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Computational Methods for Coupled fluid-structure-Electromagnetic interaction Models with Applications to Biomechanics

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MATHEMATICAL PROBLEMS IN ENGINEERING 2015年第1期2015卷 1-10页

作者： Mihai, Felix Youn, Inja Griva, Igor Seshaiyer, Padmanabhan George Mason Univ Dept Math Sci Coll Sci Fairfax VA 22030 USA

Multiphysics problems arise naturally in several engineering and medical applications which often require the solution to coupled processes, which is still a challenging problem in computational sciences and engineering. Some examples include blood flow through an arterial wall and magnetic targeted drug delivery systems. For these, geometric changes may lead to a transient phase in which the structure, flow field, and electromagnetic field interact in a highly nonlinear fashion. In this paper, we consider the computational modeling and simulation of a biomedical application, which concerns the fluid-structure-electromagnetic interaction in the magnetic targeted drug delivery process. Our study indicates that the strong magnetic fields, which aid in targeted drug delivery, can impact not only fluid (blood) circulation but also the displacement of arterial walls. A major contribution of this paper is modeling the interactions between these three components, which previously received little to no attention in the scientific and engineering community.

关键词： fluid-structure interaction ELECTROMAGNETIC interactions BIOMECHANICS BIOMEDICAL engineering DRUG delivery systems MAGNETIC couplings

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A finite-element/boundary-element method for three-dimensional, large-displacement fluid-structure-interaction

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2015年 284卷 637-663页

作者： van Opstala, T. M. van Brummelen, E. H. van Zwieten, G. J. Norwegian Univ Sci & Technol NTNU Dept Math Sci N-7491 Trondheim Norway Eindhoven Univ Technol Dept Mech Engn NL-5600 MB Eindhoven Netherlands Eindhoven Univ Technol Dept Math & Comp Sci NL-5600 MB Eindhoven Netherlands

This paper presents a hybrid finite-element/boundary-element method for fluid-structure-interaction simulations of inflatable structures. The flow model consists of the steady Stokes equation, which admits a boundary-integral formulation. The structure is represented by a Kirchhoff-Love shell. The boundary-element approximation of the Stokes equation reduces the flow problem to an integral equation on the actual structure configuration, thus obviating the need for volumetric meshing of the strongly deforming fluid domain. The Stokes model moreover exhibits a lubrication effect that acts as an intrinsic mechanism to treat the ubiquitous self-contact that occurs in inflation problems. The aggregated fluid-structure-interaction problem, composed of the boundaryintegral equation and the Kirchhoff-Love shell connected by dynamic and kinematic interface conditions, is approximated by means of isogeometric discretizations to accommodate the smoothness requirements on the approximation spaces imposed by the flexural rigidity in the Kirchhoff-Love shell and to provide an accurate and smooth representation of the boundary for the boundary-element method. Auxiliary results presented in this paper are: (1) a parametrization-free Kirchhoff-Love formulation;(2) establishment of a cubic relationship between distance and tractions due to the lubrication effect;and (3) the interpretation of the Lagrange multiplier pertaining to fluid incompressibility as the total excess pressure. (C) 2014 Elsevier B. V. All rights reserved.

关键词： fluid-structure interaction Inflatable structures Isogeometric analysis Catmull-Clark subdivision Lubrication effect Incompressibility constraint

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A partitioned scheme for fluid-composite structure interaction problems

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JOURNAL OF COMPUTATIONAL PHYSICS 2015年 281卷 493-517页

作者： Bukac, M. Canic, S. Muha, B. Univ Notre Dame Dept Appl & Computat Math & Stat Notre Dame IN 46556 USA Univ Houston Dept Math Houston TX 77204 USA Univ Zagreb Dept Math Zagreb 10000 Croatia

