Application of a pressure gradient method to a transient natural convection problem.

Abstract

The pressure gradient method using components of pressure gradients as dependent variables is applied to the simulation of two-dimensional transient natural convection in a horizontal circular cylinder, where fluid is initially at rest, and then the wall is subject to a step change of temperature. It is found that, at least in the case of a low Grashof number flow, relative errors of velocity, pressure, and temperature, produced by the present method are smaller than those produced by a primitive velocity-pressure variable method and that, over the wide range of a Grashof number, from 5×102 to 2×105, the prediction of the maximum of the magnitude of velocity at the center and of the time when the magnitude of the velocity at the center becomes maximum is in good agreement with the available experimental data.