Augmented Lagrangian Method and Open Boundary Conditions in 2d Simulation of Poiseuille–bénard Channel Flow

Abstract

SUMMARYThe main objective of this study is to compare the in¯uence of different boundary conditions upon the incompressible Poiseuille±Be Ânard channel¯ow (PBCF) in a 2D rectangular duct heated from below. In a ®rst technical part the algorithm used to carry out this work, based on the augmented Lagrangian method, is presented. The implementation details of the ®ve different open boundary conditions (OBCs) and the periodic boundary conditions (PBCs) tested in the present paper are also given. The study is then carried out for 1800`Ra 4 10,000, 0`Re 4 10 and 0Á67 4 Pr 4 6Á4. The ®ve selected OBCs, applied at the outlet of the computational domain, respectively express the following conditions: a square pro®le for the velocity (OBC1), mass conservation (OBC2), zero second derivative of the horizontal velocity component (OBC3), a mixed boundary condition combining Dirichlet and Neumann conditions (OBC4) and an Orlanski-type boundary condition (OBC5). A good estimation of the perturbation amplitude and of the length of the perturbed zone at the outlet boundary is proposed. It is shown that OBC5 causes very little perturbation in the recirculating¯ow compared with the other OBCs.

Observations d'une instabilité convective apparaissant sous la forme de rouleaux sinueux dans un écoulement de Poiseuille–Rayleigh–BénardDevelopment of a convective instability as wavy rolls in a Poiseuille–Rayleigh–Bénard flow

“…À la sortie, on applique des conditions aux limites ouvertes « non réflectives » de type Orlanski [10,11] : Le code numérique utilisé dans cette étude résout les équations de Boussinesq (2) discrétisées au second ordre en temps et en espace. Les méthodes de différences finies centrées sont appliquées en espace, sur un maillage décalé carté-sien, de taille NX × NY × NZ, uniforme dans la direction x et raffiné aux parois dans les directions y et z.…”