CALTAGIRONE, Jean-Paul; ANGOT, Philippe

doi:10.1007/978-3-030-65820-5

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CALTAGIRONE, Jean-Paul
Institut de Mécanique et d'Ingénierie [I2M]

ANGOT, Philippe

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Chapitre d'ouvrage

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Turbulence and Interactions. Notes on Numerical Fluid Mechanics and Multidisciplinary Design.. 2021, vol. 149

Springer

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The primary objective of discrete mechanics is to unify various laws fromdifferent areas of physics, such as fluid mechanics and solid mechanics. The sameobjective was also pursued by continuum mechanics, but the latter has not been en-tirely successful in accomplishing it. The Galilean invariance and the principle ofequivalence make it possible to rewrite the law of dynamics as an equality betweenaccelerations, the one undergone by the medium and the external accelerations ap-plied to it. The derivation of the equation of discrete motion leads to writing theacceleration as a Hodge-Helmholtz decomposition,i.e.the sum of a gradient of ascalar potential and the rotational of a vector potential. By choosing the accelerationas being a primary variable, we can express the velocity and the displacement simplyas quantities that accumulate over time. Potentials represent energies per unit massand are also stored over time. The resulting formulation is able to describe the mo-tion and dynamics of complex media, that can be both fluid and solid, under largedeformations and large displacements. Two examples of fluid-structure coupling,an analytical solution and a numerical solution used for a benchmark, are presentedhere. They show the ability of the model to reproduce the behavior of interactingfluid and solid media< Réduire

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Fluid-Structure Interactions in Discrete Mechanics

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