Augmented Lagrangian method and open boundary conditions in 2D simulation of Poiseuille-Benard channel flow

The main objective of this study is to compare the influence of different boundary conditions upon the incompressible Poiseuille-Benard channel flow (PBCF) in a 2D rectangular duct heated from below. In a first technical part the algorithm used to carry out this work, based on the augmented Lagrangian method, is presented. The implementation details of the five 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 less than or equal to 10,000, 0 < Re less than or equal to 10 and 0.67 less than or equal to Pr less than or equal to 6.4. The five selected OBCs, applied at the outlet of the computational domain, respectively express the following conditions: a square profile 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 flow compared with the other OBCs. (C) 1997 by John Wiley & Sons, Ltd.