We 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.

Beirao Da Veiga, L., Canuto, C., Nochetto, R., Vacca, G. (2021). Equilibrium analysis of an immersed rigid leaflet by the virtual element method. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 31(7), 1323-1372 [10.1142/S0218202521500275].

Equilibrium analysis of an immersed rigid leaflet by the virtual element method

Beirao Da Veiga, L;Vacca, G
2021

Abstract

We 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.
Articolo in rivista - Articolo scientifico
fluid-structure interaction; polygonal meshes; shape calculus; Virtual elements;
English
2021
31
7
1323
1372
open
Beirao Da Veiga, L., Canuto, C., Nochetto, R., Vacca, G. (2021). Equilibrium analysis of an immersed rigid leaflet by the virtual element method. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 31(7), 1323-1372 [10.1142/S0218202521500275].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/341226
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