A modification to the simple method for buoyancy-driven flows

The essence of the SIMPLE method lies in its coupling between the momentum and continuity equations. Almost all the algorithms of the SIMPLE family are based on one precondition, that is, the corrected velocity is obtained from the corrected pressure only. However, in buoyancy-driven flows, there are two major factors driving the fluid movement: the temperature gradients and the pressure (including kinetic pressure) gradients. In this article, the effect of the temperature correction on the velocity correction is considered during the derivation of the pressure-linked equation. A modification to the SIMPLE algorithm, SIMPLET, is proposed and two cases are tested. It is shown that this modification provides a better convergence rate and more robust results.