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A hybrid immersed boundary and material point method for simulating 3D fluid-structure interaction problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN fluidS 2008年第12期56卷 2151-2177页

作者： Gilmanov, Anvar Acharya, Sumanta Louisiana State Univ Ctr Computat & Technol Baton Rouge LA 70803 USA

A numerical method is developed for solving the 31), unsteady, incompressible Navier-Stokes equations in curvilinear coordinates containing immersed boundaries (IBs) of arbitrary geometrical complexity moving and deforming under forces acting on the body. Since simulations of flow in complex geometries with deformable surfaces require special treatment, the present approach combines a hybrid immersed boundary method (HIBM) for handling complex moving boundaries and a material point method (MPM) for resolving structural stresses and movement. This combined HIBM & MPM approach is presented as an effective approach for solving fluid-structure interaction (FSI) problems. In the HIBM, a curvilinear grid is defined and the variable values at grid points adjacent to a boundary are forced or interpolated to satisfy the boundary conditions. The MPM is used for solving the equations of solid structure and communicates with the fluid through appropriate interface-boundary conditions. The governing flow equations are discretized on a non-staggered grid layout using second-order accurate finite-difference formulas. The discrete equations are integrated in time via a second-order accurate dual time stepping, artificial compressibility scheme. Unstructured, triangular meshes are employed to discretize the complex surface of the IBs. The nodes of the surface mesh constitute a set of Lagrangian control points used for tracking the motion of the flexible body. The equations of the solid body are integrated in time via the MPM. At every instant in time, the influence of the body on the flow is accounted for by applying boundary conditions at stationary curvilinear grid nodes located in the exterior but in the immediate vicinity of the body by reconstructing the solution along the local normal to the body surface. The influence of the fluid on the body is defined through pressure and shear stresses acting on the surface of the body. The HIBM & MPM approach is validated for FSI problems

关键词： artificial compressibility dual time stepping immersed boundaries hybrid immersed boundary method material point method fluid-structure interaction

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Interface projection techniques for fluid-structure interaction modeling with moving-mesh methods

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COMPUTATIONAL MECHANICS 2008年第1期43卷 39-49页

作者： Tezduyar, Tayfun E. Sathe, Sunil Pausewang, Jason Schwaab, Matthew Christopher, Jason Crabtree, Jason Rice Univ Houston TX 77005 USA US Mil Acad West Point NY 10996 USA

The stabilized space-time fluid-structure interaction (SSTFSI) technique developed by the Team for Advanced Flow Simulation and Modeling (T*AFSM) was applied to a number of 3D examples, including arterial fluid mechanics and parachute aerodynamics. Here we focus on the interface projection techniques that were developed as supplementary methods targeting the computational challenges associated with the geometric complexities of the fluid-structure interface. Although these supplementary techniques were developed in conjunction with the SSTFSI method and in the context of air-fabric interactions, they can also be used in conjunction with other moving-mesh methods, such as the Arbitrary Lagrangian-Eulerian (ALE) method, and in the context of other classes of FSI applications. The supplementary techniques currently consist of using split nodal values for pressure at the edges of the fabric and incompatible meshes at the air-fabric interfaces, the FSI Geometric Smoothing Technique (FSI-GST), and the Homogenized Modeling of Geometric Porosity (HMGP). Using split nodal values for pressure at the edges and incompatible meshes at the interfaces stabilizes the structural response at the edges of the membrane used in modeling the fabric. With the FSI-GST, the fluid mechanics mesh is sheltered from the consequences of the geometric complexity of the structure. With the HMGP, we bypass the intractable complexities of the geometric porosity by approximating it with an "equivalent", locally-varying fabric porosity. As test cases demonstrating how the interface projection techniques work, we compute the air-fabric interactions of windsocks, sails and ringsail parachutes.

