Staggered solution procedures represent the most elementary computational strategy for the simulation of fluid-structure interaction problems. They usually consist of a predictor followed by the separate execution of ...
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Staggered solution procedures represent the most elementary computational strategy for the simulation of fluid-structure interaction problems. They usually consist of a predictor followed by the separate execution of each subdomain solver. Although it is generally possible to maintain the desired order of accuracy of the time integration, it is difficult to guarantee the stability of the overall computation. In the context of large solid over fluid mass ratios, compressible flows and explicit subsolvers, substantial development has been carried out by Felippa, Park, Farhat, Lohner and others. In this work, a new staggered scheme is presented. It is shown that, for a linear model problem, the scheme is second-order accurate and unconditionally stable. The dependency of the leading truncation error on the solid over fluid mass ratio is investigated. The strategy is applied to two-dimensional and three-dimensional fluid-structure interaction problems. It is shown that the conclusions derived from the investigation of the model problem apply. The new strategy extends the applicability of staggered schemes to problems involving relatively small solid over fluid mass ratios and incompressible fluid flow. It is suggested that the proposed scheme has the same range of applicability as the Dirichlet-Neumann or block Gau beta-Seidel type strategies. Copyright (c) 2012 John Wiley & Sons, Ltd.
A fully Eulerian framework formulation for solving time-dependent fluid-structure interaction problems is proposed in this work Although some preliminary work on this approach exists for stationary configurations, it ...
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A fully Eulerian framework formulation for solving time-dependent fluid-structure interaction problems is proposed in this work Although some preliminary work on this approach exists for stationary configurations, it remains to validate nonstationary processes. The formulation is stated in an implicit monolithic frame of reference. A finite difference scheme is used for temporal discretization whereas the spatial discretization is based on a Galerkin finite element scheme. The nonlinear problem is solved with a Newton method and with analytical evaluation of the Jacobian matrix. In contrast to interface tracking methods (for example, the arbitrary Lagrangian-Eulerian approach), the interface must be captured, which is similar to the level-set method. Consequently, the interface is allowed to intersect mesh cells, which is a crucial difficulty of this method where appropriate treatment must be suggested. The proposed formulation is substantiated by three numerical tests in which the performance of fully Eulerian fluid-structure interaction is demonstrated. (C) 2012 Elsevier B.V. All rights reserved.
In this paper we study a kinematic splitting algorithm for fluid-structure interaction problems. This algorithm belongs to the class of loosely-coupled fluid-structure interaction schemes. We will present stability an...
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In this paper we study a kinematic splitting algorithm for fluid-structure interaction problems. This algorithm belongs to the class of loosely-coupled fluid-structure interaction schemes. We will present stability analysis for a coupled problem of non-Newtonian shear-dependent fluids in moving domains with viscoelastic boundaries. fluid flow is described by the conservation laws with nonlinearities in convective and diffusive terms. For simplicity of presentation the structure is modelled by the generalized string equation, but the results presented in the paper may be generalized to more complex structure models. The arbitrary Lagrangian-Eulerian approach is used in order to take into account moving computational domain. Numerical experiments including numerical error analysis and comparison of hemodynamic parameters for Newtonian and non-Newtonian fluids demonstrate reliability of the proposed scheme. (C) 2013 Elsevier B.V. All rights reserved.
The mitral valve (MV) is one of the four cardiac valves. It consists of two leaflets that are connected to the left ventricular papillary muscles via multiple fibrous chordae tendinae. The primary functions of the MV ...
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The mitral valve (MV) is one of the four cardiac valves. It consists of two leaflets that are connected to the left ventricular papillary muscles via multiple fibrous chordae tendinae. The primary functions of the MV are to allow for the free flow of blood into the left ventricle (LV) of the heart from the left atrium (LA) during the diastolic and early systolic phases of the cardiac cycle, and to prevent regurgitant flow from the LV to the LA in deep systole. MV disorders such as mitral stenosis and regurgitation cause significant morbidity and mortality, and an improved understanding of MV biomechanics could lead to improved medical and surgical procedures to restore normal MV function in patients with such disorders. Computational models can realistically capture the anatomical and functional features of the MV and hence can provide detailed spatial and temporal data that may not be easily obtained clinically or experimentally. In this study, an anatomical model of a human MV is derived from in vivo magnetic resonance imaging (MRI) data. Using this clinical imaging-derived model, fluid-structure interaction (FSI) simulations are performed using the immersed boundary (IB) method under physiological, dynamic transvalvular pressure loads. Computational analyses show that the subject-specific MV geometry has a significant influence on the simulation results. An initial validation of the model is achieved by comparing the opening height and flow rates to clinical measurements. (c) 2012 Elsevier Ltd. All rights reserved.
We propose in this paper an Eulerian finite element approximation of a coupled chemical fluid-structure interaction problem arising in the study of mesoscopic cardiac biomechanics. We simulate the active response of a...
