Mm. Elrefaee et al., STEADY-STATE SOLUTIONS OF BUOYANCY-ASSISTED INTERNAL FLOWS USING A FAST FALSE IMPLICIT TRANSIENT SCHEME (FITS), INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW, 6(6), 1996, pp. 3-23
A fast false implicit transient scheme FITS is developed to predict th
e two-dimensional steady-state solutions of buoyancy-assisted laminar
internal flows. This new scheme uses the control volume based on power
law technique in conjugation with the alternating direction implicit
(ADI) and the successive grid refinement (SGR) procedures to solve the
transient vorticity and energy transport equations. The ADI procedure
allows the power law, which gives an excellent approximation to the e
xact I-D solution, to be applied locally in one-dimensional sense for
each sweep in the co-ordinates' directions. This in turn increased the
solution accuracy and hence permits the use of a larger time incremen
t. As a result a remarkable increase in the convergence rate to steady
-state is achieved. The final solution is obtained by successively ref
ining the grid as the solution advances in time. The efficiency of FIT
S is verified by comparing the present predictions with three steady-s
tate benchmark solutions: natural convection of a heat generating flui
d in a rectangular enclosure, natural convection inside a cavity with
two isothermal walls, and a vertical buoyancy-assisted laminar backwar
d-facing step flow.