Modelling of natural convection flows with large temperature differences: A benchmark problem for low Mach number solvers. Part 2. Contributions to the June 2004 conference

In the second part of the paper, we compare the solutions produced in the framework of the conference “Mathematical and numerical aspects of low Mach number flows” organized by INRIA and MAB in Porquerolles, June 2004, to the reference solutions described in Part 1. We make some recommendations on how to produce good quality solutions, and list a number of pitfalls to be avoided.

[1]  G. D. Davis Natural convection of air in a square cavity: A bench mark numerical solution , 1983 .

[2]  V. Polezhaev Numerical solution of the system of two-dimensional unsteady Naver-Stokes equations for a compressible gas in a closed region , 1967 .

[3]  Christophe Eric Corre,et al.  A Matrix-Free Implicit Method for Flows at All Speeds , 2006 .

[4]  S. Paolucci,et al.  Natural convection in an enclosed vertical air layer with large horizontal temperature differences , 1986, Journal of Fluid Mechanics.

[5]  G. de Vahl Davis,et al.  Natural convection in a square cavity: A comparison exercise , 1983 .

[6]  Roland Becker,et al.  Multigrid techniques for finite elements on locally refined meshes , 2000, Numer. Linear Algebra Appl..

[7]  Vincent Heuveline,et al.  On higher‐order mixed FEM for low Mach number flows: application to a natural convection benchmark problem , 2003 .

[8]  D. Gray,et al.  The validity of the boussinesq approximation for liquids and gases , 1976 .

[9]  Rolf Rannacher,et al.  Numerical simulation of laminar flames at low Mach number by adaptive finite elements , 1999 .

[10]  Roland Becker,et al.  Solution of a stationary benchmark problem for natural convection with large temperature difference , 2002 .

[11]  Samuel Paolucci,et al.  Filtering of sound from the Navier-Stokes equations , 1982 .

[12]  Masoud Darbandi,et al.  General Pressure-Correction Strategy to Include Density Variation in Incompressible Algorithms , 2003 .

[13]  Jörg Imberger,et al.  Unsteady natural convection in a rectangular cavity , 1980, Journal of Fluid Mechanics.

[14]  P. Le Quéré,et al.  A Chebyshev collocation algorithm for 2D non-Boussinesq convection , 1992 .

[15]  Jan Vierendeels,et al.  A multigrid semi-implicit line-method for viscous incompressible and low-mach-number flows on high aspect ratio grids , 1999 .

[16]  Timothy G. Trucano,et al.  Verification and Validation in Computational Fluid Dynamics , 2002 .