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Numerical methods for shape optimal design of fluid-structure interaction problems

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2024年 432卷

作者： Haubner, Johannes Ulbrich, Michael Karl Franzens Univ Graz Inst Math Heinrichstr 36 A-8010 Graz Austria Tech Univ Munich Boltzmannstr 3 D-85748 Garching Germany

We consider the method of mappings for performing shape optimization for unsteady fluid-structure interaction (FSI) problems. In this work, we focus on the numerical implementation. We model the optimization problem such that it takes several theoretical results into account, such as regularity requirements on the transformations and a differential geometrical point of view on the manifold of shapes. Moreover, we discretize the problem such that we can compute exact discrete gradients. This allows for the use of general purpose optimization solvers. We focus on problems derived from an FSI benchmark to validate our numerical implementation. The method is used to optimize parts of the outer boundary and the interface. The numerical simulations build on FEniCS, dolfin-adjoint and IPOPT. Moreover, as an additional theoretical result, we show that for a linear special case the adjoint attains the same structure as the forward problem but reverses the temporal flow of information.

关键词： fluid-structure interaction Shape optimization Method of mappings Navier-Stokes equations Saint Venant-Kirchhoff type material FSI2 benchmark

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A fully-integrated lattice Boltzmann method for fluid-structure interaction

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JOURNAL OF COMPUTATIONAL PHYSICS 2025年 526卷

作者： Sun, Yue Rycroft, Chris H. Univ Wisconsin Madison Dept Math Madison WI 53706 USA Harvard Univ John A Paulson Sch Engn & Appl Sci Cambridge MA 02138 USA Lawrence Berkeley Lab Computat Res Div Berkeley CA 94720 USA

We present a fully-integrated lattice Boltzmann (LB) method for fluid-structure interaction (FSI) simulations that efficiently models deformable solids in complex suspensions and active systems. Our Eulerian method (LBRMT) couples finite-strain solids to the LB fluid on the same fixed computational grid with the reference map technique (RMT). An integral part of the LBRMT is a new LB boundary condition for moving deformable interfaces across different densities. With this fully Eulerian solid-fluid coupling, the LBRMT is well-suited for parallelization and simulating multi-body contact without remeshing or extra meshes. We validate its accuracy via a benchmark of a deformable solid in a lid-driven cavity, then showcase its versatility through examples of soft solids rotating and settling. The LBRMT achieves a spatial convergence rate between first-order and second-order for FSI simulations and is designed for low to intermediate Reynolds number flows with finite inertia at small Mach numbers. With simulations of complex suspensions mixing, we highlight the potential of the LBRMT for studying collective behavior in soft matter and biofluid dynamics.

关键词： fluid-structure interaction Lattice Boltzmann method Complex suspensions Collective motion

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Improved unsteady fluid-structure interaction analysis using the dynamic mode decomposition on a composite marine propeller

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OCEAN ENGINEERING 2025年 319卷

作者： Kim, Sunghoon Shin, Sangjoon Seoul Natl Univ Dept Aerosp Engn Seoul 08826 South Korea HD Hyundai Heavy Ind Ship Performance Res Dept Ulsan 44032 South Korea Seoul Natl Univ Inst Adv Aerosp Technol Seoul 08226 South Korea

Unlike conventional metallic propellers, a composite blade's structural deformation must be considered. Composite marine propellers typically require additional computational time for unsteady analysis to accommodate the structural deflection. This study proposes a fast fluid-structure interaction (FSI) analysis method that considers the blade deformation of composite marine propellers. The unsteady boundary element method was modified for fluid analysis to include the effects of blade deformation. The structural response was predicted by considering the added mass and time-dependent hydrodynamic damping effects. Because an FSI analysis typically requires numerous iterative computations, a structural analysis was conducted using the mode superposition methodology, with hydrodynamic loads converted into the frequency domain via dynamic mode decomposition. Additionally, a quasi-Newton-based algorithm was employed in the iterative FSI analysis to improve the convergence. We performed FSI analyses on two composite propellers and validated the results by comparing them with existing numerical results. Our results show good agreement with existing numerical results, while significantly reducing the computational time.

