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Modelling of natural convection flows with large temperature differences: a benchmark problem for low Mach number solvers. I: Reference solutions. (English) Zbl 1130.76047

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heated square cavity problem to the case of large temperature differences for which the Boussinesq approximation is no longer valid. The paper is split in two parts: in this first part, we propose as yet unpublished reference solutions for cases characterized by a non-dimensional temperature difference of 0.6, Ra=10\(^6\) (constant property and variable property cases)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

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76R10 Free convection
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
76M12 Finite volume methods applied to problems in fluid mechanics
76M20 Finite difference methods applied to problems in fluid mechanics
76M22 Spectral methods applied to problems in fluid mechanics

Citations:

Zbl 1130.76049
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References:

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