Penalization model for navier-stokes-darcy equation with application to porosity-oriented topology optimization - Université de La Réunion Accéder directement au contenu
Article Dans Une Revue Mathematical Models and Methods in Applied Sciences Année : 2018

Penalization model for navier-stokes-darcy equation with application to porosity-oriented topology optimization

Résumé

Topology optimization for fluid flow aims at finding the location of a porous medium minimizing a cost functional under constraints given by the Navier-Stokes equations. The location of the porous media is usually taken into account by adding a penalization term αu, where α is a kinematic viscosity divided by a permeability and u is the velocity of the fluid. The fluid part is obtained when α = 0 while the porous (solid) part is defined for large enough α since this formally yields u = 0. The main drawback of this method is that only solid that does not let the fluid to enter, that is perfect solid, can be considered. In this paper, we propose to use the porosity of the media as optimization parameter hence to minimize some cost function by finding the location of a porous media. The latter is taken into account through a singular perturbation of the Navier-Stokes equations for which we prove that its weak-limit corresponds to an interface fluid-porous medium problem modeled by the Navier-Stokes-Darcy equations. This model is then used as constraint for a topology optimization problem. We give necessary condition for such problem to have at least an optimal solution and derive first order necessary optimality condition. This paper ends with some numerical simulations, for Stokes flow, to show the interest of this approach.
Fichier principal
Vignette du fichier
Penalization_NSD_AB_PHC_DR_HAL.pdf (724.73 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01618605 , version 1 (18-10-2017)

Identifiants

Citer

Alain Bastide, Pierre-Henri Cocquet, Delphine Ramalingom. Penalization model for navier-stokes-darcy equation with application to porosity-oriented topology optimization. Mathematical Models and Methods in Applied Sciences, 2018, ⟨10.1142/S0218202518500409⟩. ⟨hal-01618605⟩
546 Consultations
548 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More