TEMPORAL, SPATIAL AND THERMAL FEATURES OF 3-D RAYLEIGH-BENARD CONVECTION BY A LEAST-SQUARES FINITE-ELEMENT METHOD

Numerical solutions of 3-D time-dependent Rayleigh-Benard convection a re presented in this work. The temporal, spatial and thermal features of convective patterns are studied for four different geometric aspect ratios, 2:1:2, 4:1:4, 5:1:5 and 3.5:1:2.1 at supercritical Rayleigh n umbers Ra = 8 x 10(3), 2.4 x 10(4) and Prandtl numbers Pr = 0.71, 2.5. Several physical phenomena, such as multicellular flow pattern, oscil latory transient solution,'T-shaped' rolls at the ends of a rectangula r box, and roll alignment, are observed in our simulations. The numeri cal technique is based on an implicit, fully coupled, and time-accurat e method, which consists of the Crank-Nicolson scheme for time integra tion, Newton's method for the convective terms with extensive lineariz ation steps, and a least-squares finite element method. A matrix-free algorithm of the Jacobi conjugate gradient method is implemented to so lve the symmetric, positive definite linear system of equations.