A Spectral Collocation Method for TwoDimensional Compressible Convection
Abstract
A FourierChebyshev spectral simulation of twodimensional compressible convection is presented. The fluid is a perfect gas with constant dynamic viscosity and thermal conductivity. Both slippery and rigid boundary conditions for the velocity are used here. The temperature is maintained fixed at the upper and lower boundaries. An explicit AdamsBashforth predictorcorrector numerical scheme is used in order to overcome the CourantFriedriechsLewy condition. The nonlinear diffusion terms are handled by an iterative method, with finite differences or spectral preconditioning. Steady state solutions have been obtained for both types of boundary conditions. Critical exponents are found to be the same as in the incompressible case, at least for a weak value of the stratification parameter.
 Publication:

Journal of Computational Physics
 Pub Date:
 March 1988
 DOI:
 10.1016/00219991(88)901088
 Bibcode:
 1988JCoPh..75..217G
 Keywords:

 Compressible Flow;
 Computational Fluid Dynamics;
 Free Convection;
 Spectral Methods;
 Two Dimensional Flow;
 Collocation;
 Iterative Solution;
 Nusselt Number;
 Rayleigh Number;
 Fluid Mechanics and Heat Transfer