Time‐dependent natural convection in a square cavity: Application of a new finite volume method

Abstract

Abstract A new finite volume (FV) approach with adaptive upwind convection is used to predict the two‐dimensional unsteady flow in a square cavity. The fluid is air and natural convection is induced by differentially heated vertical walls. The formulation is made in terms of the vorticity and the integral velocity (induction) law. Biquadratic interpolation formulae are used to approximate the temperature and vorticity fields over the finite volumes, to which the conservation laws are applied in integral form. Image vorticity is used to enforce the zero‐penetration condition at the cavity walls. Unsteady predictions are carried sufficiently forward in time to reach a steady state. Results are presented for a Prandtl number ( Pr ) of 0‐71 and Rayleigh numbers equal to 10 3 , 10 4 and 10 5 . Both 11 × 11 and 21 × 21 meshes are used. The steady state predictions are compared with published results obtained using a finite difference (FD) scheme for the same values of Pr and Ra and the same meshes, as well as a numerical bench‐mark solution. For the most part the FV predictions are closer to the bench‐mark solution than are the FD predictions.