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heated square cavity problem to the case of large temperature differences for which the Boussinesq approximation is no longer valid. The paper is split in two parts: in this first part, we propose as yet unpublished reference solutions for cases characterized by a non-dimensional temperature difference of 0.6, $\mathrm{Ra}={10}^{6}$ (constant property and variable property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.

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

^{}; Weisman, Catherine

^{}; Paillère, Henri

^{1}; Vierendeels, Jan

^{2}; Dick, Erik

^{}; Becker, Roland

^{3}; Braack, Malte

^{3}; Locke, James

^{4}

@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 }, pages = {609--616}, publisher = {EDP-Sciences}, volume = {39}, number = {3}, year = {2005}, doi = {10.1051/m2an:2005027}, zbl = {1130.76047}, mrnumber = {2157153}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2005027/} }

TY - JOUR AU - Quéré, Patrick Le AU - Weisman, Catherine AU - Paillère, Henri AU - Vierendeels, Jan AU - Dick, Erik AU - Becker, Roland AU - Braack, Malte AU - Locke, James TI - Modelling of natural convection flows with large temperature differences : a benchmark problem for low Mach number solvers. Part 1. Reference solutions JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2005 SP - 609 EP - 616 VL - 39 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2005027/ DO - 10.1051/m2an:2005027 LA - en ID - M2AN_2005__39_3_609_0 ER -

%0 Journal Article %A Quéré, Patrick Le %A Weisman, Catherine %A Paillère, Henri %A Vierendeels, Jan %A Dick, Erik %A Becker, Roland %A Braack, Malte %A Locke, James %T Modelling of natural convection flows with large temperature differences : a benchmark problem for low Mach number solvers. Part 1. Reference solutions %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2005 %P 609-616 %V 39 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2005027/ %R 10.1051/m2an:2005027 %G en %F 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 , Volume 39 (2005) no. 3, pp. 609-616. doi : 10.1051/m2an:2005027. http://www.numdam.org/articles/10.1051/m2an:2005027/

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