AN EQUAL-ORDER VELOCITY-PRESSURE ALGORITHM FOR INCOMPRESSIBLE THERMAL FLOWS, PART 1: FORMULATION

Abstract

A finite-element algorithm is presented for the solution of two- and three-dimensional incompressible laminar thermal flows. The algorithm is cast in a time-dependent form and can be classified as a projection finite-element method. However, the procedure utilized for handling Ike velocity-pressure coupling shares many features with the SIMPLER finite-difference method. In fact, given an initial or guessed velocity field, the pseudo-velocities, i.e., the velocities that would prevail in the absence of the pressure field, are found first. Then, by enforcing continuity on the pseudo-velocity field, the tentative pressure is estimated and the momentum equations are solved in sequence for the velocity components. Afterward, continuity is enforced again to find corrections that are used to modify the velocity field and the estimated pressure field. Finally, if required, the energy equation is solved before moving to the next step.