Convergence of approximate deconvolution models to the mean Navier-Stokes Equations

Luigi C. Berselli (1) , Roger Lewandowski (2, 3)

1 DMA - Dipartimento di Matematica Applicata [Pisa]
2 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences
3 IRMAR - Institut de Recherche Mathématique de Rennes

We consider a 3D~Approximate Deconvolution Model (ADM) which belongs to the class of Large Eddy Simulation (LES) models. We aim at proving that the solution of the ADM converges towards a dissipative solution of the mean Navier-Stokes Equations. The study holds for periodic boundary conditions. The convolution filter we first consider is the Helmholtz filter. We next consider generalized convolution filters for which the convergence property still holds.

Mots clés: Navier-Stokes equations; Large eddy simulation; Deconvolution models

Domaines: Equations aux dérivées partielles [math.AP]

Luigi C. Berselli, Roger Lewandowski. Convergence of approximate deconvolution models to the mean Navier-Stokes Equations. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2012, 29 (2), pp.171-198. ⟨10.1016/j.anihpc.2011.10.001⟩. ⟨hal-00584115⟩