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A 3D SPECTRAL METHOD FOR CONVECTION EQUATIONS IN LOW MACH NUMBER APPROXIMATION

DOI: 10.1615/ICHMT.2008.CHT.1290
16 pages

Ouafa Bouloumou
MSNM-GP UMR 6181 CNRS. 38, rue Frédéric Joliot Curie. 13451, Marseille Cedex 20

Eric Serre
Aix-Marseille Universite, CNRS, Ecole Centrale Marseille, Laboratoire M2P2, Marseille, France

要約

A three-dimensional spectral method based on Chebyshev-Chebyshev-Fourier discretizations is presented in the framework of the low Mach number approximation of Navier-Stokes equations. The working fluid is assumed to be a perfect gas with constant thermodynamic properties. The generalized Stokes problem, which arises from the time discretization by a second-order semi-implicit scheme, is solved by a preconditionned iterative Uzawa algorithm. Several validation results are presented in the case of steady and unsteady flows. This model is also evaluated for natural convection flows with large density variations in the case of a tall differentially heated cavity of aspect ratio 8. It is found that on contrary to convection at small temperature differences (Boussinesq), the 2D unsteady solution at Ra = 3.4×105 is unstable to 3D perturbations.

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