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Article

A Monolithic Approach of Fluid–Structure Interaction by Discrete Mechanics

1
Université Gustave Eiffel, Laboratoire MSME UMR CNRS 8208, Université PAris-Est Créteil, 5 boulevard Descartes, 77454 Champs-Sur-Marne, France
2
Bordeaux INP, University of Bordeaux, CNRS, Arts et Metiers Institute of Technology, INRAE, I2M Bordeaux, 33400 Talence, France
3
Département TREFLE, Institut de Mécanique et d’Ingéniérie, Université de Bordeaux, UMR CNRS 5295, 16 Avenue Pey-Berland CEDEX, 33607 Pessac, France
*
Author to whom correspondence should be addressed.
Academic Editor: Iman Borazjani
Fluids 2021, 6(3), 95; https://doi.org/10.3390/fluids6030095
Received: 25 January 2021 / Revised: 15 February 2021 / Accepted: 19 February 2021 / Published: 1 March 2021
(This article belongs to the Special Issue Fluid Structure Interaction: Methods and Applications)
The unification of the laws of fluid and solid mechanics is achieved on the basis of the concepts of discrete mechanics and the principles of equivalence and relativity, but also the Helmholtz–Hodge decomposition where a vector is written as the sum of divergence-free and curl-free components. The derived equation of motion translates the conservation of acceleration over a segment, that of the intrinsic acceleration of the material medium and the sum of the accelerations applied to it. The scalar and vector potentials of the acceleration, which are the compression and shear energies, give the discrete equation of motion the role of conservation law for total mechanical energy. Velocity and displacement are obtained using an incremental time process from acceleration. After a description of the main stages of the derivation of the equation of motion, unique for the fluid and the solid, the cases of couplings in simple shear and uniaxial compression of two media, fluid and solid, make it possible to show the role of discrete operators and to find the theoretical results. The application of the formulation is then extended to a classical validation case in fluid–structure interaction. View Full-Text
Keywords: fluid–structure interaction; discrete mechanics; Helmholtz–Hodge decomposition; Navier–Stokes equations; Navier–Lamé equations fluid–structure interaction; discrete mechanics; Helmholtz–Hodge decomposition; Navier–Stokes equations; Navier–Lamé equations
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MDPI and ACS Style

Vincent, S.; Caltagirone, J.-P. A Monolithic Approach of Fluid–Structure Interaction by Discrete Mechanics. Fluids 2021, 6, 95. https://doi.org/10.3390/fluids6030095

AMA Style

Vincent S, Caltagirone J-P. A Monolithic Approach of Fluid–Structure Interaction by Discrete Mechanics. Fluids. 2021; 6(3):95. https://doi.org/10.3390/fluids6030095

Chicago/Turabian Style

Vincent, Stéphane, and Jean-Paul Caltagirone. 2021. "A Monolithic Approach of Fluid–Structure Interaction by Discrete Mechanics" Fluids 6, no. 3: 95. https://doi.org/10.3390/fluids6030095

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