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A comparative analysis of Lagrange multiplier and penalty approaches for modelling fluid-structure interaction

ENGINEERING COMPUTATIONS 2021年第4期38卷 1677-1705页

作者： Brandsen, Jacobus D. Vire, Axelle Turteltaub, Sergio R. Van Bussel, Gerard J. W. Delft Univ Technol Wind Energy Grp Fac Aerosp Engn Delft Netherlands Delft Univ Technol Aerosp Struct & Computat Mech Grp Fac Aerosp Engn Delft Netherlands

Purpose When simulating fluid-structure interaction (FSI), it is often essential that the no-slip condition is accurately enforced at the wetted boundary of the structure. This paper aims to evaluate the relative strengths and limitations of the penalty and Lagrange multiplier methods, within the context of modelling FSI, through a comparative analysis. Design/methodology/approach In the immersed boundary method, the no-slip condition is typically imposed by augmenting the governing equations of the fluid with an artificial body force. The relative accuracy and computational time of the penalty and Lagrange multiplier formulations of this body force are evaluated by using each to solve three test problems, namely, flow through a channel, the harmonic motion of a cylinder through a stationary fluid and the vortex-induced vibration (VIV) of a cylinder. Findings The Lagrange multiplier formulation provided an accurate solution, especially when enforcing the no-slip condition, and was robust as it did not require "tuning" of problem specific parameters. However, these benefits came at a higher computational cost relative to the penalty formulation. The penalty formulation achieved similar levels of accuracy to the Lagrange multiplier formulation, but only if the appropriate penalty factor was selected, which was difficult to determine a priori. Originality/value Both the Lagrange multiplier and penalty formulations of the immersed boundary method are prominent in the literature. A systematic quantitative comparison of these two methods is presented within the same computational environment. A novel application of the Lagrange multiplier method to the modelling of VIV is also provided.

关键词： Penalty Finite element fluid-structure interaction Lagrange multiplier Immersed boundary

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An optimal control method for time-dependent fluid-structure interaction problems

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2021年第4期64卷 1939-1962页

作者： Wang, Yongxing Jimack, Peter K. Walkley, Mark A. Yang, Dongmin Thompson, Harvey M. Univ Leeds Sch Mech Engn Leeds W Yorkshire England Univ Leeds Sch Comp Leeds W Yorkshire England Univ Edinburgh Sch Engn Edinburgh Midlothian Scotland

In this article, we derive an adjoint fluid-structure interaction (FSI) system in an arbitrary Lagrangian-Eulerian (ALE) framework, based upon a one-field finite element method. A key feature of this approach is that the interface condition is automatically satisfied and the problem size is reduced since we only solve for one velocity field for both the primary and adjoint system. A velocity (and/or displacement)-matching optimisation problem is considered by controlling a distributed force. The optimisation problem is solved using a gradient descent method, and a stabilised Barzilai-Borwein method is adopted to accelerate the convergence, which does not need additional evaluations of the objective functional. The proposed control method is validated and assessed against a series of static and dynamic benchmark FSI problems, before being applied successfully to solve a highly challenging FSI control problem.

关键词： Optimal control Adjoint optimisation fluid-structure interaction Finite element Arbitrary Lagrangian-Eulerian

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In Vitro Clot Trapping Efficiency of the FDA Generic Inferior Vena Cava Filter in an Anatomical Model: An Experimental fluid-structure interaction Benchmark

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CARDIOVASCULAR ENGINEERING AND TECHNOLOGY 2021年第3期12卷 339-352页

作者： Riley, J. M. Price, N. S. Saaid, H. M. Good, B. C. Aycock, K. I. Craven, B. A. Manning, K. B. Penn State Univ Dept Biomed Engn 122 Chem & Biomed Engn Bldg University Pk PA 16802 USA US FDA Div Appl Mech Off Sci & Engn Labs Ctr Devices & Radiol Hlth Silver Spring MD USA Penn State Hershey Med Ctr Dept Surg Hershey PA USA

Purpose-Robust experimental data for performing validation of fluid-structure interaction (FSI) simulations of the transport of deformable solid bodies in internal flow are currently lacking. This in vitro experimental study characterizes the clot trapping efficiency of a new generic conical-type inferior vena cava (IVC) filter in a rigid anatomical model of the IVC with carefully characterized test conditions, fluid rheological properties, and clot mechanical properties. Methods-Various sizes of spherical and cylindrical clots made of synthetic materials (nylon and polyacrylamide gel) and bovine blood are serially injected into the anatomical IVC model under worst-case exercise flow conditions. Clot trapping efficiencies and their uncertainties are then quantified for each combination of clot shape, size, and material. Results-Experiments reveal the clot trapping efficiency increases with increasing clot diameter and length, with trapping efficiencies ranging from as low as approximately 42% for small 3.2 mm diameter spherical clots up to 100% for larger clot sizes. Because of the asymmetry of the anatomical IVC model, the data also reveal the iliac vein of clot origin influences the clot trapping efficiency, with the trapping efficiency for clots injected into the left iliac vein up to a factor of 7.5 times greater than that for clots injected into the right iliac (trapping efficiencies of approximately 10% versus 75%, respectively). Conclusion-Overall, this data set provides a benchmark for validating simulations predicting IVC filter clot trapping efficiency and, more generally, low-Reynolds number FSI modeling.

