeabilities which is important in several examples in application. Different aspects of the presented formulation are analyzed in a numerical example including spatial convergence, the sensitivity of the solution to the Nitsche penalty parameters, varying porosities and permeabilities, and a varying Beavers-Joseph interface model constant. Finally, a numerical example analyzing the fluid induced bending of a poroelastic beam provides evidence of the general applicability of the presented approach.C. Ager et al. / 1-25 2 mechanics model valid for "small" deformation. In the fluid domain, the Stokes equations [3,5,7,8] or, including the effect of convection, the Navier-Stokes equations [4,6] are applied. On the fluid-poroelastic interface, either the Beavers-Joseph-Saffmann [3][4][5]7] or a "no-slip" condition [5,6,8] in tangential interface direction are consulted. Details on these interface conditions for the coupling of fluid and (rigid-)porous flow can be found in [10][11][12][13][14] and the references therein.Motivated by the specific requirements of a fluid-poroelastic interaction (FPI) formulation to model rough surface contact in fluid-structure interaction (as in [2]), we extend the range of applicability of these formulations by several aspects. First, a more general formulation for the poroelastic domain, which is based on the same fundamental physical equations as the classical Biot-system, is applied. This formulation allows one to take into account large deformation and the motion of the poroelastic domain, a wide variety of material models by arbitrary strain energy density functions, and varying deformation dependent porosity (see [15][16][17] for details on this formulation and [18] for fundamentals). Second, in order to allow for large deformation and motion or even topological changes of the fluid domain, a cut finite element method (CutFEM) is applied. Herein, a non-interface-fitted, fixed-grid Eulerian computational mesh for the fluid domain is combined with an interface fitted computational mesh of the poroelastic domain in Lagrangian description w.r.t. the displacements of the poroelastic solid phase. Development of the CutFEM, as it will be applied to fluid equations, started by analyses on the Poisson equation [19], the Stok...

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“…In the first one, a problem specific solver is written to find the solution in a monolithic way. This solver takes the interaction between the governing equations into account directly by solving them simultaneously [1]. In the second approach, the calculation is done in a partitioned way.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Different Quasi-Newton Techniques for Coupling of Black Box Solvers

Delaissé¹,

Demeester²,

Fauconnier³

et al. 2021

14th WCCM-ECCOMAS Congress

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Fluid-structure interaction (FSI) problems are frequently solved using partitioned simulation techniques with black-box solvers, reusing reliable and optimized codes. These problems can principally be reduced to solving a root-finding problem. In case of strong coupling, pure Gauss-Seidel iterations between the structure and flow solvers are unstable for lower modes. In these cases, quasi-Newton techniques are used, which construct an approximation of the Jacobian or its inverse by reusing information from previous iterations and time steps. Four different quasi-Newton techniques are compared: the interface quasi-Newton algorithm with an approximation for the inverse of the Jacobian from a least-squares model (IQN-ILS), the interface block quasi-Newton algorithm with approximate Jacobians from least-squares models (IBQN-LS), the interface quasi-Newton technique with multiple vector Jacobian (IQN-MVJ) and the multi-vector update quasi-Newton technique (MVQN). These coupling algorithms are differentiated based on whether the approximation of the Jacobian is performed for the entire black-box system (IQN-ILS and IQN-MVJ) or for both individual solvers (IBQN-LS and MVQN). Moreover, a distinction is made between methods which perform the approximation with either least-squares models (IQN-ILS and IBQN-LS) or multivector techniques (IQN-MVJ and MVQN). Their performance is compared by solving a 1D flexible tube case, using the in-house coupling software CoCoNuT. Both the memory usage and number of iterations between structure and flow solvers in each time step are examined. The techniques using a multi-vector approach require explicit matrix construction, so that memory requirements scale quadratically, whereas the least-squares techniques have a matrix-free implementation, resulting in linear scaling. In terms of convergence they are comparable.

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A monolithic approach to fluid‐structure interaction based on a hybrid Eulerian‐ALE fluid domain decomposition involving cut elements

Cited by 25 publications

References 51 publications

Monolithic cut finite element–based approaches for fluid‐structure interaction

Monolithic cut finite element–based approaches for fluid‐structure interaction

A Nitsche-based cut finite element method for the coupling of incompressible fluid flow with poroelasticity

Comparison of Different Quasi-Newton Techniques for Coupling of Black Box Solvers

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