A numerical approach for simulating fluid structure interaction of flexible thin shells undergoing arbitrarily large deformations in complex domains
01 Nov 2015-Journal of Computational Physics (Academic Press Professional, Inc.)-Vol. 300, pp 814-843
TL;DR: 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.
About: This article is published in Journal of Computational Physics.The article was published on 2015-11-01 and is currently open access. It has received 105 citations till now. The article focuses on the topics: Immersed boundary method & Finite element method.
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TL;DR: In this paper, an experimental study of wind energy harvesting by self-sustained oscillations (flutter) of a flexible piezoelectric membrane fixed in a novel orientation called the "inverted flag" is presented.
304 citations
TL;DR: A versatile numerical method to predict the fluid-structure interaction of bodies with arbitrary thickness immersed in an incompressible fluid is presented, able to provide results comparable with those of sharp direct-forcing approaches, and can manage high pressure differences across the surface, still obtaining very smooth hydrodynamic forces.
131 citations
Cites methods from "A numerical approach for simulating..."
...Different direct-forcing 53 IB methods have been used for studying flow-induced bodies deformation 54 [18, 19, 20, 21, 22] with good accuracy....
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TL;DR: The current understanding of flow phenomena induced by heart valves are summarized, their linkage with disease pathways are discussed, and the research advances required to translate in-depth understanding of valvular hemodynamics into effective patient treatment are emphasized.
Abstract: As the pulsatile cardiac blood flow drives the heart valve leaflets to open and close, the flow in the vicinity of the valve resembles a pulsed jet through a nonaxisymmetric orifice with a dynamically changing area. As a result, three-dimensional vortex rings with intricate topology emerge that interact with the complex cardiac anatomy and give rise to shear layers, regions of recirculation, and flow instabilities that could ultimately lead to transition to turbulence. Such complex flow patterns, which are inherently valve- and patient-specific, lead to mechanical forces at scales that can cause blood cell damage and thrombosis, increasing the likelihood of stroke, and can trigger the pathogenesis of various life-threatening valvular heart diseases. We summarize the current understanding of flow phenomena induced by heart valves, discuss their linkage with disease pathways, and emphasize the research advances required to translate in-depth understanding of valvular hemodynamics into effective patient ther...
114 citations
TL;DR: This paper uses a divergence-conforming B-spline fluid discretization to address the long-standing issue of poor mass conservation in immersed methods for computational fluid-structure interaction (FSI) that represent the influence of the structure as a forcing term in the fluid subproblem.
95 citations
TL;DR: The new developed AMR-IBM algorithm is validated using a benchmark data of fluid past a cylinder and the results show that there is good agreement under laminar flow, confirming the robustness of the new algorithms in simulating flow characteristics in the boundary layers of thin structures.
Abstract: This study aims to develop an adaptive mesh refinement (AMR) algorithm combined with Cut-Cell IBM using two-stage pressure–velocity corrections for thin-object FSI problems. To achieve the objectiv ...
90 citations
References
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Book•
01 Jan 1959
TL;DR: In this article, the authors describe the bending of long RECTANGULAR PLATES to a cycloidal surface, and the resulting deformation of shels without bending the plates.
Abstract: CONTENTS: BENDING OF LONG RECTANGULAR PLATES TO A CYLINDRICAL SURFACE PURE BENDING OF PLATES SYMMETRICAL BENDING OF CIRCULAR PLATES SMALL DEFLECTIONS OF LATERALLY LOADED PLATES SIMPLY SUPPORTED RECTANGULAR PLATES RECTANGULAR PLATES WITH VARIOUS EDGE CONDITIONS CONTINUOUS RECTANGULAR PLATES PLATES ON ELASTIC FOUNDATION PLATES OF VARIOUS SHAPES SPECIAL AND APPROXIMATE METHODS IN THEORY OF PLATES BENDING OF ANISTROPIC PLATES BENDING OF PLATES UNDER THE COMBINED ACTION OF LATERAL LOADS AND FORCES IN THE MIDDLE PLANE OF THE PLATE LARGE DEFLECTIONS OF PLATES DEFORMATION OF SHELLS WITHOUT BENDING GENERAL THEORY OF CYLINDRICAL SHELLS SHELLS HAVING THE FORM OF A SURFACE OF REVOLUTION AND LOADED SYMMETRICALLY WITH RESPECT TO THEIR AXIS.
