Numerical exploration of 1+2 type laminar natural convection in a differentially heated square cavity using Chebyshev spectral collocation method

Chuanta Lin, Hongxing Yang, Zuojin Zhu

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In this paper, the Chebyshev spectral collocation method is applied to explore the unsteady two dimensional (1+2 type) laminar natural convection in a differentially heated square cavity at a Rayleigh number (Ra) of 107. The method has embedded the traditional Chorin's algorithm so as to avoid the trouble of seeking the pressure field in the buoyancy driven wall-jet flow. The sensitivity of the δ- parameter has been numerically investigated. It is found that when the δ value is over 11.6173, numerical instability occurs. Comparing the maximum horizontal velocity component with the existing numerical data obtained by solving the Poisson's equation of pressure field reveals that the Chorin's algorithm should be inapplicable for the solution of the benchmark problem of natural convection at Ra=107in thermal science.
Original languageEnglish
Pages (from-to)593-597
Number of pages5
JournalInternational Communications in Heat and Mass Transfer
Issue number5
Publication statusPublished - 1 May 2012


  • Chebyshev spectral collocation method
  • Chorin's algorithm
  • Laminar natural convection

ASJC Scopus subject areas

  • Chemical Engineering(all)
  • Condensed Matter Physics
  • Atomic and Molecular Physics, and Optics

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