Abstract
This paper outlines some recent developments in the process of generating well centered tetrahedral meshes. A well centered tetrahedron contains its circumcentre, which is a basic property required for a valid co-volume discretisation. Although most work in this area has focussed on improving meshes generated using classical techniques, in this paper we consider modification of the generation procedure itself. A simple lattice point insertion technique is introduced and the potential of the technique for generating well centered meshes is demonstrated. This is accomplished by comparing, for some complex geometries, the meshes generated with the meshes created by a standard Delaunay mesh refinement technique. Despite the simplicity of the lattice point insertion method, the comparison is found to be favourable and the method is shown to produce good well centered elements in the vicinity of the geometry.
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Acknowledgements
Sean Walton acknowledges the financial support for this work provided by the UK Engineering and Physical Sciences Research Council (EPSRC) under Research Grant EP/K000705.
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Walton, S., Hassan, O., Morgan, K. (2015). Strategies for Generating Well Centered Tetrahedral Meshes on Industrial Geometries. In: Perotto, S., Formaggia, L. (eds) New Challenges in Grid Generation and Adaptivity for Scientific Computing. SEMA SIMAI Springer Series, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-06053-8_8
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DOI: https://doi.org/10.1007/978-3-319-06053-8_8
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