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We propose in this paper an Eulerian finite element approximation of a coupled chemical fluid-structure interaction problem arising in the study of mesoscopic cardiac biomechanics. We simulate the active response of a myocardial cell (here considered as an anisotropic, hyperelastic, and incompressible material), the propagation of calcium concentrations inside it, and the presence of a surrounding Newtonian fluid. An active strain approach is employed to account for the mechanical activation, and the deformation of the cell membrane is captured using a level set strategy. We address in detail the main features of the proposed method, and we report several numerical experiments aimed at model validation. Copyright (c) 2013 John Wiley & Sons, Ltd.
A three-dimensional immersed smoothed finite element method (3D IS-FEM) using four-node tetrahedral element is proposed to solve 3D fluid-structure interaction (FSI) problems. The 3D IS-FEM is able to determine accura...
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A three-dimensional immersed smoothed finite element method (3D IS-FEM) using four-node tetrahedral element is proposed to solve 3D fluid-structure interaction (FSI) problems. The 3D IS-FEM is able to determine accurately the physical deformation of the nonlinear solids placed within the incompressible viscous fluid governed by Navier-Stokes equations. The method employs the semi-implicit characteristic-based split scheme to solve the fluid flows and smoothed finite element methods to calculate the transient dynamics responses of the nonlinear solids based on explicit time integration. To impose the FSI conditions, a novel, effective and sufficiently general technique via simple linear interpolation is presented based on Lagrangian fictitious fluid meshes coinciding with the moving and deforming solid meshes. In the comparisons to the referenced works including experiments, it is clear that the proposed 3D IS-FEM ensures stability of the scheme with the second order spatial convergence property;and the IS-FEM is fairly independent of a wide range of mesh size ratio.
The study examined the effect of fluid-structure interaction on global dynamic properties such as vibrational frequency, mode shape, modal curvature, as well as free vibrational responses along E-glass composite, carb...
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The study examined the effect of fluid-structure interaction on global dynamic properties such as vibrational frequency, mode shape, modal curvature, as well as free vibrational responses along E-glass composite, carbon composite, and aluminum beams, respectively. The digital image correlation technique was used to measure the free vibrational responses along the beams in air and water, respectively. The vibration submerged in water exhibited higher frequency modes than the dry vibration under the same excitation. Experimental modal analysis showed that the mode shapes were very close for an aluminum beam with and without the FSI effect while there was a modest difference for a carbon composite beam because the PSI effect is greater for the composite beam. Modal curvatures for the both beams are more influenced by PSI, especially for the composite beam. The curvature is directly related to the bending strain of the beam. This explains why the difference in strains measured for composite structures in air and water, respectively, varies significantly from location to location of the structures under impact loading. One location has much greater difference in strains than another location. The FSI can change potential failure locations of the composite structures because of the change in modal curvatures. Published by Elsevier Ltd.
We consider the Navier-Stokes equations in a half-plane with a drift term parallel to the boundary and a small source term of compact support. We provide detailed information on the behavior of the velocity and the vo...
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We consider the Navier-Stokes equations in a half-plane with a drift term parallel to the boundary and a small source term of compact support. We provide detailed information on the behavior of the velocity and the vorticity at infinity in terms of an asymptotic expansion at large distances from the boundary. The expansion is universal in the sense that it only depends on the source term through some constants. The expansion also applies to the problem of an exterior flow past a small body moving at constant velocity parallel to the boundary, and can be used as an artificial boundary condition on the edges of truncated domains for numerical simulations. (C) 2012 Elsevier Ltd. All rights reserved.
Advanced non-linear dynamics, finite element computational methods and tools are utilized in order to assess the blast wave mitigation potential of the fluid-structure interaction phenomena involving rigid and deforma...
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Advanced non-linear dynamics, finite element computational methods and tools are utilized in order to assess the blast wave mitigation potential of the fluid-structure interaction phenomena involving rigid and deformable structures. The employed computational methods and tools are verified and validated by first demonstrating that they can quite accurately reproduce analytical solutions for a couple of well-defined blast wave propagation and interaction problems. Then the methods/tools are used to investigate the fluid-structure interaction phenomena involving deformable structures while accounting for both the interaction of the incident blast wave with the structure and for the structure-motion induced blast wave (at the back-face of the structure). To assess the role of the structure deformability, i.e. the role of the shock waves generated within the structure, the results obtained are compared with their rigid structure counterparts. This comparison established that no additional structure-deformability-related blast-mitigation effects are observed in the case of fully supported blast wave loading while, under exponentially decaying blast wave loading, such effects are observed but only under conditions when the shock wave propagation time within the structure is comparable with the incident wave decay time.
Simulating fluid-structure interactions is challenging due to the tight coupling between the fluid and solid substructures. Explicit and implicit decoupling methods often either fail or require relaxation when densiti...
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Simulating fluid-structure interactions is challenging due to the tight coupling between the fluid and solid substructures. Explicit and implicit decoupling methods often either fail or require relaxation when densities of the two materials are close. In this paper, a fluid-structure interaction problem is formulated as a least squares problem, where the jump in velocities of the two substructures is minimized by a Neumann control enforcing the continuity of stress on the interface. A decoupling optimization algorithm is discussed, which requires few nonlinear solves at each time step, and numerical results are presented. (C) 2013 Elsevier B.V. All rights reserved.
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