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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 3, p. 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 : https://doi.org/10.1051/m2an:2005025
Classification:  65M50,  76M10,  76M12,  76M20,  76M22,  76R10
Keywords: natural convection, non-Boussinesq, low Mach number
@article{M2AN_2005__39_3_617_0,
     author = {Paill\`ere, Henri and Qu\'er\'e, Patrick Le and Weisman, Catherine and Vierendeels, Jan and Dick, Erik and Braack, Malte and Dabbene, Fr\'ed\'eric and Beccantini, Alberto and Studer, Etienne and Kloczko, Thibaud and Corre, Christophe and Heuveline, Vincent and Darbandi, Masoud and Hosseinizadeh, Seyed Farid},
     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},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {3},
     year = {2005},
     pages = {617-621},
     doi = {10.1051/m2an:2005025},
     zbl = {1130.76049},
     mrnumber = {2157154},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2005__39_3_617_0}
}
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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 3, pp. 617-621. doi : 10.1051/m2an:2005025. http://www.numdam.org/item/M2AN_2005__39_3_617_0/

[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 1051.65117

[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 1047.76045

[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 0955.76067