Temporal, spatial and thermal features of 3-D Rayleigh-Bénard convection by a least-squares finite element method

• Published in: Computer methods in applied mechanics and engineering 1997-01, Vol.140 (3), p.201-219
• Main Authors: Tang, Li Q., Tsang, Tate T.H.
• Format: Article
• Language: English
• Subjects: Convection and heat transfer; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Physics; Turbulent flows, convection, and heat transfer
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/S0045-7825(96)01053-5

Numerical solutions of 3-D time-dependent Rayleigh-Bénard convection are 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 numbers Ra = 8 × 10 3, 2.4 × 10 4 and Prandtl numbers Pr = 0.71, 2.5. Several physical phenomena, such as multicellular flow pattern, oscillatory transient solution, ‘T-shaped’ rolls at the ends of a rectangular box, and roll alignment, are observed in our simulations. The numerical technique is based on an implicit, fully coupled, and time-accurate method, which consists of the Crank-Nicolson scheme for time integration, Newton's method for the convective terms with extensive linearization steps, and a least-squares finite element method. A matrix-free algorithm of the Jacobi conjugate gradient method is implemented to solve the symmetric, positive definite linear system of equations.