GDQ Method for Natural Convection in a Cubic Cavity Using Velocity–Vorticity Formulation

ABSTRACT

Natural convection in a differentially heated cubic enclosure is studied by solving the velocity–vorticity form of the Navier–Stokes equations by a generalized differential quadrature (GDQ) method. The governing equations in the form of velocity Poisson equations, vorticity transport equations, and energy equation are solved using a coupled numerical scheme via a single global matrix for velocities, vorticities, and temperature. Vorticity and velocity coupling at the solid boundaries is enforced through a higher-order approximation by the GDQ method, thus assuring accurate satisfaction of the continuity equation. Nusselt numbers computed for Ra = 10³, 10⁴, 10⁵, and 10⁶ show good agreement with the benchmark results. A mesh independence study indicates that the present numerical procedure requires much coarse mesh compared to other numerical schemes to produce the benchmark solutions of the flow and heat transfer problems.

We acknowledge financial support from the National Science Council of Taiwan through Grant NSC-93-E-002-017, and it is gratefully appreciated.