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EnglishWe study, both theoretically and numerically, the equilibrium of a hinged rigid leaflet with an attached rotational spring, immersed in a stationary incompressible fluid within a rigid channel. Through a careful investigation of the properties of the domain functional describing the angular momentum exerted by the fluid on the leaflet (which depends on both the leaflet angular position and its thickness), we identify sufficient conditions on the spring stiffness function for the existence (and uniqueness) of equilibrium positions. This study resorts to techniques from shape differential calculus. We propose a numerical technique that exploits the mesh flexibility of the Virtual Element Method (VEM). A (polygonal) computational mesh is generated by cutting a fixed background grid with the leaflet geometry, and the problem is then solved with stable VEM Stokes elements of degrees 1 and 2 combined with a bisection algorithm. We prove quasi-optimal error estimates and present a large array of numerical experiments to document the accuracy and robustness with respect to degenerate geometry of the proposed methodology.
Equilibrium analysis of an immersed rigid leaflet by the virtual element method / Beirao Da Veiga, L.; Canuto, C.; Nochetto, R. H.; Vacca, G.. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - ELETTRONICO. - 31:7(2021), pp. 1323-1372. [10.1142/S0218202521500275]
| Titolo: | Equilibrium analysis of an immersed rigid leaflet by the virtual element method | |
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| Data di pubblicazione: | 2021 | |
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| Digital Object Identifier (DOI): | http://dx.doi.org/10.1142/S0218202521500275 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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| File | Descrizione | Tipologia | Licenza | |
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| Equilibrium analysis of an immersed rigid leaflet by the virtual element method.pdf | 2a Post-print versione editoriale / Version of Record | PUBBLICO - Tutti i diritti riservati | Visibile a tuttiVisualizza/Apri |
http://hdl.handle.net/11583/2948474
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