关键词： Composite marine propeller Dynamic mode decomposition fluid-structure interaction Boundary element method

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Comparison and identification of human coronary plaques with/without erosion using patient-specific optical coherence tomography-based fluid-structure interaction models: a pilot study

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BIOMECHANICS AND MODELING IN MECHANOBIOLOGY 2025年第1期24卷 213-231页

作者： Zhu, Yanwen Zhao, Chen Wu, Zheyang Maehara, Akiko Tang, Dalin Wang, Liang Gao, Zhanqun Xu, Yishuo Lv, Rui Huang, Mengde Zhang, Xiaoguo Zhu, Jian Jia, Haibo Yu, Bo Chen, Minglong Mintz, Gary S. Southeast Univ Sch Biol Sci & Med Engn Nanjing 210096 Peoples R China Harbin Med Univ Affiliated Hosp 2 Dept Cardiol Natl Key Lab Frigid Zone Cardiovasc Dis Harbin 150086 Peoples R China Chinese Minist Educ Key Lab Myocardial Ischemia Harbin 150086 Peoples R China Worcester Polytech Inst Math Sci Dept Worcester MA 01609 USA Columbia Univ Cardiovasc Res Fdn New York NY 10022 USA Shandong Second Prov Gen Hosp Dept Cardiac Surg Jinan 250022 Peoples R China Southeast Univ Zhongda Hosp Dept Cardiol Nanjing 210009 Peoples R China Nanjing Med Univ Affiliated Hosp 1 Nanjing 210029 Peoples R China

Plaque erosion (PE) with secondary thrombosis is one of the key mechanisms of acute coronary syndrome (ACS) which often leads to drastic cardiovascular events. Identification and prediction of PE are of fundamental significance for disease diagnosis, prevention and treatment. In vivo optical coherence tomography (OCT) data of eight eroded plaques and eight non-eroded plaques were acquired to construct three-dimensional fluid-structure interaction models and obtain plaque biomechanical conditions for investigation. Plaque stenosis severity, plaque burden, plaque wall stress (PWS) and strain (PWSn), flow shear stress (FSS), and Delta FSS (FSS variation in time) were extracted for comparison and prediction. A logistic regression model was used to predict plaque erosion. Our results indicated that the combination of mean PWS and mean Delta FSS gave best prediction (AUC = 0.866, 90% confidence interval (0.717, 1.0)). The best single predictor was max Delta FSS (AUC = 0.819, 90% confidence interval (0.624, 1.0)). The average of maximum FSS values from eroded plaques was 76% higher than that from the non-eroded plaques (127.96 vs. 72.69 dyn/cm2) while the average of mean FSS from erosion sites of the eight eroded plaques was 48.6% higher than that from sites without erosion (71.52 vs. 48.11 dyn/cm2). The average of mean PWS from plaques with erosion was 22.83% lower than that for plaques without erosion (83.2 kPa vs. 107.8 kPa). This pilot study suggested that combining plaque stress, strain and flow shear stress could help better identify patients with potential plaque erosion, enabling possible early intervention therapy. Further studies are needed to validate our findings.

关键词： Plaque erosion fluid-structure interaction Vulnerable plaque Optical coherence tomography Erosion identification

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A hybrid strategy for numerical simulations of fluid-structure interaction problems in ocean engineering

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APPLIED OCEAN RESEARCH 2025年 155卷

作者： Liao, Xin Koh, Chan Ghee Chow, Yean Khow Natl Univ Singapore Dept Civil & Environm Engn Singapore 117576 Singapore

A hybrid strategy combining the advantages of the meshless Consistent Particle Method (CPM) and the meshbased Finite Element Method (FEM) is proposed in this paper to solve fluid-structure interaction problems. Water is modelled by CPM, whereas deformable structure is solved by FEM. Unlike some traditional particle methods that require a kernel function in computing spatial derivatives, CPM utilizes Taylor series expansion and avoids the use of artificial values of physical parameters (such as artificial viscosity and sound speed). The interaction between water and structure is achieved by a partitioned approach for its flexibility and ease of implementation. To ensure compatibility between CPM and FEM solutions at the fluid-structure interface, an iteration scheme of enforcing pressure Poisson equation (PPE) is proposed. The accuracy and stability of the proposed hybrid strategy are validated through three benchmark examples: water column on an elastic plate, sloshing of sunflower oil interacting with an elastic baffle, and a dam break with an elastic gate. Comparisons between CPM-FEM results with published experimental and numerical results demonstrate the effectiveness and advantages of the proposed hybrid strategy.

