An arbitrary lagrangian-eulerian finite element method for transient dynamic fluid-structure interactions

Donéa, J.; Giuliani, S.; Halleux, J.P.

doi:10.1016/0045-7825(82)90128-1

Cited by 1,325 publications

(782 citation statements)

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“…The advective velocity is correspondingly corrected to take into account the grid motion, and the interface is tracked by following the Lagrangian motion of vertices aligned initially with the interface. The flexibility in dealing with the motion of mesh vertices makes the ALE-type methods very attractive for free-surface flow simulations, and the algorithms of this type were successfully used in Hughes et al (1981), Belytschko & Flanagan (1982), Donea et al (1982), Ramaswamy & Kawahara (1986), Maury & Pironneau (1996), Bänsch (1998). All these works relied on the finite-element method and on the segregated treatment of flow-interface coupling.…”

Section: Introductionmentioning

confidence: 99%

Finite-element/level-set/operator-splitting (FELSOS) approach for computing two-fluid unsteady flows with free moving interfaces

Smolianski

2005

Int. J. Numer. Meth. Fluids

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The present work is devoted to the study on unsteady flows of two immiscible viscous fluids separated by free moving interface. Our goal is to elaborate a unified strategy for numerical modeling of twofluid interfacial flows, having in mind possible interface topology changes (like merger or break-up) and realistically wide ranges for physical parameters of the problem. The proposed computational approach essentially relies on three basic components: the finite element method for spatial approximation, the operator-splitting for temporal discretization and the level-set method for interface representation. We show that the finite element implementation of the level-set approach brings some additional benefits as compared to the standard, finite difference level-set realizations. In particular, the use of finite elements permits to localize the interface precisely, without introducing any artificial parameters like the interface thickness; it also allows to maintain the second-order accuracy of the interface normal, curvature and mass conservation. The operator-splitting makes it possible to separate all major difficulties of the problem and enables us to implement the equal-order interpolation for the velocity and pressure. Diverse numerical examples including simulations of bubble dynamics, bifurcating jet flow and Rayleigh-Taylor instability are presented to validate the computational method.

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Section: Introductionmentioning

confidence: 99%

Finite-element/level-set/operator-splitting (FELSOS) approach for computing two-fluid unsteady flows with free moving interfaces

Smolianski

2005

Int. J. Numer. Meth. Fluids

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“…In a general case, the ALE formulation allows arbitrary motion of points within a mesh with respect to their frame of reference by taking the convection of these points into account, as described in [15,16] and many others. In the case of a FSI analysis, points within the reference spatial domain are moved in a Lagrangian manner to capture the moving interface between the fluid and the structure.…”

Section: Introductionmentioning

confidence: 99%

A partitioned coupling approach for dynamic fluid–structure interaction with applications to biological membranes

Wood

Gil

Hassan

et al. 2008

Numerical Methods in Fluids

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SUMMARYThis paper presents a fully coupled three-dimensional solver for the analysis of time-dependent fluidstructure interaction. A partitioned time-marching algorithm is employed for the solution to the timedependent coupled discretized problem, thus enabling the use of highly developed, robust and well-tested solvers for each field. Coupling of the fields is achieved through a conservative transfer of information at the fluid-structure interface. An implicit coupling is achieved when the solutions to the fluid and structure subproblems are cycled at each time step until convergence is reached. The three-dimensional unsteady incompressible fluid is solved using a powerful implicit dual time-stepping technique with an explicit multistage Runga-Kutta time stepping in pseudo-time and arbitrary Lagrangian-Eulerian formulation for the moving boundaries. A finite element dynamic analysis of the highly deformable structure is carried out with a numerical strategy combining the implicit Newmark time integration algorithm with a NewtonRaphson second-order optimization method. Various test cases are presented for benchmarking and to demonstrate the potential applications of this method.

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“…The essential idea of ALE method is to formulate and solve the fluid problem on a deforming mesh, which deforms with the structure at the interface and then the fluid mesh is smoothed within the fluid domain. First introduced for finite element discretizations of the incompressible fluids in [30,19], the ALE method provides an approach to find the fluid mesh that can fit the moving fluid domain Ω f . This mapping is a diffeomorphism on the continuous level, and we use piecewise polynomials to approximate it on the discrete level.…”

Section: Application Of Ale Methods To the Fsi Problemmentioning

confidence: 99%

Modeling and simulations for fluid and rotating structure interactions

Yang

Sun

Wang

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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In this paper, we study a dynamic fluid-structure interaction (FSI) model for an elastic structure that is immersed and spinning in the fluid. We develop a linear constitutive model to describe the motion of a rotational elastic structure which is suitable for the application of arbitrary LagrangianEulerian (ALE) method in FSI simulation. Additionally, a novel ALE mapping method is designed to generate the moving fluid mesh while the deformable structure spins in a non-axisymmetric fluid channel. The structure velocity is adopted as the principle unknown to form a monolithic saddle-point system together with fluid velocity and pressure. We discretize the nonlinear saddle-point system with mixed finite element method and Newton's linearization, and prove that the derived saddle-point problem is well-posed. The developed methodology is applied to a self-defined elastic structure and a realistic hydroturbine under a prescribed angular velocity. Both illustrate the satisfactory numerical results of an elastic structure that is deforming and rotating while interacting with the fluid. The numerical validation is also conducted to demonstrate the modeling consistency.

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An arbitrary lagrangian-eulerian finite element method for transient dynamic fluid-structure interactions

Cited by 1,325 publications

References 10 publications

Finite-element/level-set/operator-splitting (FELSOS) approach for computing two-fluid unsteady flows with free moving interfaces

Finite-element/level-set/operator-splitting (FELSOS) approach for computing two-fluid unsteady flows with free moving interfaces

A partitioned coupling approach for dynamic fluid–structure interaction with applications to biological membranes

Modeling and simulations for fluid and rotating structure interactions

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