关键词： Pulmonary embolism Inferior vena cava filter Blood clots Clot trapping efficiency fluid-structure interaction

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Investigation the effect of geometry and position of polymeric heart valves on hemodynamic with fluid-structure interaction numerical method

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MEDICAL ENGINEERING & PHYSICS 2021年 97卷 10-17页

作者： Farokhi, Ehsan Alizad Niroomand-Oscuii, Hanieh Yazdanpanah, Kohyar Sahand Univ Technol Dept Biomed Engn Tabriz Iran

ABS T R A C T Computational modeling and numerical simulation of heart valve dynamics incorporating both fluid dynamics and valve structural replications has been challenging. In this study, we developed a double-coupled fluid-structure interaction (FSI) model using arbitrary lagrangian eulerian(ALE) and steered adaptive mesh(SAM). So we were looking to simulate transcatheter aortic valve (TAV) hemodynamic performance throughout entire cardiac cycles [1]. To reach this object, semi-real geometry of aorta and aortic polymeric valves has been created. At model inlet, left ventricular pressure and at the model outlet the elastic porous tube have been considered. Nonlinear finite element way and Sparse solver was utilized to couple fluid and solid equation. Consequently, extensive and comparative simulation were performed to investigate the impact of valve elasticity and valve positions on hemodynamics and solid parameters. Effective Orifice Area(EOA) also has been calculated [1]. The simulation results indicated that the lower of the elastic modulus cause to increase the EOA. Furthermore, the result of valve position showed, whenever the valve is closer to sinuses, a greater EOA and lower stresses impose on the leaflet are achievable.

关键词： Transcatheter aortic valve fluid-structure interaction Arbitrary Lagrangian Eulerian Steered adaptive mesh Effective orifice area

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Non-Newtonian fluid-structure interaction: Flow of a viscoelastic Oldroyd-B fluid in a deformable channel

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JOURNAL OF NON-NEWTONIAN fluid MECHANICS 2023年第1期313卷

作者： Boyko, Evgeniy Christov, Ivan C. Purdue Univ Sch Mech Engn W Lafayette IN 47907 USA Purdue Univ Davidson Sch Chem Engn W Lafayette IN 47907 USA Technion Israel Inst Technol Fac Mech Engn IL-3200003 Hefa Israel

We analyze the steady non-Newtonian fluid-structure interaction between the flow of an Oldroyd-B fluid and a deformable channel. Specifically, we provide a theoretical framework for calculating the leading-order effect of the fluid's viscoelasticity on the flow rate-pressure drop relation and on the deformation of the channel's elastic wall. We first identify the characteristic scales and dimensionless parameters governing the fluid- structure interaction in slender and shallow channels. Applying the lubrication approximation for the flow and employing a perturbation expansion in powers of the Deborah number De, we derive a closed-form expression for the pressure as a function of the non-uniform shape of the channel in the weakly viscoelastic limit up to O(De). Coupling the hydrodynamic pressure to the elastic deformation, we provide the leading-order effect of the interplay between the viscoelasticity of the fluid and the compliance of the channel on the pressure and deformation fields, as well as on the flow rate-pressure drop relation. For the flow-rate-controlled regime and in the weakly viscoelastic limit, we show analytically that both the compliance of the deforming top wall and the viscoelasticity of the fluid decrease the pressure drop. Furthermore, we reveal a trade-off between the influence of compliance of the channel and the fluid's viscoelasticity on the deformation. While the channel's compliance increases the deformation, the fluid's viscoelasticity decreases it.

