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Benchmarking the immersed finite element method for fluid-structure interaction problems

COMPUTERS & MATHEMATICS WITH APPLICATIONS 2015年第10期69卷 1167-1188页

作者： Roy, Saswati Heltai, Luca Costanzo, Francesco Penn State Univ Dept Engn Sci & Mech University Pk PA 16802 USA Scuola Int Super Studi Avanzati I-34136 Trieste Italy Penn State Univ Ctr Neural Engn University Pk PA 16802 USA

We present an implementation of a fully variational formulation of an immersed method for fluid-structure interaction problems based on the finite element method. While typical implementation of immersed methods are characterized by the use of approximate Dirac delta distributions, fully variational formulations of the method do not require the use of said distributions. In our implementation the immersed solid is general in the sense that it is not required to have the same mass density and the same viscous response as the surrounding fluid. We assume that the immersed solid can be either viscoelastic of differential type or hyperelastic. Here we focus on the validation of the method via various benchmarks for fluid-structure interaction numerical schemes. This is the first time that the interaction of purely elastic compressible solids and an incompressible fluid is approached via an immersed method allowing a direct comparison with established benchmarks. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： fluid-structure interaction fluid-structure interaction benchmarking Immersed boundary methods Immersed finite element method Finite element immersed boundary method

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A time splitting fictitious domain algorithm for fluid-structure interaction problems (A fictitious domain algorithm for FSI)

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JOURNAL OF fluidS AND structureS 2015年 58卷 109-126页

作者： Roshchenko, Andriy Minev, Peter D. Finlay, Warren H. Univ Alberta Dept Math & Stat Sci Edmonton AB T6G 2G1 Canada Univ Alberta Dept Mech Engn Edmonton AB T6G 2G1 Canada

A Finite Element Method in mixed Eulerian and Lagrangian formulation is developed to allow direct numerical simulations of dynamical interaction between an incompressible fluid and a hyper-elastic incompressible solid. A Fictitious Domain Method is applied so that the fluid is extended inside the deformable solid volume and the velocity field in the entire computational domain is resolved in an Eulerian framework. Solid motion, which is tracked in a Lagrangian framework, is imposed through the body force acting on the fluid within the solid boundaries. Solid stress smoothing on the Lagrangian mesh is performed with the Zienlciewicz-Zhu patch recovery method. High-order Gaussian integration quadratures over cut elements are used in order to avoid sub-meshing within elements in the Eulerian mesh that are intersected by the Lagrangian grid. The algorithm is implemented and verified in two spatial dimensions by comparing with the well validated simulations of solid deformation in a lid driven cavity and periodic elastic wall deformation driven by a time-dependent flow. It shows good agreement with the numerical results reported in the literature. In 3-D the method is validated against previously reported numerical simulations of 3-D rhythmically contracting alveolated ducts. (c) 2015 Elsevier Ltd. All rights reserved.

关键词： fluid-structure interaction Finite elements Eulerian formulation Body force Alveoli

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Generalized Robin-Neumann explicit coupling schemes for incompressible fluid-structure interaction: Stability analysis and numerics

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2015年第3期101卷 199-229页

作者： Fernandez, Miguel A. Mullaert, Jimmy Vidrascu, Marina Inria REO Project Team F-78153 Le Chesnay France Univ Paris 06 UMR 7958 LJLL REO Project Team F-75005 Paris France

We introduce a new class of explicit coupling schemes for the numerical solution of fluid-structure interaction problems involving a viscous incompressible fluid and an elastic structure. These methods generalize the arguments reported in [Comput. Methods Appl. Mech. Engrg., 267:566-593, 2013, Numer. Math., 123(1):21-65, 2013] to the case of the coupling with thick-walled structures. The basic idea lies in the derivation of an intrinsic interface Robin consistency at the space semi-discrete level, using a lumped-mass approximation in the structure. The fluid-solid splitting is then performed through appropriate extrapolations of the solid velocity and stress on the interface. Based on these methods, a new, parameter-free, Robin-Neumann iterative procedure is also proposed for the partitioned solution of implicit coupling. A priori energy estimates, guaranteeing the stability of the schemes and the convergence of the iterative procedure, are established within a representative linear setting. The accuracy and performance of the methods are illustrated in several numerical examples. Copyright (c) 2014 John Wiley & Sons, Ltd.

