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
ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 3, pp. 617-621.

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.

DOI : 10.1051/m2an:2005025
Classification : 65M50, 76M10, 76M12, 76M20, 76M22, 76R10
Mots clés : natural convection, non-Boussinesq, low Mach number
Paillère, Henri 1 ; Quéré, Patrick Le  ; Weisman, Catherine  ; Vierendeels, Jan 2 ; Dick, Erik  ; Braack, Malte 3 ; Dabbene, Frédéric  ; Beccantini, Alberto  ; Studer, Etienne  ; Kloczko, Thibaud  ; Corre, Christophe 4 ; Heuveline, Vincent  ; Darbandi, Masoud 5 ; Hosseinizadeh, Seyed Farid 

1 CEA Saclay, DEN/DM2S/SFME,91191 Gif-sur-Yvette Cedex, France.
2 Ghent University, 9000 Gent, Belgium. ; ; Ghent University, B-9000 Gent, Belgium.
3 Heidelberg University, Germany
4 SINUMEF Lab., ENSAM, 151 bd. de l’Hôpital, 75013 Paris, France
5 Sharif University of Technology, Tehran, Iran
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     title = {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},
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Paillère, Henri; Quéré, Patrick Le; Weisman, Catherine; Vierendeels, Jan; Dick, Erik; Braack, Malte; Dabbene, Frédéric; Beccantini, Alberto; Studer, Etienne; Kloczko, Thibaud; Corre, Christophe; Heuveline, Vincent; Darbandi, Masoud; Hosseinizadeh, Seyed Farid. 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. ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 3, pp. 617-621. doi : 10.1051/m2an:2005025. http://archive.numdam.org/articles/10.1051/m2an:2005025/

[1] A. Beccantini et al., Simulation of Hydrogen Release and Combustion in large Scale Geometries: Models and Methods, Int. Conf. Supercomputing for Nuclear Applications (SNA 2003), Paris, 22-24 September, 2003.

[2] R. Becker and M. Braack, Multigrid techniques for finite elements on locally refined meshes. Numer. Linear Algebra Appl. 7 (2000) 363-379. | Zbl

[3] M. Darbandi and S.F. Hosseinizadeh, General pressure-correction strategy to include density variation in incompressible algorithms. AIAA J. Thermophysics Heat Transfer 17 (2003) 372-380.

[4] V. Heuveline, On higher-order mixed FEM for low Mach number flows: application to a natural convection benchmark problem. Internat. J. Numer. Methods Fluids 41 (2003) 1339-1356. | Zbl

[5] T. Kloczko, C. Corre and A. Beccantini, A Matrix-Free Implicit Method for Flows at all Speeds, Proc. ICCFD3 Conference, Toronto, Canada, 11-15 July, 2004.

[6] H. Paillère and J.P. Magnaud, A Finite Element Elliptic Flow Solver for Low-Mach Number Compressible Flows, in 10th Int. Conf. Finite Elements in Fluids, Tuscon, Az, USA, 5-8 January (1998).

[7] 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. | Zbl

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