10,200 citations
TL;DR: In this article, a new eddy viscosity model is presented which alleviates many of the drawbacks of the existing subgrid-scale stress models, such as the inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes.
Abstract: One major drawback of the eddy viscosity subgrid‐scale stress models used in large‐eddy simulations is their inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes. In the present work a new eddy viscosity model is presented which alleviates many of these drawbacks. The model coefficient is computed dynamically as the calculation progresses rather than input a priori. The model is based on an algebraic identity between the subgrid‐scale stresses at two different filtered levels and the resolved turbulent stresses. The subgrid‐scale stresses obtained using the proposed model vanish in laminar flow and at a solid boundary, and have the correct asymptotic behavior in the near‐wall region of a turbulent boundary layer. The results of large‐eddy simulations of transitional and turbulent channel flow that use the proposed model are in good agreement with the direct simulation data.
6,747 citations
TL;DR: Method is capable of application to structures of any degree of complication, with any relationship between force and displacement, from linear elastic behavior through various degrees of inelastic behavior or plastic response, up to failure.
Abstract: A general procedure for the solution of problems in structural dynamics is described herein. The method is capable of application to structures of any degree of complication, with any relationship ...
4,436 citations
"A numerical approach for simulating..." refers methods in this paper
...We employ the Newmark time integration algorithm [38] to solve solid-structure equation (25), which is formulated as follows:...
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TL;DR: In this paper, the method is capable of application to structures of any degree of complication, with any relationship between force and displacement, from linear elastic behavior through various degrees of inelastic behavior or plastic response, up to failure; any type of dynamic loading, due to shock or impact, vibration, earthquake, or nuclear blast can be considered.
Abstract: Method is capable of application to structures of any degree of complication, with any relationship between force and displacement, from linear elastic behavior through various degrees of inelastic behavior or plastic response, up to failure; any type of dynamic loading, due to shock or impact, vibration, earthquake, or nuclear blast can be considered; use of high-speed digital computers.
4,176 citations
TL;DR: The term immersed boundary (IB) method is used to encompass all such methods that simulate viscous flows with immersed (or embedded) boundaries on grids that do not conform to the shape of these boundaries.
Abstract: The term “immersed boundary method” was first used in reference to a method developed by Peskin (1972) to simulate cardiac mechanics and associated blood flow. The distinguishing feature of this method was that the entire simulation was carried out on a Cartesian grid, which did not conform to the geometry of the heart, and a novel procedure was formulated for imposing the effect of the immersed boundary (IB) on the flow. Since Peskin introduced this method, numerous modifications and refinements have been proposed and a number of variants of this approach now exist. In addition, there is another class of methods, usually referred to as “Cartesian grid methods,” which were originally developed for simulating inviscid flows with complex embedded solid boundaries on Cartesian grids (Berger & Aftosmis 1998, Clarke et al. 1986, Zeeuw & Powell 1991). These methods have been extended to simulate unsteady viscous flows (Udaykumar et al. 1996, Ye et al. 1999) and thus have capabilities similar to those of IB methods. In this review, we use the term immersed boundary (IB) method to encompass all such methods that simulate viscous flows with immersed (or embedded) boundaries on grids that do not conform to the shape of these boundaries. Furthermore, this review focuses mainly on IB methods for flows with immersed solid boundaries. Application of these and related methods to problems with liquid-liquid and liquid-gas boundaries was covered in previous reviews by Anderson et al. (1998) and Scardovelli & Zaleski (1999). Consider the simulation of flow past a solid body shown in Figure 1a. The conventional approach to this would employ structured or unstructured grids that conform to the body. Generating these grids proceeds in two sequential steps. First, a surface grid covering the boundaries b is generated. This is then used as a boundary condition to generate a grid in the volume f occupied by the fluid. If a finite-difference method is employed on a structured grid, then the differential form of the governing equations is transformed to a curvilinear coordinate system aligned with the grid lines (Ferziger & Peric 1996). Because the grid conforms to the surface of the body, the transformed equations can then be discretized in the
3,184 citations
"A numerical approach for simulating..." refers methods in this paper
...The interested reader is referred to this paper as well as the earlier review by Mittal and Iaccarino [5] for details....
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