Open AccessA 3D Chebyshev-Fourier algorithm for convection equations in low Mach number approximation
Author(s) -
Ouafa Bouloumou,
Éric Serre,
Jochen Fröhlich
Publication year - 2009
Publication title -
european journal of computational mechanics
Language(s) - English
Resource type - Journals
eISSN - 2642-2085
pISSN - 2642-2050
DOI - 10.13052/ejcm.18.607-625
Subject(s) - discretization , mach number , mathematics , chebyshev filter , mathematical analysis , fourier transform , natural convection , chebyshev polynomials , reynolds number , fast fourier transform , boussinesq approximation (buoyancy) , convection , physics , mechanics , rayleigh number , algorithm , turbulence
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 preconditioned 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 x 105 is unstable to 3D perturbations.