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Analyse mathématique et asymptotique de modèles couplés fluide-cinétique issus de la mécanique des fluides et des sciences du vivant

Abstract : We consider fluid-kinetic models that describe the evolution of particles flowing through a fluid under the assumption that the latter can be described by macroscopic quantities, its velocity and pressure, thanks to the incompressible Navier-Stokes equations. As for the particle spray, it is described at the mesoscopic scale by its density function in the phase space, which obeys a Vlasov-type equation. Taking into account the drag acceleration exerted by the fluid on the particles and the corresponding drag force leads to a strong coupling of the system of equations under study. First, we take into account, in addition to the interactions presented above, the effects of the airway humidity on the particle size and temperature by introducing convection-diffusion equations as well as integrating the size and temperature variations into the equations. We prove the existence of global weak solutions in a time-dependent domain and present some numerical experiments. Finally, we study several high-friction regimes for the Vlasov-Navier-Stokes system presented above. We define a framework allowing to properly justify these hydrodynamic limits in the case where the particles are light (resp. small) with respect to the fluid.
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https://tel.archives-ouvertes.fr/tel-03336024
Contributor : David Michel Connect in order to contact the contributor
Submitted on : Monday, September 6, 2021 - 4:56:06 PM
Last modification on : Tuesday, September 28, 2021 - 5:16:09 PM

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  • HAL Id : tel-03336024, version 1
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David Michel. Analyse mathématique et asymptotique de modèles couplés fluide-cinétique issus de la mécanique des fluides et des sciences du vivant. Equations aux dérivées partielles [math.AP]. Sorbonne Université, 2021. Français. ⟨tel-03336024⟩

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