关键词： interface projection techniques air-fabric interaction fluid-structure interaction space-time FSI technique sails parachutes

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Homogenisation method for the modal analysis of tube bundle with fluid-structure interaction modelling

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FINITE ELEMENTS IN ANALYSIS AND DESIGN 2008年第6-7期44卷 323-333页

作者： Sigrista, Jean-Francois Broc, Daniel DCNS Propuls Serv Tech Sci F-44620 La Montague France CEA Saclay Lab Etud Mecan & Sism F-91191 Gif Sur Yvette France

The present paper is concerned with the modal analysis of a two-dimensional tube bundle with fluid-structure interaction (FSI) modelling. The numerical modelling of FSI effects is performed with a homogenisation approach, using a method whose principles have been presented in a previous paper for the modal analysis of a nuclear reactor with internal structures and FSI modelling [J. F. Sigrist, D. Broc, Homogenisation method for the modal analysis of a nuclear reactor with internal structures modelling and fluid structure-interaction coupling, Nucl. Eng. Des. 237 (2007) 431-440]. The method is adapted here in the case of tube bundle and compared with the classical approach, based on a direct finite element discretisation of the coupled problem with all tubes modelling. The theoretical background of the method is recalled, the numerical implementation in a finite element code is exposed and a comparison of the '' homogenisation '' and '' coupled '' methods is proposed in the case of a 10 x 10 tube bundle. Calculation of eigenmode shapes, frequencies and effective masses with the two methods is performed;it is concluded that: (i) the computational time is significantly lowered when using the homogenisation method instead of the coupled method, since the problem size is reduced by 90%;(ii) the tube bundle dynamic is described in a space-averaged manner, which is sufficient to account for the main inertial coupling effects. Extension of the method to a three-dimensional case can now be considered;implementation of the method in a commercial finite element code is also currently investigated. (c) 2007 Elsevier B. V. All rights reserved.

关键词： fluid-structure interaction tube bundle modal analysis homogenisation method

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An effective fluid-structure interaction formulation for vascular dynamics by generalized Robin conditions

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2008年第2期30卷 731-763页

作者： Nobile, F. Vergara, C. Politecn Milan Dept Matemat F Brioschi MOX Modellist & Calcolo Sci I-20133 Milan Italy

In this work we focus on the modeling and numerical simulation of the fluid-structure interaction mechanism in vascular dynamics. We first propose a simple membrane model to describe the deformation of the arterial wall, which is derived from the Koiter shell equations and is applicable to an arbitrary geometry. Secondly, we consider a reformulation of the fluid-structure problem, in which the newly derived membrane model, thanks to its simplicity, is embedded into the fluid equations and will appear as a generalized Robin boundary condition. The original problem is then reduced to the solution of subsequent fluid equations defined on a moving domain and may be achieved with a fluid solver only. We also derive a stability estimate for the resulting numerical scheme. Finally, we propose new out flow absorbing boundary conditions, which are easy to implement and allow us to reduce significantly the spurious pressure wave reflections that typically appear in artificially truncated computational domains. We present several numerical results showing the effectiveness of the proposed approaches.

关键词： fluid-structure interaction membrane model absorbing boundary conditions Navier-Stokes equations Womersley profile finite elements time marching schemes

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Mechanical stresses in carotid plaques using MRI-based fluid-structure interaction models

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JOURNAL OF BIOMECHANICS 2008年第8期41卷 1651-1658页

作者： Kock, Samuel A. Nygaard, Jens V. Eldrup, Nikolaj Fruend, Ernst-Torben Klaerke, Anette Paaske, William P. Falk, Erling Kim, W. Yong Aarhus Univ Hosp MR Ctr DK-8200 Aarhus N Denmark Aarhus Univ Interdisciplinary Nanosci Ctr DK-8000 Aarhus C Denmark Aarhus Univ Hosp Dept Cardiothorac & Vasc Surg T Skejby Denmark Aarhus Univ Hosp Inst Clin Med Skejby Denmark Aarhus Univ Hosp Dept Cardiol Skejby Denmark

