A Quasi-Implicit Time-Advancing Scheme for 3-D Rayleigh-Bénard Convection

Abstract

A quasi-implicit time-advancing scheme based on an unstructured finite-volume formulation is presented for solving unsteady thermofluid flows. The developed model is first used to simulate 2-D natural convection with Rayleigh number ranging from 10³ to 10⁶. Steady-state solution is obtained in an unsteady time-marching manner. Heat transfer from conduction-dominant to convection-dominant is illustrated. The method is then applied to unsteady 3-D Rayleigh-Bénard convective flows. 3-D Rayleigh-Bénard convections with Rayleigh number 3,416 and 13,900 are studied. Evolution of thermofluid flow undergoing a sequence of transitions is identified. Spatially periodic patterns of polygonal cells are reproduced. Decrease of number of Rayleigh-Bénard cells as Rayleigh number increases is discerned. Results of the computed wave number and Nusselt number compare well with available experimental data and other numerical results.