关键词： fluid-structure interaction incompressible fluid thick-walled structure explicit coupling scheme Robin-Neumann methods

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Time consistent fluid structure interaction on collocated grids for incompressible flow

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2016年 298卷 159-182页

作者： Gillebaart, T. Blom, D. S. van Zuijlen, A. H. Bijl, H. Delft Univ Technol Fac Aerosp Engn NL-2600 GB Delft Netherlands

Consistent time integration on collocated grids for incompressible flow has been studied for static grids using the PISO method, in which the dependencies on time-step size and under-relaxation has been studied in detail. However, for moving grids a detailed description is still missing. Therefore, a step by step analysis of a time consistent fluid-structure interaction (FSI) method for incompressible flow on collocated grids is presented. The method consist of: face normal and area correction for moving grids, treatment of velocity boundary conditions for no-slip walls, time integration of structure equations and fluid force interpolation to structure. The basis of the method is the PISO method of the incompressible Navier-Stokes equations. Time consistency on static grids is shown first, after which time consistency on moving grids is described and analyzed. For moving grids consistent time integration is described in two ways: (1) constructing the face velocities from a normal and tangential component, and (2) correcting the face flux with a face normal and face area correction. For both descriptions the general formulation for the backward differencing schemes (BDF) are given and the correct behavior of the first, second and third order schemes is demonstrated by means of an academic test case (circular cavity flow). Additionally, the (force) coupling from the fluid to the structure is discussed in detail for combining a fourth order explicit Runge Kutta scheme for the structure with a BDF scheme for the fluid. Three interpolations for the fluid forces are shown, which result in either a first order or second order FSI scheme. Third order FSI is demonstrated when the third order BDF scheme is applied on both the structure and fluid equations. Also, under-relaxation for the fluid equations is considered and it is demonstrated that the order of the three BDF schemes are independent of the underrelaxation factor. Finally, the proposed method of time consistent FSI

关键词： fluid-structure interaction Consistent time integration Collocated grids Incompressible flow Moving grids PISO

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A computational framework for the simulation of high-speed multi-material fluid-structure interaction problems with dynamic fracture

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2015年第7期104卷 585-623页

作者： Wang, K. G. Lea, P. Farhat, C. Virginia Polytech Inst & State Univ Dept Aerosp & Ocean Engn Blacksburg VA 24061 USA Stanford Univ Dept Aeronaut & Astronaut Stanford CA 94305 USA Stanford Univ Dept Mech Engn Stanford CA 94305 USA Stanford Univ Inst Computat & Math Engn Stanford CA 94305 USA

A robust computational framework for the solution of fluid-structure interaction problems characterized by compressible flows and highly nonlinear structures undergoing pressure-induced dynamic fracture is presented. This framework is based on the finite volume method with exact Riemann solvers for the solution of multi-material problems. It couples a Eulerian, finite volume-based computational approach for solving flow problems with a Lagrangian, finite element-based computational approach for solving structural dynamics and solid mechanics problems. Most importantly, it enforces the governing fluid-structure transmission conditions by solving local, one-dimensional, fluid-structure Riemann problems at evolving structural interfaces, which are embedded in the fluid mesh. A generic, comprehensive, and yet effective approach for representing a fractured fluid-structure interface is also presented. This approach, which is applicable to several finite element-based fracture methods including inter-element fracture and remeshing techniques, is applied here to incorporate in the proposed framework two different and popular approaches for computational fracture in a seamless manner: the extended FEM and the element deletion method. Finally, the proposed embedded boundary computational framework for the solution of highly nonlinear fluid-structure interaction problems with dynamic fracture is demonstrated for one academic and three realistic applications characterized by detonations, shocks, large pressure, and density jumps across material interfaces, dynamic fracture, flow seepage through narrow cracks, and structural fragmentation. Correlations with experimental results, when available, are also reported and discussed. For all four considered applications, the relative merits of the extended FEM and element deletion method for computational fracture are also contrasted and discussed. Copyright (C) 2015 John Wiley & Sons, Ltd.