关键词： fluid-structure interaction Viscoelasticity Oldroyd-B fluid Lubrication theory Pressure drop Microfluidics

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Vibration analysis of the steel shell flow tube in a vertical axial pumping station based on fluid-structure interaction (FSI) method

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SADHANA-ACADEMY PROCEEDINGS IN ENGINEERING SCIENCES 2021年第1期46卷 1-12页

作者： Wang, Shuo Zhang, Liaojun Yin, Guojiang Chen, Jian Wang, Li Hohai Univ Coll Water Conservancy & Hydropower Engn Nanjing 210098 Peoples R China Huaian Water Conservancy Survey & Design Res Inst Huaian 223001 Peoples R China

Design scheme of steel shell flow tube in the inflow and outflow passage of the vertical axial pumping stations takes advantages of conventional concrete scheme in simple construction and convenient installation of the pump. A three-dimensional pumping station model was established based on fluid-structure interaction method in ADINA. Typical measure points were selected to analyze the features of the unsteady turbulent flow in fluid zone and vibration responses of the steel shell tube in solid zone. Time and frequency domain investigation of fluid domain revealed the transmission path of pressure pulsation, that was the pulsation transferred from the pump to the inlet and outlet respectively with amplitudes sharply decreasing, which verified the rationality of calculation and established the basis on structure analysis. Dynamic displacement, velocity and acceleration analysis of measure points in steel shell tube showed that top shell domain near the inlet of steel shell flow tube had obvious vibration amplitude, which required great attention. The first main frequency equaled the rotational frequency of the blade, indicating one of the most important vibration sources in the pump was the pressure pulsation induced by blade rotation. The design scheme of steel shell flow tube is practical and could be promoted to other similar pumping stations because the vibration amplitude is much lower than the regularity. This research provides great importance to the design and application of the steel shell flow tube in pumping stations.

关键词： fluid-structure interaction steel shell flow tube axial pump vibration ADINA

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A sharp interface Lagrangian-Eulerian method for flexible-body fluid-structure interaction

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JOURNAL OF COMPUTATIONAL PHYSICS 2023年第1期488卷 112174页

作者： Kolahdouz, Ebrahim M. Wells, David R. Rossi, Simone Aycock, Kenneth I. Craven, Brent A. Griffith, Boyce E. Simons Fdn Flatiron Inst Ctr Computat Biol New York NY 10010 USA Univ N Carolina Dept Math Chapel Hill NC 27599 USA US FDA Div Appl Mech Off Sci & Engn Labs Ctr Devices & Radiol Hlth Silver Spring MD USA Univ N Carolina Dept Biomed Engn Chapel Hill NC USA Univ N Carolina Carolina Ctr Interdisciplinary Appl Math Chapel Hill NC USA Univ N Carolina Computat Med Program Chapel Hill NC USA Univ N Carolina McAllister Heart Inst Chapel Hill NC USA

This paper introduces a sharp-interface approach to simulating fluid-structure interaction (FSI) involving flexible bodies described by general nonlinear material models and across a broad range of mass density ratios. This new flexible-body immersed Lagrangian-Eulerian (ILE) scheme extends our prior work on integrating partitioned and immersed approaches to rigid-body FSI. Our numerical approach incorporates the geometrical and domain solution flexibility of the immersed boundary (IB) method with an accuracy comparable to body-fitted approaches that sharply resolve flows and stresses up to the fluid-structure interface. Unlike many IB methods, our ILE formulation uses distinct momentum equations for the fluid and solid subregions with a Dirichlet-Neumann coupling strategy that connects fluid and solid subproblems through simple interface conditions. As in earlier work, we use approximate Lagrange multiplier forces to treat the kinematic interface conditions along the fluid-structure interface. This penalty approach simplifies the linear solvers needed by our formulation by introducing two representations of the fluid-structure interface, one that moves with the fluid and another that moves with the structure, that are connected by stiff springs. This approach also enables the use of multi-rate time stepping, which allows us to use different time step sizes for the fluid and structure subproblems. Our fluid solver relies on an immersed interface method (IIM) for discrete surfaces to impose stress jump conditions along complex interfaces while enabling the use of fast structured-grid solvers for the incompressible Navier-Stokes equations. The dynamics of the volumetric structural mesh are determined using a standard finite element approach to large-deformation nonlinear elasticity via a nearly incompressible solid mechanics formulation. This formulation also readily accommodates compressible structures with a constant total volume, and it can handle fully compressibl

关键词： fluid-structure interaction Nonlinear continuum mechanics Immersed Lagrangian-Eulerian method Immersed interface method Inferior vena cava filter

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A stable loosely-coupled scheme for cardiac electro-fluid-structure interaction

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JOURNAL OF COMPUTATIONAL PHYSICS 2023年第1期490卷

作者： Bucelli, Michele Gabriel, Martin Geraint Quarteroni, Alfio Gigante, Giacomo Vergara, Christian Politecn Milan Dipartimento Matemat MOX Pzza Leonardo Vinci 32 I-20133 Milan Italy Politecn Milan Dipartimento Chim Materiali & Ingn Chim Giulio Nat LABS Pzza Leonardo Vinci 32 I-20133 Milan Italy Ecole Polytech Fed Lausanne Math Inst Av Piccard CH-1015 Lausanne Switzerland Univ Bergamo Dipartimento Ingn Gestionale Informaz & Prod Viale Marconi 5 I-24044 Dalmine BG Italy

