A wavelet based numerical simulation of Navier-Stokes equations under uncertainty

Souleymane Kadri Harouna (1) , Etienne Mémin (2)

1 MIA - Mathématiques, Image et Applications - EA 3165
2 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences

In this work we explore the numerical simulation of Navier-Stokes equations representation incorporating an uncertainty component on the fluid flow velocity. The uncertainty considered is formalized through a random field uncorrelated in time but correlated in space. This model enables the constitution of large scale dynamical models of the flows in which emerges an anisotropic subgrid tensor reminiscent to the Reynolds stress tensor. This subgrid model is directly related to the uncertainty variance tensor. This property allows us to propose simple models of this stress tensor that are computed directly on the resolved component. These models are here assessed on a standard Green-Taylor vortex at Reynolds 1600 and on a Crow instability at Reynolds 3200. We also describe in this paper an efficient divergence free wavelet scheme for the numerical simulation of this model. The stability condition of the divergence-free wavelet based numerical scheme we used in this study is also discussed.

Mots clés: Navier-Stokes; uncertainty modeling; Wavelet numerical scheme; subgrid modeling; Green-Taylor vortex; Crow instability

Domaines: Equations aux dérivées partielles [math.AP]; Océan, Atmosphère; Analyse numérique [math.NA]

Souleymane Kadri Harouna, Etienne Mémin. A wavelet based numerical simulation of Navier-Stokes equations under uncertainty. 2014. ⟨hal-00958137⟩