There are very few reference solutions in the literature on non-Boussinesq natural convection flows. We propose here a test case problem which extends the well-known De Vahl Davis differentially heated square cavity problem to the case of large temperature differences for which the Boussinesq approximation is no longer valid. The paper is split in two parts: in this first part, we propose as yet unpublished reference solutions for cases characterized by a non-dimensional temperature difference of 0.6, $\mathrm{Ra}={10}^{6}$ (constant property and variable property cases) and $\mathrm{Ra}={10}^{7}$ (variable property case). These reference solutions were produced after a first international workshop organized by CEA and LIMSI in January 2000, in which the above authors volunteered to produce accurate numerical solutions from which the present reference solutions could be established.

Classification: 65M50, 76M10, 76M12, 76M20, 76M22, 76R10

Keywords: natural convection, non-Boussinesq, low Mach number

@article{M2AN_2005__39_3_609_0, author = {Qu\'er\'e, Patrick Le and Weisman, Catherine and Paill\`ere, Henri and Vierendeels, Jan and Dick, Erik and Becker, Roland and Braack, Malte and Locke, James}, title = {Modelling of natural convection flows with large temperature differences : a benchmark problem for low Mach number solvers. Part 1. Reference solutions}, 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 = {609-616}, doi = {10.1051/m2an:2005027}, zbl = {1130.76047}, mrnumber = {2157153}, language = {en}, url = {http://www.numdam.org/item/M2AN_2005__39_3_609_0} }

Quéré, Patrick Le; Weisman, Catherine; Paillère, Henri; Vierendeels, Jan; Dick, Erik; Becker, Roland; Braack, Malte; Locke, James. Modelling of natural convection flows with large temperature differences : a benchmark problem for low Mach number solvers. Part 1. Reference solutions. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 3, pp. 609-616. doi : 10.1051/m2an:2005027. http://www.numdam.org/item/M2AN_2005__39_3_609_0/

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