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Octree-Based Projection Mesh Generation for Complex 'Dirty' Geometries Octree-based Projection Mesh Generation for Complex 'Dirty' Geometries ALEXANDER V. SHEVELKO A thesis submitted in partial fulfilment of the requirements of the University of Brighton for the degree of Doctor of Philosophy April 2006 The University of Brighton in collaboration with Ricardo UK Limited Abstract The problem of robust fully automatic 3D body-fitted mesh generation for industrial geometries is considered. A new projection-based method is developed for a general-type unstructured solver. Unlike other projection techniques, it starts with generation of a high quality prismatic dummy boundary layer. The nodes are gradually moved towards the domain boundaries and important geometric features are resolved. The minimum mesh quality is preserved at every stage of the process. This guarantees that the obtained grid is valid for calculations. The algorithm uses octree data structure as a base mesh. Its implementation is described in detail. Geometry localisation and the refinement criteria for 'dirty' geometries are further developed. The method starts with triangulated geometric boundaries. The quality of the input data can be extremely poor. A problem of leaking of the base mesh is considered. Several strategies to overcome it are proposed. The generated polyhedral mesh can also be used for fully automatic tetrahedral or hybrid grid generation. Near boundary prismatic cells can be anisotropically refined for boundary layer mesh generation for viscous flow calculations. The developed methodology can also be used for polygonal, triangular or hybrid surface mesh generation and shrink-wrapping to achieve the following basic aims: 'cleaning' of 'dirty' geometries, reduction of model elements, generation of external surfaces, thickening and offset of geometries. The spatial and surface mesh generation and shrink-wrapping are implemented as a computer program. User intervention can be reduced to a setting of several control parameters leading to a fully automatic mesh generation process. Examples of generated meshes and calculations for several engineering models are given. 11 Dedication This thesis is dedicated to my deeply beloved friend Lesya (24 April 1990 - 25 September 2004), whom I miss dearly ... iii Table of Contents ABSTRACT ............................................................................................................................................... 11 DEDICATION ......................................................................................................................................... III TABLE OF CONTENTS ........................................................................................................................ IV LIST OF FIGURES ................................................................................................................................. VI LIST OF TABLES ..................................................................................................................................... X ACKNOWLEDGMENTS ....................................................................................................................... XI DECLARATION .................................................................................................................................... XII ABBREVIATIONS ............................................................................................................................... XIII CHAPTER 1. INTRODUCTION .............................................................................................................. ! 1.1 BACKGROUND .................................................................................................................................... 1 1.2 THE AIM OF THE THESIS .............................................................. ...................................................... .4 1.3 CONTRIBUTION ................................................................................................................................... 5 1.4 THESIS OUTLINE ................................................................................................................................. 6 CHAPTER 2. LITERATURE REVIEW .................................................................................................. 8 2.1 INTRODUCTION ................................................................................................................................... 8 2.2 MESH REQUIREMENTS ........................................................................................................................ 9 2.3 MESH CHARACTERISTICS .................................................................................................................. 11 2.4 MESH CLASSIFICATION ..................................................................................................................... 14 2.5 CLASSIFICATION OF MESH GENERATION METHODS ......................................................................... 17 2.5.1 Parametric Methods .... .... ........... ................................................................ ..... ...... ............ .... ... 17 2.5.2 Insertion I Creation Methods ........... .... ........................... .... ...... ... ............................... .. ........... 18 2.5.3 Spatial Decomposition and Hybrid Methods ........................................................ .... ........ .. ..... 18 2.6 CLASSIFICATION OF CARTESIAN-BASED METHODS ........................................................................... 19 2.7 NON-BODY-FITTED CARTESIAN-BASED METHODS ............................................................................ 20 2. 7.1 Stair-cased Methods ....... .................................................. ........................................................ 20 2. 7.2 Cut-cell Methods .............................. ...... ..... ...... ....... ... ... ...................... ............ ...... ........ ..... .. ... 21 2. 7. 3 Treatments ofthe Small Cell Problem ............ ........ .. .................... .. ............... ................ .......... 24 2. 7. 4 MC-based Methods ... ..... ... ... .... .. ...... .. ........ .. .......................................... ...... ............ ................ 26 2.8 HYBRID CARTESIAN-BASED METHODS ............................................................................................. 29 2. 8.1 Structured/Unstructured Methods ............................ ................................................................ 29 2.8.2 Overset Methods .... ....... ........ .................. .............................. .. ....... .. .... .............. .. ...... .............. 31 2.9 PROJECTION-BASED METHODS ......................................................................................................... 32 2. 9.1 Modified-Quadtree/Octree Method .. ..... ........... .... .... ... .......... .......................... ...... ................... 33 2.9.2 Multiple Projections Methods .................... ....................... .......................... ..... .... .. ........ ... .... ... 34 2.9.3 Minimum Distance Methods ................................................ .... ... ................... ...... ... ................. 37 2.9.4 Hybrid Projection Methods .............. ............ ........... .... ... .... ...................................................... 40 2.10 CONCLUSIONS TO CHAPTER 2 ........................................................................................................ .41 CHAPTER 3. OCTREE MESH GENERATION .................................................................................. 44 3.1 INTRODUCTION ................................................................................................................................ .44 3.2 OCTREE DOMAIN DECOMPOSITION ................................................................................................... 45 3.2.1 Basic Notions .................................................... ................................... .. ......... ..... ... ................. 45 3.2.2 Octree Data Structure ....................... .. ..... ... ..... ............... .... ........................... ........... ............... 47 3.2.3 Tree Operations .................................... ........... ................... .................... .. .......... .... .......... ....... 50 3.3 GEOMETRY LOCALISATION ............................................................................................................... 53 3. 3.1 Localisation Methods ......................................... ................ .. .. ... .................. ............................. 54 3.3.2 VG+ Octree Localisation ... ....................................................................... .. ........................... 56 3 .4 CELL REFINEMENT ........................................................................................................................... 60 3. 4.1 Refinement Criteria for 'Clean' Geometries ............................ ................................................ 60 3.4.2 Internal and External Notions ........................... .... ........... ....... ............................................... .. 62 3. 4. 3 Refinement Criteria for 'Dirty' Geometries ..... ..... .... .... ..................................... ...................... 64 lV 3.4.4 Summary ofthe Refinement Criteria .............................................. ........ ...... .. ................... .... ... 68 3.5 FRONT GENERATION ......................................
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