Numerical approaches in natural convection problems

Natural convection in vertical long shaped cavities, for which the motion is two dimensional and steady, is studied numerically using classical, hermitian, and combined finite difference methods. Spectral and pseudospectral methods are also used and compared. Due to the high resolution of Chebyshev polynomials the spectral approximations are more efficient in terms of the number of degrees of freedom than hermitian finite difference approximations. However, due to the use of purely unstationary methods with explicit schemes which make the marching easier, the global cost of spectral solutions is three times greater than the cost of accurate finite difference solutions.