AN EQUAL-ORDER VELOCITY-PRESSURE ALGORITHM FOR INCOMPRESSIBLE THERMAL-FLOWS .1. FORMULATION

A finite-element algorithm is presented for the solution of two- and t hree-dimensional incompressible laminar thermal flows. The algorithm i s cast in a time-dependent form and can be classified as a projection finite-element method. However, the procedure utilized for handling th e velocity-pressure coupling shares many features with the SIMPLER fin ite-difference method. In fact, given an initial or guessed velocity f ield, the pseudo-velocities, i.e., the velocities that would prevail i n the absence of the pressure field, are found first. Then, by enforci ng continuity on the pseudo-velocity field, the tentative pressure is estimated and the momentum equations are solved in sequence for the ve locity components. Afterward, continuity is enforced again to find cor rections that are used to modify the velocity field and the estimated pressure feed. Finally, if required, the energy equation is solved bef ore moving to the next step.