Modelling of natural convection flows with large temperature differences: A benchmark problem for low mach number solvers. Part 1. Reference solutions

Mathematical Modelling and Numerical Analysis

Volumn 39, Issue 3, 2005, Pages 609-616

  Le Quéré, Patrick ^a   Weisman, Catherine ^a   Paillère, Henri ^b   Vierendeels, Jan ^c   Dick, Erik ^c   Becker, Roland ^d   Braack, Malte ^d   Locke, James ^e  

^a UFR 919 Laboratoire d'Informatique Pour la Mécanique et les Sciences de l'Ingénieur   (France)

^b CEA SACLAY   (France)

^c GHENT UNIVERSITY   (Belgium)

^d UNIVERSITY OF HEIDELBERG   (Germany)

^e UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

Low Mach number; Natural convection; Non Boussinesq

Indexed keywords

EID: 22144477150     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:2005027     Document Type: Conference Paper

References (15)

1. R. Becker, M. Braack and R. Rannacher, Numerical simulation of laminar flames at low Mach number with adaptive finite elements. Combustion Theory and Modelling, Bristol 3 (1999) 503-534.
2. R. Becker, M. Braack, Solution of a stationary benchmark problem for natural convection with high temperature difference. Int. J. Thermal Sci. 41 (2002) 428-439.
3. D.R. Chenoweth and S. Paolucci, Natural Convection in an enclosed vertical air layer with large horizontal temperature differences. J. Fluid Mech. 169 (1986) 173-210.
4. G. de Vahl Davis, Natural convection of air in a square cavity: a benchmark solution. Int. J. Numer. Methods Fluids 3 (1983) 249-264.
5. G. de Vahl Davis and I.P. Jones, Natural convection of air in a square cavity: a comparison exercice. Int. J. Numer. Methods Fluids 3 (1983) 227-248.
6. FEAT User Guide, Finite Element Analysis Toolbox, British Energy, Gloucester, UK (1997).
7. D.D. Gray and A. Giorgini, The Validity of the Boussinesq approximation for liquids and gases. Int. J. Heat Mass Transfer 15 (1976) 545-551.
8. P. Le Quéré, Accurate solutions to the square differentially heated cavity at high Rayleigh number. Comput. Fluids 20 (1991) 19-41.
9. P. Le Quéré, R. Masson and P. Perrot, A Chebyshev collocation algorithm for 2D Non-Boussinesq convection. J. Comput. Phys. 103 (1992) 320-335.
10. W.L. Oberkampf and T. Trucano, Verification and validation in Computational Fluid Dynamics. Sandia National Laboratories report SAND2002-0529 (2002).
11. H. Paillère and P. Le Quéré, Modelling and simulation of natural convection flows with large temperature differences: a benchmark problem for low Mach number solvers, 12th Séminaire de Mécanique des Fluides Numérique, CEA Saclay, France, 25-26 Jan., 2000.
12. S. Paolucci, On the filtering of sound from the Navier-Stokes equations. Sandia National Laboratories report SAND82-8257 (1982).
13. J.C. Patterson and J. Imberger, Unsteady natural convection in a rectangular cavity. J. Fluid Mech. 100 (1980) 65-86.
14. V.L. Polezhaev, Numerical solution of the system of two-dimensional unsteady Navier-Stokes equations for a compressible gas in a closed region. Fluid Dyn. 2 (1967) 70-74.
15. J. Vierendeels, K. Riemslagh and E. Dick, A Multigrid semi-implicit line-method for viscous incompressible and low-Mach number flows on high aspect ratio grids. J. Comput. Phys. 154 (1999) 310-341.