On a Grid Generation Method Based Upon Inhomogeneous Elliptic Partial Differential Equations

Abstract

A nearly-orthogonal boundary-conforming grid generation technique based upon inhomogeneous elliptic partial differential equations is presented. The method has been designed to generate grids for multiply-connected domains in a block-structure fashion. It also allows for control of point distribution along boundaries, as well as control of grid spacing inside the domain by using a slightly modified version of the renowned Thompson's control functions, which is reported to work well. Although not fully-automatic, the process is automatized in order to make it more usable and speed-up computational time, which is usually a demotivating factor in elliptic grid generation techniques. This is also the reason why the implementation has been performed in an objected-oriented fashion using C++ and as relaxation method the Alternating Direction Implicit (ADI) with-sequence, generating appealing results. The method presented can be fully extended to 3D. Some results are presented and discussed.