A Simplified Mesh Generation Scheme for 3D Geometries Composed by Planar Faces to be used with BEM

Abstract

This paper presents the development of a simplified mesh generation scheme for three-dimensional boundary element method (BEM). The developed program presented in this work takes into account three-dimensional geometries composed by planar faces. This is a simplification regarding the form of the acceptable geometries, but a great variety of geometries and problems can be modelled with sufficient accuracy to perform numerical analysis. The main program’s idea consists of moving each face belonging to the three-dimensional geometry to bi-dimensional space using geometrical transformation matrices. In bi-dimensional space, then, it is applied a bi-dimensional mesh generation algorithm for element generation. After element generation is done, new geometrical transformations are applied in order to send the meshed face back to its original position in three-dimensional space. The continuity of the final mesh is assured by promoting the discretization of the edges of the geometry only once. The proposed scheme has several positive aspects regarding simplicity, efficiency and robustness. A practical and immediate use of the proposed algorithm can be found for those who already have a bi-dimensional mesh generator code implemented and intent to expand its functionalities to treat simple three-dimensional geometries composed by planar faces. Several examples of meshes in arbitrary three-dimensional geometries composed by planar faces are presented in order to illustrate the capabilities of the developed computational program and some computational simulations have been performed to show the quality of the meshes in problems with specific boundary conditions.