关键词： fluid-structure interaction Consistent particle method Finite element method Taylor series expansion Pressure Poisson equation Elastic structure

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Numerical model for calculation of hydraulic transients with two-phase flow and fluid-structure interaction

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JOURNAL OF THE BRAZILIAN SOCIETY OF MECHANICAL SCIENCES AND ENGINEERING 2024年第4期46卷 1-12页

作者： Rocha, Pedro Henrique do Nascimento de Campos, Josie Aguila Alves Camargo, Micelli Rodrigues Rocha, Marcelo da Silva Univ Sao Paulo Inst Pesquisas Energet & Nucl IPEN Sao Paulo Brazil

fluid transport systems such as pipelines are subject to loads whenever changes in fluid momentum or in pipeline structure occur. These loads can generate extremely harmful hydraulic transients which may be responsible for several major accidents. This paper presents a model for the solution of these hydraulic transients, considering two-phase flow and fluid-structure interaction. Mathematical and numerical solutions are proposed and analyzed for the proper capture of the physical phenomena associated with the fluid compressibility and fluid celerity, which are variable in two-phase fluid, together with the disturbances generated by the fluid-structure interaction. The proposed solution for the model considers the simultaneous action of these phenomena. The developed numerical model is based on the solution of the mathematical model formed by a system of four partial differential equations, in which the necessary adaptations are integrated in fluid-structural equations and in the nonlinear mathematical coefficients for the solution of the compressible and two-phase flow in question. Classical formulation is selected for the implementation of friction between fluid and pipe in the model. For the solution, it is applied the method of characteristics and finite difference, with subsequent numerical integration. The validation of the results is carried out based on comparisons with experimental and analytical data. The model presented, in general, was quite adherent to the experimental and analytical results, mainly in relation to the first pressure peak, which is one of the main focuses of the transient analyses.

关键词： Hydraulic transients fluid-structure interaction Method of characteristics Two-phase gas-liquid flow Numerical model

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Gevrey Regularity for A fluid-structure interaction Model

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2025年第1期205卷 1-17页

作者： Avalos, George Mcknight, Dylan Mcknight, Sara Univ Nebraska Lincoln Lincoln NE 68588 USA Colorado Mesa Univ Grand Junction CO 81501 USA

A result of Gevrey regularity is ascertained for a semigroup which models a fluid-structure interaction problem. In this model, the fluid evolves in a piecewise smooth or convex geometry O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {O}$$\end{document}. On a portion of the boundary, a fourth order plate equation is coupled with the fluid through pressure and matching velocities. The key to obtaining the conclusion of Gevrey regularity is an appropriate estimation of the resolvent of the associated C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_0$$\end{document}-semigroup operator. Moreover, a numerical scheme and example is provided which empirically demonstrates smoothing of the fluid-structure semigroup.

关键词： fluid-structure interaction Stokes equations Kirchoff plate Gevrey class semigroups

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Parameterization, algorithmic modeling, and fluid-structure interaction analysis for generative design of transcatheter aortic valves

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ENGINEERING WITH COMPUTERS 2024年第6期40卷 3405-3427页

作者： Pan, Xianyu George Corpuz, Ashton M. Rajanna, Manoj R. Johnson, Emily L. Univ Notre Dame Dept Aerosp & Mech Engn Notre Dame IN 46556 USA Iowa State Univ Dept Mech Engn Ames IA USA Global Engn & Mat Inc Princeton NJ USA