We present a benchmark problem and a loosely-coupled partitioned scheme for fluid-structure interaction with composite structures. The benchmark problem consists of an incompressible, viscous fluid interacting with a structure composed of two layers: a thin elastic layer with mass which is in contact with the fluid and modeled by the Koiter membrane/shell equations, and a thick elastic layer with mass modeled by the equations of linear elasticity. An efficient, modular, partitioned operator-splitting scheme is proposed to simulate solutions to the coupled, nonlinear FSI problem, without the need for sub-iterations at every time-step. An energy estimate associated with unconditional stability is derived for the fully nonlinear FSI problem defined on moving domains. Two instructive numerical benchmark problems are presented to test the performance of numerical FSI schemes involving composite structures. It is shown numerically that the proposed scheme is at least first-order accurate both in time and space. This work reveals a new physical property of FSI problems involving thin interfaces with mass: the inertia of the thin fluid-structure interface regularizes solutions to the full FSI problem. (C) 2014 Elsevier Inc. All rights reserved.

关键词： fluid-structure interaction Composite structure Partitioned scheme Blood flow

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A Study of Using 2D In Vivo IVUS-Based Models for Human Coronary Plaque Progression Analysis To Compare With 3D fluid-structure interaction Models

A Study of Using 2D In Vivo IVUS-Based Models for Human Coro...

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2015年中国生物医学工程联合学术年会

作者： Hongjian Wang Jie Zheng Liang Wang Akiko Maehara Chun Yang David Muccigrosso Richard Bach Jian Zhu Gary S.Mintz Dalin Tang School of Biological Science and Medical Engineering Southeast UniversityNanjing210096China Mallinckrodt Institute of Radiology Washington UniversitySt.LouisMO USA Mathematical Sciences Department Worcester Polytechnic InstituteMAUSA The Cardiovascular Research Foundation NYNYUSA Network Technology Research Institute China United Network Communications Co.Ltd.BeijingChina Cardiovascular Division Washington University School of MedicineSaint LouisMOUSA Department of Cardiology Zhongda HospitalSoutheast UniversityNanjingChina School of Biological Science and Medical Engineering Southeast UniversityNanjing210096China Mathe

Computational modeling has been used extensively in cardiovascular and biological research,providing valuable ***,3D vulnerable plaque model construction with complex geometrical features and multi-components is often very time consuming and not practical for clinical *** paper investigated if 2D atherosclerotic plaque models could be used to replace 3D models to perform correlation analysis and achieve similar *** vivo intravascular ultrasound(IVUS)coronary plaque data were acquired from a patient follow-up study to construct 2D structure-only and 3D FSI models to obtain plaque wall stress(PWS)and strain(PWSn)*** hundred and twenty-seven(127)matched IVUS slices at baseline and follow up were obtained from 3 *** results showed that 2D models overestimated stress and strain by 30%and 32.5%,respectively,compared to results from 3D FSI models.2D/3D correlation comparison indicated that 116 out of 127 slices had a consistent correlation between plaque progression(WTI)and wall thickness;103 out of 127 slices had a consistent correlation between WTI and PWS;and 99 out of 127 slices had a consistent correlation between WTI and *** leads to the potential that 2D models could be used in actual clinical implementation where quick analysis delivery time is essential.

关键词： Coronary 2D structure-only fluid-structure interaction plaque rupture plaque progression IVUS

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A numerical approach for simulating fluid structure interaction of flexible thin shells undergoing arbitrarily large deformations in complex domains

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JOURNAL OF COMPUTATIONAL PHYSICS 2015年 300卷 814-843页

作者： Gilmanov, Anvar Le, Trung Bao Sotiropoulos, Fotis Univ Minnesota St Anthony Falls Lab Minneapolis MN 55414 USA Univ Minnesota Dept Civil Environm & Geoengn Minneapolis MN 55414 USA

