Generation of three-dimensional body-fitted coordinates using hyperbolic partial differential equations

Abstract : The purpose of this research has been to further develop a simple efficient grid generation procedure for external aerodynamics applications. The grid generation scheme is based on solving hyperbolic partial differential equation constraints of grid angularity and mesh incremental volumes. The grid generation scheme has been previously used in two dimensional applications to generate grids about smooth body shapes. The main thrust of this AFOSR supported research has been to extend the hyperbolic partial differential equation procedure to three dimensional applications and to study ways of applying the procedure to body shapes that have discontinuous derivatives. The main part of this report, Part I, is devoted to describing the three dimensional hyperbolic grid generator. This Section first reviews the hyperbolic grid generation procedure in two dimensions and then describes the extension to three dimensions. Part II of this report is both brief and sketchy in its presentation. In this section we describe some of our success in treating bodies with sharp edges and bodies that are exceptionally concave. The last part of this report describes a flow field algorithm development. During the course of this research we had some considerable interaction with AFWAL, and at one point became 'side-tracked' into a successful approach of improving the efficiency of our general implicit Euler and navier-Stokes code.