In the second part of the paper, we compare the solutions producedin the framework of the conference “Mathematical and numericalaspects of low Mach number flows” organized by INRIA and MAB inPorquerolles, June 2004, to the reference solutions described inPart 1. We make some recommendations on how to produce goodquality solutions, and list a number of pitfalls to be avoided.

There are very few reference solutions in the literature onnon-Boussinesq natural convection flows. We propose here a testcase problem which extends the well-known De Vahl Davisdifferentially heated square cavity problem to the case of largetemperature differences for which the Boussinesq approximation isno longer valid. The paper is split in two parts: in this firstpart, we propose as yet unpublished reference solutions for casescharacterized by a non-dimensional temperature difference of 0.6,Ra = 106 (constant property and variable property cases) andRa = 107 (variable property case). These reference solutions wereproduced after a first international workshop organized by CEA andLIMSI in January 2000, in which the above authors volunteered toproduce accurate numerical solutions from which the presentreference solutions could be established.