Generating elliptic grids in three dimensions by a method of false transients

A finite difference method based scheme incorporating a method of false transients and an approximate factorisation technique is presented for solution of a system of Poisson's equations used for grid generation. A time step cycling process with repeated endpoints is incorporated into the scheme to enhance the convergence rate. The scheme required much less computational effort than all other numerical schemes compared in this article, to obtain a high quality grid over a body (converged solution) in three dimensions. Although, the superiority of the scheme has been demonstrated for a grid generation problem, it may be applied for other problems requiring the numerical solution of a set of similar partial differential equations.