A 3D Chebyshev-Fourier algorithm for convection equations in low Mach number approximation

Authors

  • Ouafa Bouloumou MSNM-GP UMR 6181 38 rue F. Joliot-Curie, 13451 Marseille cedex 20, France
  • Eric Serre MSNM-GP UMR 6181 38 rue F. Joliot-Curie, 13451 Marseille cedex 20, France
  • Jochen Fröhlich Institute for Fluid Mechanics, Technical University of Dresden 01062 Dresden, Germany

DOI:

https://doi.org/10.13052/EJCM.18.607-625

Keywords:

spectral methods, convection, low Mach number

Abstract

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.

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Published

2009-02-04

How to Cite

Bouloumou, O. ., Serre, E. ., & Fröhlich, J. . (2009). A 3D Chebyshev-Fourier algorithm for convection equations in low Mach number approximation. European Journal of Computational Mechanics, 18(7-8), 607–625. https://doi.org/10.13052/EJCM.18.607-625

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