We present a new numerical methodology for simulating fluid-structure interaction (FSI) problems involving thin flexible bodies in an incompressible fluid. The FSI algorithm uses the Dirichlet-Neumann partitioning technique. The curvilinear immersed boundary method (CURVIB) is coupled with a rotation-free finite element (FE) model for thin shells enabling the efficient simulation of FSI problems with arbitrarily large deformation. Turbulent flow problems are handled using large-eddy simulation with the dynamic Smagorinsky model in conjunction with a wall model to reconstruct boundary conditions near immersed boundaries. The CURVIB and FE solvers are coupled together on the flexible solid-fluid interfaces where the structural nodal positions, displacements, velocities and loads are calculated and exchanged between the two solvers. Loose and strong coupling FSI schemes are employed enhanced by the Aitken acceleration technique to ensure robust coupling and fast convergence especially for low mass ratio problems. The coupled CURVIB-FE-FSI method is validated by applying it to simulate two FSI problems involving thin flexible structures: 1) vortex-induced vibrations of a cantilever mounted in the wake of a square cylinder at different mass ratios and at low Reynolds number;and 2) the more challenging high Reynolds number problem involving the oscillation of an inverted elastic flag. For both cases the computed results are in excellent agreement with previous numerical simulations and/or experiential measurements. Grid convergence tests/studies are carried out for both the cantilever and inverted flag problems, which show that the CURVIB-FE-FSI method provides their convergence. Finally, the capability of the new methodology in simulations of complex cardiovascular flows is demonstrated by applying it to simulate the FSI of a tri-leaflet, prosthetic heart valve in an anatomic aorta and under physiologic pulsatile conditions. (C) 2015 Elsevier Inc. All rights reserved.

关键词： fluid-structure interaction Immersed boundary method Finite element Thin shells Rotation-free approach

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Simulation of fluid-structure interaction in a microchannel using the lattice Boltzmann method and size-dependent beam element on a graphics processing unit

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Chinese Physics B 2014年第8期23卷 389-395页

作者： Vahid Esfahanian Esmaeil Dehdashti Amir Mehdi Dehrouye-Semnani Department of Mechanical Engineering University of Tehran

fluid-structure interaction （FSI） problems in microchannels play a prominent role in many engineering applications. The present study is an effort toward the simulation of flow in microchannel considering FSI. The bottom boundary of the microchannel is simulated by size-dependent beam elements for the finite element method （FEM） based on a modified cou- ple stress theory. The lattice Boltzmann method （LBM） using the D2Q13 LB model is coupled to the FEM in order to solve the fluid part of the FSI problem. Because of the fact that the LBM generally needs only nearest neighbor information, the algorithm is an ideal candidate for parallel computing. The simulations are carried out on graphics processing units （GPUs） using computed unified device architecture （CUDA）. In the present study, the governing equations are non-dimensionalized and the set of dimensionless groups is exhibited to show their effects on micro-beam displacement. The numerical results show that the displacements of the micro-beam predicted by the size-dependent beam element are smaller than those by the classical beam element.

关键词： fluid-structure interaction graphics processing unit lattice Boltzmann method size-dependentbeam element

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Study of parachute inflation process using fluid–structure interaction method

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Chinese Journal of Aeronautics 2014年第2期27卷 272-279页

作者： Yu Li Cheng Han Zhan Ya'nan Li Shaoteng College of Aerospace Engineering Nanjing University of Aeronautics and Astronautics

A direct numerical modeling method for parachute is proposed firstly, and a model for the star-shaped folded parachute with detailed structures is established. The simplified arbitrary Lagrangian-Eulerian fluid structure interaction （SALE/FSI） method is used to simulate the infla- tion process of a folded parachute, and the flow field calculation is mainly based on operator split- ting technique. By using this method, the dynamic variations of related parameters such as flow field and structure are obtained, and the load jump appearing at the end of initial inflation stage is cap- tured. Numerical results including opening load, drag characteristics, swinging angle, etc. are well consistent with wind tunnel tests. In addition, this coupled method can get more space-time detailed information such as geometry shape, structure, motion, and flow field. Compared with previous inflation time method, this method is a completely theoretical analysis approach without relying on empirical coefficients, which can provide a reference for material selection, performance optimi- zation during parachute design.