Heart valves play a critical role in maintaining proper cardiovascular function in the human heart;however, valve diseases can lead to improper valvular function and reduced cardiovascular performance. Depending on the extent and severity of the valvular disease, replacement operations are often required to ensure that the heart continues to operate properly in the cardiac system. Transcatheter aortic valve replacement (TAVR) procedures have recently emerged as a promising alternative to surgical replacement approaches because the percutaneous methods used in these implant operations are significantly less invasive than open heart surgery. Despite the advantages of transcatheter devices, the precise deployment, proper valve sizing, and stable anchoring required to securely place these valves in the aorta remain challenging even in successful TAVR procedures. This work proposes a parametric modeling approach for transcatheter heart valves (THVs) that enables flexible valvular development and sizing to effectively generate existing and novel valve designs. This study showcases two THV configurations that are analyzed using an immersogeometric fluid-structure interaction (IMGA FSI) framework to demonstrate the influence of geometric changes on THV performance. The proposed modeling framework illustrates the impact of these features on THV behavior and indicates the effectiveness of parametric modeling approaches for enhancing THV performance and efficacy in the future.

关键词： Parametric modeling Transcatheter heart valve fluid-structure interaction Immersogeometric analysis TAVR

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Parametric model order reduction by machine learning for fluid-structure interaction analysis

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ENGINEERING WITH COMPUTERS 2024年第1期40卷 45-60页

作者： Lee, SiHun Jang, Kijoo Lee, Sangmin Cho, Haeseong Shin, SangJoon Seoul Natl Univ Dept Aerosp Engn Seoul 08226 South Korea Jeonbuk Natl Univ Dept Aerosp Engn Jeonju 54896 South Korea Seoul Natl Univ Inst Adv Aerosp Technol Seoul 08226 South Korea

An improved nonintrusive parametric model order reduction (pMOR) approach is proposed for the flow field interpolation regarding fluid-structure interaction (FSI) objects. Flow field computation using computational fluid dynamics (CFD) requires excessive computational time and memory. Nonintrusive and data-driven MOR schemes have been proposed to overcome such limitations. The present methodology is implemented by both proper orthogonal decomposition (POD) and a modified Nouveau variational autoencoder (mNVAE). POD attempts to reduce the number of degrees of freedom (DOFs) on the precomputed series of the full-order model parametric result. The reduced DOF yields parametrically independent reduced bases and dependent coefficients. Then, mNVAE is employed for the interpolation of POD coefficients, which will be combined with POD modes for parametrically interpolated flow field generation. The present approach is assessed on the benchmark problem of a two-dimensional plunging airfoil and the highly nonlinear FSI phenomenon of the limit cycle oscillation. The comparison was executed against other POD-based generative neural network approaches. The proposed methodology demonstrates applicability on highly nonlinear FSI objects with improved accuracy and efficiency.

关键词： Nonintrusive parametric reduced-order modeling Machine learning fluid-structure interaction Proper orthogonal decomposition Variational autoencoder

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Analysis of seismic response parameters of double-trough aqueduct structure considering two-way fluid-structure interaction effect

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ALEXANDRIA ENGINEERING JOURNAL 2025年 118卷 606-617页

作者： Huang, Liang Li, Ge Li, Haotian Xu, Jianguo Wan, Ruizhuo Zhengzhou Univ Coll Civil Engn Zhengzhou 450000 Peoples R China

As a pivotal component within water diversion engineering, the aqueduct has experienced substantial growth in recent years. Scholars have extensively explored the interaction between water and solid structures within aqueducts. Notably, the question of whether the presence of water in the aqueduct can either enhance seismic absorption or exacerbate seismic responses has emerged as a crucial concern in aqueduct structural seismic resistance. To address this quandary, a refined two-way fluid-structure interaction methodology has been employed. This method accounts for variations in water pressure, water inertia forces, excitation frequencies, and aqueduct aspect ratios. It meticulously monitors liquid level changes using the Volume of fluid (VOF) method, while FLUENT tracks wall pressure. Consequently, it calculates the aqueduct displacement under different influencing factors. The outcomes reveal that the water within the aqueduct exhibits Tuned Liquid Damping (TLD) effects, with the shock absorption effectiveness being directly related to water quality rather than differences in moving water pressure. Higher excitation frequencies result in increased peak aqueduct displacements but reduced water body oscillations. Under consistent water quality conditions, greater aspect ratios yield higher moving water pressures and, consequently, improved shock absorption capabilities.

关键词： Aqueduct fluid-structure interaction TLD effect Water action Parametric analysis

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