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

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 Chorinʹs 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 Poissonʹs equation of pressure field reveals that the Chorinʹs algorithm should be inapplicable for the solution of the benchmark problem of natural convection at Ra = 107 in thermal science.