A locally anisotropic fluid–structure interaction remeshing strategy for thin structures with application to a hinged rigid leaflet |
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| Authors: | Ferdinando Auricchio Adrien Lefieux Alessandro Reali Alessandro Veneziani |
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| Affiliation: | 1. Dipartimento di Ingegneria Civile e Architettura (DICAr), Università degli Studi di Pavia, Pavia, Italy;2. Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI‐CNR), Pavia, Italy;3. Technische Universit?t München – Institute for Advanced Study, Garching, Germany;4. Department of Mathematics and Computer Science (MathCS), Emory University, Atlanta, GA, USA |
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| Abstract: | An immersed finite element fluid–structure interaction algorithm with an anisotropic remeshing strategy for thin rigid structures is presented in two dimensions. One specific feature of the algorithm consists of remeshing only the fluid elements that are cut by the solid such that they fit the solid geometry. This approach allows to keep the initial (given) fluid mesh during the entire simulation while remeshing is performed locally. Furthermore, constraints between the fluid and the solid may be directly enforced with both an essential treatment and elements allowing the stress to be discontinuous across the structure. Remeshed elements may be strongly anisotropic. Classical interpolation schemes – inf–sup stable on isotropic meshes – may be unstable on anisotropic ones. We specifically focus on a proper finite element pair choice. As for the time advancing of the fluid–structure interaction solver, we perform a geometrical linearization with a sequential solution of fluid and structure in a backward Euler framework. Using the proposed methodology, we extensively address the motion of a hinged rigid leaflet. Numerical tests demonstrate that some finite element pairs are inf–sup unstable with our algorithm, in particular with a discontinuous pressure. Copyright © 2015 John Wiley & Sons, Ltd. |
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| Keywords: | finite elements fluid– structure interaction thin structures rigid leaflet inf– sup stability strongly coupled |
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