| Summary: | The discretisation of geometry into a mesh is a critical part of numerical simulation. Fully automatic' push-button' algorithms are available for generating tri and tet meshes but they are often eschewed in favour of multiblock structured meshes because they offer significant advantages. However, their generation technology is considerably less mature and it is standard practice in industry for skilled personnel to interactively construct multiblock decompositions in specialised software graphical interfaces. There is generally a poor understanding of the essential underlying properties of quad and hex meshes and heuristic experience-based techniques are used to build the block structures in stages. This is a very time consuming and expensive process for complex geometries and it stands as the biggest bottleneck in the simulation process. In this thesis, new reasoned approaches to automatically generating multiblock decompositions in 2-D and 3-D are explored. A recent precise theoretical study of the properties of quad meshes has shown that mesh singularities, where the regular grid structure is disrupted, are vitally important features and the overall shape and topology of a multiblock structured mesh hinges on their properties. Inspired by this insight, an original method is developed for using the medial axis to find a valid and effective arrangement of mesh singularities. A novel cross-field generation algorithm on a tet mesh discretisation of a surface is also developed with a similar line of reasoning. This method can create well-shaped multiblock decompositions that are adjusted to suit target element sizes and alignments. Finally, preliminary work on extending the approach to 3-D for generating a cross-frame field on a tet mesh is presented. New ideas and perspectives are offered for understanding the 3-D problem's fundamental difficulties and a novel initialisation method is used with a following optimisation method to produce cross-frame fields with conspicuous line singularity networks.
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