关键词： Empirical formula fluid-structure interaction Inflation process Opening shockiParachute Wind tunnel test

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Full Eulerian finite element method of a phase field model for fluid-structure interaction problem

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COMPUTERS & fluidS 2014年 90卷 1-8页

作者： Sun, Pengtao Xu, Jinchao Zhang, Lixiang Univ Nevada Dept Math Sci Las Vegas NV 89154 USA Penn State Univ Dept Math University Pk PA 16802 USA Kunming Univ Sci & Technol Dept Mech Engn Kunming Yunnan Peoples R China

In this paper we present a full Eulerian model for a dynamic fluid-structure interaction (FSI) problem in terms of phase field approach, and design its full Eulerian finite element discretization and effective iterative method. The present full Eulerian FSI model effectively demonstrates the interaction between fluid flow and solid structure in terms of a uniform system of governing equations defined in a single domain, thus the computational grid is fixed, and the re-meshing and interpolation techniques which are always required by other FSI modeling approaches are no longer needed here. We develop a new stable scheme to discretize the Euler equation of an incompressible hyperelastic structure in Eulerian description, and employ Galerkin/least-square (GLS) stabilization scheme, streamline-upwind/Petrov-Galerkin (SUPG) method, and the second-order backward difference formula (BDF) to solve the derived transient nonlinear system of Navier-Stokes equations and transport equations. Numerical experiment is carried out for a cross spinning around its rotation of axis due to the passing flow field, and the numerical results dramatically show the spinning motion of the cross due to the interaction with the fluid, showing that our model and numerical methods are effective to simulate the dynamic fluid-structure interaction phenomena. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： fluid-structure interaction Full Eulerian model Phase field model Mixed finite element method Deformation gradient tensor Streamline diffusion scheme

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A combined fluid-structure interaction and multi-field scalar transport model for simulating mass transport in biomechanics

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2014年第4期100卷 277-299页

作者： Yoshihara, L. Coroneo, M. Comerford, A. Bauer, G. Kloeppel, T. Wall, W. A. Tech Univ Munich Inst Computat Mech D-85747 Munich Germany

Mass transport processes are known to play an important role in many fields of biomechanics such as respiratory, cardiovascular, and biofilm mechanics. In this paper, we present a novel computational model considering the effect of local solid deformation and fluid flow on mass transport. As the transport processes are assumed to influence neither structure deformation nor fluid flow, a sequential one-way coupling of a fluid-structure interaction (FSI) and a multi-field scalar transport model is realized. In each time step, first the non-linear monolithic FSI problem is solved to determine current local deformations and velocities. Using this information, the mass transport equations can then be formulated on the deformed fluid and solid domains. At the interface, concentrations are related depending on the interfacial permeability. First numerical examples demonstrate that the proposed approach is suitable for simulating convective and diffusive scalar transport on coupled, deformable fluid and solid domains. Copyright (c) 2014 John Wiley & Sons, Ltd.

关键词： mass transport fluid-structure interaction cardiovascular mechanics respiratory mechanics biofilm mechanics

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A fluid-structure interaction Model of the Cell Membrane Deformation: Formation of a Filopodium

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MATHEMATICAL MODELLING OF NATURAL PHENOMENA 2014年第1期9卷 27-38页

作者： El Khatib, N. Lebanese Amer Univ Dept Comp Sci & Math Byblos Lebanon

In this paper we present a fluid-structure interaction model of neuron's membrane deformation. The membrane-actin is considered as an elastic solid layer, while the cytoplasm is considered as a viscous fluid one. The membrane-actin layer is governed by elasticity equations while the cytoplasm is described by the Navier-Stokes equations. At the interface between the cytoplasm and the membrane we consider a match between the solid velocity displacement and the fluid velocity as well as the mechanical equilibrium. The membrane, which faces the extracellular medium, is free to move. This will change the geometry in time. To take into account the deformation of the initial configuration, we use the Arbitrary Lagrangian Eulerian method in order to take into account the mesh displacement. The numerical simulations, show the emergence of a filopodium, a typical structure in cells undergoing deformation.

关键词： partial differential equations cell membrane fluid-structure interaction numerical simulations

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