The Method of Variable False Tranelents for the Solution of Coupled Elliptic Equations

Abstract

A method for the numerical solution of coupled, non-linear elliptic, partial differential equation is described. The essential feature of the formulation is the use of different false transient factors in different flow regions. In regions where velocity gradients are high, small time steps are required so that small false transient factor are used, elsewhere large time steps and false transients factors are employed. The number of iteration required for convergence was significantly reduced when compared with the conventional method. The effectiveness of the method is demonstrated by applying it to the problem of natural convection in a three dimensional enclosure heated and cooled on one wall.