Divergence-free Wavelet Projection Method for Incompressible Viscous Flow

Souleymane Kadri Harouna (1) , Valérie Perrier (2)

1 MIA - Mathématiques, Image et Applications - EA 3165
2 MGMI - Modélisation Géométrique & Multirésolution pour l'Image

We present a new wavelet numerical scheme for the discretization of Navier-Stokes equations with physical boundary conditions. The temporal discretization of the method is inspired from the projection method. Helmholtz-Hodge decomposition using divergence-free and curl-free wavelet bases satisfying physical boundary conditions allows to define the projection operator. This avoids the use of Poisson equation solver and reduce the steps of usual methods with more accuracy. Numerical experiments conducted on lid driven cavity flow simulation show the effectiveness and the precision of the method.

Mots clés: Divergence-free wavelets; Navier-Stokes simulation; physical boundary conditions

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

Souleymane Kadri Harouna, Valérie Perrier. Divergence-free Wavelet Projection Method for Incompressible Viscous Flow. 2012. ⟨hal-00798417⟩