Computation of buoyancy-driven flows using a block-implicit numerical scheme

Abstract

Numerical results for natural convection flows obtained by a point-wise locally-implicit scheme are reported. Computations are presented for incompressible laminar thermally-driven flow inside a square cavity. Governing equations are written in terms of the so-called primitive variables and are recast into a general form. Finite-differencing is obtained by means of the widely-used control-volume approach. The discretized momentum equations are applied to each cell face and then, together with the mass-continuity and energy equations, are simultaneously solved by means of a direct method in each computational node. An Alternating Symmetrical Coupled Gauss-Siedel procedure is employed in which iterations are performed alternating the most varying index in every sweep over the computational domain. Flow pattern and mass residual behavior are reported.