We present a loosely coupled scheme for the numerical simulation of the cardiac electrofluid-structure interaction problem, whose solution is typically computationally intensive due to the need to suitably treat the coupling of the different submodels. Our scheme relies on a segregated treatment of the subproblems, in particular on an explicit Robin-Neumann algorithm for the fluid-structure interaction, aiming at reducing the computational burden of numerical simulations. The results, both in an ideal and a realistic cardiac setting, show that the proposed scheme is stable at the regimes typical of cardiac simulations. From a comparison with a scheme with implicit fluid-structure interaction, it emerges that, while conservation properties are not fully preserved, computational times significantly benefit from the explicit scheme. Overall, the explicit discretization represents a good trade-off between accuracy and cost, and is a valuable alternative to implicit schemes for fast largescale simulations. & COPY;2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by-nc -nd /4 .0/).

关键词： Cardiac modeling Multiphysics Electromechanics fluid-structure interaction Robin-Neumann interface conditions

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A Study of fluid-structure interaction of Unsteady Flow in the Blood Vessel Using Finite Element Method

A Study of Fluid-Structure Interaction of Unsteady Flow in t...

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International Conference on Modern Mechanics and Applications, ICOMMA 2020

作者： Ha, S.T. Nguyen, T.D. Vu, V.C. Nguyen, M.H. Nguyen, M.D. Department of Mechanical Engineering Le Quy Don Technical University Hanoi Viet Nam

ISBN: (纸本)9789811632389

The paper presents a numerical simulation for fluid-structure interaction (FSI) of unsteady blood flow interacting with the vessel wall. The present work aims to provide a simple approach for very large deformation of the wall. The implementation of the method is straightforward and can be employed for a large scale problem with a cheap computational cost. The classical finite element discretization is adopted both for fluid and solid domains on tetrahedral elements. The monolithic scheme is used for the strong coupling of fluid and structure to satisfy kinematic and dynamic equilibrium conditions at the interface. The Navier-Stokes equations of an incompressible flow are solved by using the integrated method based on the Arbitrary Lagrangian-Eulerian (ALE) formula for the moving grid, and the total Lagrangian formulation is used for the non-linear hyper-elastic material of the vessel wall with the Mooney-Rivlin material model adopted as a constitutive equation for the solid domain. The numerical solutions for the FSI of blood vessel problem are quite similar to the experimental data. After validation the code, two problems of the blood vessel walls are considered: The carotid bifurcation and the aortic valve problems. The simulation results can be used for predicting the risk of cardiovascular diseases. © 2022, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

关键词： Blood vessel Finite element method fluid-structure interaction Unsteady flow

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Strongly coupled fluid-structure interaction analysis of aquatic flapping wings based on flexible multibody dynamics and the modified unsteady vortex lattice method

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OCEAN ENGINEERING 2023年第1期281卷

作者： Luo, Ming Wu, Zhigang Yang, Chao Beihang Univ Sch Aeronaut Sci & Engn Beijing 100191 Peoples R China

Because of their superior efficiency and low detectability compared to conventional submarine-shaped vehicles, bionic underwater vehicles such as Mantabot are playing increasingly important roles in ocean exploration. However, current research on manta-inspired robots is limited to structural design and pure hydrodynamics analysis of pectoral fin performance, with other aspects such as hydroelasticity and optimal design of flapping wings rarely addressed. This work presents a novel method for analyzing aquatic flapping wings by coupling flexible multibody dynamics with a modified unsteady vortex lattice method. The flexible multibody system is solved by using the absolute nodal coordinate formulation, and the conventional unsteady vortex lattice method is modified to accommodate dynamic stall. Compactly supported radial basis functions are used to transfer the hydroelastic forces and structural displacements across the interface meshes while satisfying global energy conservation, and a predictor-corrector method is used to stabilize the iteration procedure. Three different experiments are used to validate the flexible multibody dynamics solver, the modified unsteady vortex lattice solver, and the proposed fluid-structure interaction framework, respectively. Finally, the hydroelastic framework is demonstrated for a fin-like wing, and how flexibility and movement affect the flapping wing dynamics is examined. Numerical examples show that reducing the structural stiffness of the aquatic flapping wing within a certain range improves the propulsive efficiency but also reduces the thrust coefficient, and how the stiffness distribution affects the thrust and propulsive efficiency remains consistent over a range of the Strouhal number.

关键词： fluid-structure interaction Manta ray robot Flexibility Strouhal number

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