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Title: Radial basis function interpolation applied to discontinuous mesh interfaces
Author: Costin, William James
Awarding Body: University of Bristol
Current Institution: University of Bristol
Date of Award: 2013
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For large-scale Computational Fluid Dynamics (CFD) simulations it is often necessary to divide the domain into a mesh of discrete points or volumes. However, the domain can also be split into a set of zones separated by interfaces, allowing the zones to be meshed individually. Discontinuous or nonmatching mesh spacing across the zonal interfaces offers many advantages, particularly in terms of easing the mesh generation process, reduction of required mesh densities, and relative motion between mesh zones. However, accurate data transfer across the interfaces is required for global solution accuracy to be maintained. A more versatile data transfer method for discontinuous interfaces has the potential to reduce both the complexity of, and constraints place on, the process of discretising complex domains. This research was motivated by work on large-scale parallelised CFD simulations using high quality structured multiblock meshes. For such tasks the accuracy of the final result has a significant dependence on the quality of the mesh used to discretise the domain. The mesh is split into separate zones for parallel computation but must be generated as a topographically consistent whole, rather than individually for each zone. The objective therefore was to create a new method of discontinuous interface data transfer that does not place topographic limitations on the mesh, simplifying the mesh generation process. To this end, the fields of flow solution, high accuracy interpolation and mesh generation have been investigated with the aim of formulating and assessing a new data transfer approach. A new data transfer method based on Radial Basis Function (RBF) interpolation is developed and presented. Strategies for the construction of the interpolation data set are compared and a new more advanced approach developed. A series of analytical tests are used to assess the properties of the new method: Both the order of accuracy of the method and the ability to accurately model the full range of frequency content are considered. The method is applied to both finite difference and finite volume numerical solutions. For the latter both multi-grid discretisation and parallelised solution have been ,j ABSTRACT implemented as part of integration into an existing parallel, multiblock, multi grid compressible flow solver. Additionally, the relative merits and cost of localised and global forms of the method are assessed. The method has been applied to a series of aeronautical test cases including a subsonic and transonic aerofoil. The results show that the method is both effective and robust, providing accurate transmission for well and poorly conceived interface geometries. One great success is that in generic form the method remains applicable to all iterative solution methods with similar domain discretisation requirements; as a result there are many opportunities for further work.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available