关键词： crack element deletion embedded boundary method FIVER fluid-structure interaction fracture immersed boundary method multi-phase flow XFEM

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A three-field stabilized finite element method for fluid-structure interaction: elastic solid and rigid body limit

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2015年第7期104卷 566-584页

作者： Hachem, E. Feghali, S. Coupez, T. Codina, R. MINES ParisTech Ctr Mat Forming CEMEF UMR CNRS 7635 Sophia Antipolis France Univ Politecn Cataluna ES-08034 Barcelona Spain

We propose a full Eulerian framework for solving fluid-structure interaction (FSI) problems based on a unified formulation in which the FSIs are modelled by introducing an extra stress in the momentum equation. The obtained three-field velocity, pressure and stress system is solved using a stabilized finite element method. The key feature of this unified formulation is the ability to describe different kind of interactions between the fluid and the structure, which can be either elastic or a perfect rigid body, without the need of treating this last case via penalization. The level-set method combined with a dynamic anisotropic mesh adaptation is used to track the fluid-solid interface. Copyright (C) 2015 John Wiley & Sons, Ltd.

关键词： fluid-structure interaction Eulerian description rigid body limit stabilized finite element method anisotropic mesh adaptation

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Numerical simulation of fluid-structure interaction with the volume penalization method

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JOURNAL OF COMPUTATIONAL PHYSICS 2015年 281卷 96-115页

作者： Engels, Thomas Kolomenskiy, Dmitry Schneider, Kai Sesterhenn, Joern CNRS Lab Mecan Modelisat & Proc Propres M2P2 F-75700 Paris France Aix Marseille Univ Marseille France TU Berlin ISTA Berlin Germany McGill Univ Dept Math & Stat Montreal PQ Canada

We present a novel scheme for the numerical simulation of fluid-structure interaction problems. It extends the volume penalization method, a member of the family of immersed boundary methods, to take into account flexible obstacles. We show how the introduction of a smoothing layer, physically interpreted as surface roughness, allows for arbitrary motion of the deformable obstacle. The approach is carefully validated and good agreement with various results in the literature is found. A simple one-dimensional solid model is derived, capable of modeling arbitrarily large deformations and imposed motion at the leading edge, as it is required for the simulation of simplified models for insect flight. The model error is shown to be small, while the one-dimensional character of the model features a reasonably easy implementation. The coupled fluid-solid interaction solver is shown not to introduce artificial energy in the numerical coupling, and validated using a widely used benchmark. We conclude with the application of our method to models for insect flight and study the propulsive efficiency of one and two wing sections. (C) 2014 Elsevier Inc. All rights reserved.

关键词： fluid-structure interaction Insect flight Volume-penalization method Spectral method

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Hemodynamic and thrombogenic analysis of a trileaflet polymeric valve using a fluid-structure interaction approach

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JOURNAL OF BIOMECHANICS 2015年第13期48卷 3641-3649页

作者： Piatti, Filippo Sturla, Francesco Marom, Gil Sheriff, Jawaad Claiborne, Thomas E. Slepian, Marvin J. Redaelli, Alberto Bluestein, Danny Politecn Milan Dept Elect Informat & Bioengn I-20133 Milan Italy SUNY Stony Brook Dept Biomed Engn Stony Brook NY 11794 USA Univ Arizona Sarver Heart Ctr Tucson AZ USA

