Numerical Simulation of Natural Convection in Closed Containers by a Fully Implicit Method

Abstract

Numerical solutions have been obtained for two-dimensional free convective flow in rectangular and annular cavities by the strongly implicit procedure (SIP) and the cyclic reduction-fast Fourier transform (CR-FFT) technique. Rayleigh numbers range from 104 to 106 , Prandtl numbers from 0.713 to 103 , radius ratios from 1 to 3 (annular cavities), and aspect ratios (height/width) from 1 to 15. Motion is generated by either uniformly heating the bottom wall or heating a vertical wall and cooling the opposite wall. Both time-dependent and steady-state solutions confirm results previously obtained by others. Because SIP uses a common set of matrix algorithms, the governing equations of motion can be solved simultaneously without major modification to the method for each equation.