Risk assessment in patients with carotid atherosclerosis relies on the degree of luminal stenosis. Incorporating morphological information on plaque composition obtained noninvasively through the use of magnetic resonance imaging (MRI) could include other variables besides the degree of stenosis into carotid plaque risk assessment. Knowledge of the morphologic composition of the plaque allows determination of mechanic stresses exerted on the protective fibrous cap, which may be of importance in the assessment of plaque vulnerability. Based on image processing of transverse MRI scans, longitudinal 2D fluid-structure interaction (FSI) simulations of carotid atherosclerotic plaques were performed facilitating in-vivo estimation of longitudinal internal fibrous cap stresses. The FSI simulation combined finite element analysis (FEA) with computational fluid dynamics (CFD) simulations of blood-flow variables. Preliminary results from two symptomatic patients revealed longitudinal stress levels (max. 254.1 and 143.2 kPa) approaching established criteria for plaque rupture at known predilection sites of plaque rupture. Determination of longitudinal fibrous cap stresses may prove useful in assessing plaque vulnerability and improve risk stratification in patients with carotid atherosclerosis. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： atherosclerosis carotid artery computational fluid dynamics fluid-structure interaction plaque rupture

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Modelling vortex-induced fluid-structure interaction

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PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 2008年第1868期366卷 1231-1274页

作者： Benaroya, Haym Gabbai, Rene D. Rutgers State Univ Dept Mech & Aerosp Engn Piscataway NJ 08854 USA NIST Gaithersburg MD 20899 USA

The principal goal of this research is developing physics-based, reduced-order, analytical models of nonlinear fluid structure interactions associated with offshore structures. Our primary focus is to generalize the Hamilton's variational framework so that systems of flow-oscillator equations can be derived from first principles. This is an extension of earlier work that led to a single energy equation describing the fluid - structure interaction. It is demonstrated here that flow-oscillator models are a subclass of the general, physical-based framework. A flow-oscillator model is a reduced-order mechanical model, generally comprising two mechanical oscillators, one modelling the structural oscillation and the other a nonlinear oscillator representing the fluid behaviour coupled to the structural motion. Reduced-order analytical model development continues to be carried out using a Hamilton's principle-based variational approach. This provides flexibility in the long run for generalizing the modelling paradigm to complex, three-dimensional problems with multiple degrees of freedom, although such extension is very difficult. As both experimental and analytical capabilities advance, the critical research path to developing and implementing fluid - structure interaction models entails formulating generalized equations of motion, as a superset of the flow-oscillator models;and developing experimentally derived, semi-analytical functions to describe key terms in the governing equations of motion. The developed variational approach yields a system of governing equations. This will allow modelling of multiple d.f. systems. The extensions derived generalize the Hamilton's variational formulation for such problems. The Navier Stokes equations are derived and coupled to the structural oscillator. This general model has been shown to be a superset of the flow-oscillator model. Based on different assumptions, one can derive a variety of flow-oscillator models.

关键词： vortex-induced vibration reduced-order modelling circular cylinder Hamilton's principle fluid-structure interaction

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Hydrodynamic pressure on a vertical gate considering fluid-structure interaction

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FINITE ELEMENTS IN ANALYSIS AND DESIGN 2008年第12-13期44卷 759-766页

作者： Pani, P. K. Bhattacharyya, S. K. IGIT Dept Civil Engn Sarang 759146 Orissa India Indian Inst Technol Dept Civil Engn Kharagpur 721302 W Bengal India

The hydrodynamic pressure on a vertical rectangular gate attached to a rigid dam and subjected toa ground acceleration is investigated using finite element technique to investigate the fluid-structure interaction effect on the dynamic pressure. In the governing equations, pressure for the fluid domain and displacement for the gate are considered as independent nodal variables. interaction is maintained by transferring the acceleration of the gate to the fluid and pressure of the fluid to the gate in sequence. The unbounded reservoir interacting with the gate is truncated at a closer proximity to the gate simulating a condition for the far boundary. The roles of the frequency of excitation, compressibility of the fluid and flexibility of the gate on dynamic pressure are investigated. (C) 2008 Elsevier B. V. All rights reserved.

