A FULL DISCRETISATION OF THE TIME-DEPENDENT BOUSSINESQ (BUOYANCY) MODEL WITH NONLINEAR VISCOSITY

Rim El Dbaissy † ‡ (1) , Frédéric Hecht (1) , Gihane Mansour (2) , Toni Sayah (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 FS - Faculté des sciences-USJ

In this article, we study the time dependent Boussinesq (buoyancy) model with nonlinear viscosity depending on the temperature. We propose and analyze first and second order numerical schemes based on finite element methods. An optimal a priori error estimate is then derived for each numerical scheme. Numerical experiments are presented that confirm the theoretical accuracy of the discretization.

Mots clés: Navier-Stokes equations; heat equation; Buoyancy; Boussinesq; finite element method; a priori error estimates

Domaines: Mécanique des fluides [physics.class-ph]

Rim El Dbaissy † ‡, Frédéric Hecht, Gihane Mansour, Toni Sayah. A FULL DISCRETISATION OF THE TIME-DEPENDENT BOUSSINESQ (BUOYANCY) MODEL WITH NONLINEAR VISCOSITY. 2017. ⟨halshs-01646611v2⟩