Automatic elliptic grid generation by an approximate factorisation

Abstract

A procedure for automatic numerical generation of a structured grid system with coordinate lines coinciding with all boundaries of a general two-dimensional region containing a body of arbitrary shape is presented. The solution procedure incorporated the method of false transients and the approximate factorisation algorithm, where a sequence of time steps is cycled in a geometric fashion with repeated endpoints, and has a capability for clustering grid lines close to the body. The procedure requires significantly much less computational effort to obtain a converged solution than a point or line successive over-relaxation iterative scheme. Although, the superiority of the presented algorithm has been demonstrated for the grid generation problem, it can be utilised for other problems requiring the solution of a set of elliptic partial differential equations of similar nature.