关键词： fluid-structure interaction truncated far boundary hydrodynamic pressure

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Isogeometric fluid-structure interaction: theory, algorithms, and computations

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COMPUTATIONAL MECHANICS 2008年第1期43卷 3-37页

作者： Bazilevs, Y. Calo, V. M. Hughes, T. J. R. Zhang, Y. Univ Calif San Diego Dept Struct Engn La Jolla CA 92093 USA Univ Texas Austin Inst Computat Engn & Sci Austin TX 78712 USA Carnegie Mellon Univ Pittsburgh PA 15213 USA

We present a fully-coupled monolithic formulation of the fluid-structure interaction of an incompressible fluid on a moving domain with a nonlinear hyperelastic solid. The arbitrary Lagrangian-Eulerian description is utilized for the fluid subdomain and the Lagrangian description is utilized for the solid subdomain. Particular attention is paid to the derivation of various forms of the conservation equations;the conservation properties of the semi-discrete and fully discretized systems;a unified presentation of the generalized-alpha time integration method for fluid-structure interaction;and the derivation of the tangent matrix, including the calculation of shape derivatives. A NURBS-based isogeometric analysis methodology is used for the spatial discretization and three numerical examples are presented which demonstrate the good behavior of the methodology.

关键词： blood flow cardiovascular modeling fluid-structure interaction hyperelastic solids incompressible fluids isogeometric analysis mesh movement moving domains NURBS shape derivatives space-time Piola transformation

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Dynamic analysis of a tube bundle with fluid-structure interaction modelling using a homogenisation method

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2008年第9-12期197卷 1080-1099页

作者： Sigrist, Jean-Francois Broc, Daniel DCN Prouls Serv Rech & Sci F-44620 La Montagne France CEA Saclay Lab Etud Sism F-91919 Gif Sur Yvette France

The present paper is concerned with the dynamic analysis of a tube bundle with fluid-structure interaction (FSI) modelling. Modelling of FSI is performed with a homogenisation approach which is compared with the classical coupled approach;this latter is based on a direct finite element discretisation of the coupled problem with all tubes modelling, while the former lies on a description of the fluid-tubes system through an equivalent continuous medium, characterised by a set of dynamic equations which describe the behaviour of the tubes and the fluid from a global point of view. Theoretical background of the method is recalled, numerical implementation in a finite element code is exposed and comparison of the "homogenisation" and "coupled" method is proposed in the case of a 10 x 10 tube bundle, in 2D and 3D configurations. Calculation of eigenmode shapes, frequencies and effective masses with the two methods is performed, as well as the dynamic response of the coupled system subjected to seismic loading. It is concluded that: (i) the computational time are significantly lowered when using the homogenisation method instead of the coupled method, since the problem size is reduced by 90%;(ii) the tube bundle dynamic is described in a space-averaged manner, which is sufficient to account for the main inertial coupling effects: no significant discrepancies are reported in the modal and dynamic analysis, when performed with the homogenisation and the coupled approaches, which makes the proposed method of practical interest for future engineering applications. (C) 2007 Elsevier B.V. All rights reserved.

关键词： fluid-structure interaction homogenisation method tube bundle modal analysis dynamic analysis temporal method spectral method effective masses

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Modelling and simulation of the sea-landing of aerial vehicles using the Particle Finite Element Method

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OCEAN ENGINEERING 2013年 66卷 92-100页

作者： Ryzhakov, P. Rossi, R. Vina, A. Onate, E. [a] Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE) Spain [b] CIMSA Ingenieria de Sistemas Spain

In this paper the Particle Finite Element Method (PFEM) is applied to the simulation of the sea-landing of an unmanned aerial vehicle (UAV). The problem of interest consists in modelling the impact of the vehicle against the water surface, analyzing the main kinematic and dynamic quantities (such as loads exerted upon the capsule at the moment of the impact). The PFEM, a methodology well-suited for free-surface flow simulation is used for modelling the water while a rigid body model is chosen for the vehicle. The vehicle under consideration is characterized by low weight. This leads to difficulties in modelling the fluid-structure interaction using standard Dirichlet-Neumann coupling. We apply a modified partitioned strategy introducing the interface Laplacian into the pressure Poisson's equation for obtaining a convergent FSI solution. The paper concludes with an industrial example of a vehicle sea-landing modelled using PFEM. (c) 2013 Elsevier Ltd. All rights reserved.

关键词： fluid-structure interaction Water landing UAV PFEM Wedge impact Incompressible flows

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