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

Abstract

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.