Surgical valve replacement in patients with severe calcific aortic valve disease using either bioprosthetic or mechanical heart valves is still limited by structural valve deterioration for the former and thrombosis risk mandating anticoagulant therapy for the latter. Prosthetic polymeric heart valves have the potential to overcome the inherent material and design limitations of these valves, but their development is still ongoing. The aim of this study was to characterize the hemodynamics and thrombogenic potential of the Polynova polymeric trileaflet valve prototype using a fluid-structure interaction (FSI) approach. The FSI model replicated experimental conditions of the valve as tested in a left heart simulator. Hemodynamic parameters (transvalvular pressure gradient, flow rate, maximum velocity, and effective orifice area) were compared to assess the validity of the FSI model. The thrombogenic footprint of the polymeric valve was evaluated using a Lagrangian approach to calculate the stress accumulation (SA) values along multiple platelet trajectories and their statistical distribution. in the commissural regions, platelets were exposed to the highest SA values because of highest stress levels combined with local reverse flow patterns and vortices. Stress-loading waveforms from representative trajectories in regions of interest were emulated in our hemodynamic shearing device (HSD). Platelet activity was measured using our platelet activation state (PAS) assay and the results confirmed the higher thrombogenic potential of the commissural hotspots. In conclusion, the proposed method provides an in depth analysis of the hemodynamic and thrombogenic performance of the polymer valve prototype and identifies locations for further design optimization. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Trileaflet polymeric valve fluid-structure interaction Hemodynamic prediction Particle tracking analysis Platelet activation

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Partitioned solution algorithms for fluid-structure interaction problems with hyperelastic models

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2015年第0期276卷 47-61页

作者： Langer, Ulrich Yang, Huidong Austrian Acad Sci Johann Radon Inst Computat & Appl Math A-4040 Linz Austria

In this work, we consider fluid-structure interaction simulation with nonlinear hyperelastic models in the solid part. We use a partitioned approach to deal with the coupled nonlinear fluid-structure interaction problems. We focus on handling the nonlinearity of the fluid and structure sub-problems using (adaptive) Newton's method, the near-incompressibility of materials, the stabilization of employed finite element discretization, and the robustness and efficiency of Krylov subspace and algebraic multigrid methods for the linearized algebraic equations. (C) 2014 Elsevier B.V. All rights reserved.

关键词： fluid-structure interaction Hyperelastic models Stabilized finite element discretization (adaptive) Newton's method Krylov subspace method Algebraic multigrid method

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Influential fluid-structure interaction modelling parameters on the response of bridges vulnerable to coastal storms

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structure AND INFRAstructure ENGINEERING 2015年第3期11卷 321-333页

作者： Ataei, Navid Padgett, Jamie E. Rice Univ Dept Civil & Environm Engn Houston TX 77005 USA

Analysis of coastal bridges under hurricane-induced wave and surge loads is essential for safety and performance assessment of water crossing bridge inventories. A reliable numerical model that can be employed to study the behaviour of bridges in hurricane events is beneficial because it reduces the cost and effort required for experimental models. Furthermore, it is important to identify modelling parameters that have a significant effect on the simulated response in order to guide uncertainty treatment for future bridge reliability studies. To address these needs, a high fidelity numerical model for simulation of coastal bridges is utilised that takes into account the fluid-structure interaction and includes contact surfaces that permit deck shifting and unseating during surge and wave passage. After validation of the model with experimental test data, it is implemented to examine the response of a typical water crossing bridge in the Houston area, revealing the values of wave and surge loads and also the potential of deck unseating under extreme wave and surge conditions. A sensitivity study is conducted to determine the uncertain structural modelling parameters that significantly affect the bridge response when subjected to surge and wave. Concrete strength and density, coefficient of friction between super- and substructure and soil shear strength are found to influence the bridge response and should be considered in probabilistic analyses and reliability assessments of coastal bridges.

关键词： coastal bridges fluid-structure interaction sensitivity study hurricane

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