Abstract. 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heated square cavity problem to the case of large temperature differences for which the Boussinesq approximation is no longer valid. The paper is split in two parts: in this first part, we propose as yet unpublished reference solutions for cases characterized by a non-dimensional temperature difference of 0.6, Ra = 10 6 (constant property and variable property cases) and 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.Mathematics Subject Classification. 65M50, 76M10, 76M12, 76M20, 76M22, 76R10.
Abstract. 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.Mathematics Subject Classification. 65M50, 76M10, 76M12, 76M20, 76M22, 76R10.
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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible.
AbstractNumerical simulations of compressible Navier-Stokes equations in closed twodimensional channels are performed. A plane standing wave is excited inside the channel and the associated acoustic streaming is investigated for high intensity waves, in the nonlinear streaming regime. Significant distortion of streaming cells is observed, with the centers of streaming cells pushed towards the end-walls. The mean temperature evolution associated to the streaming motion is also investigated.
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