The generation of curvilinear, high-order meshes for CFD applications remains a significant bottleneck in the progress and application of high-order CFD methods. These methods have superior numerical accuracy over low-order methods due to their use of piecewise polynomial representations of domains and solutions. As such they are viewed as a potential source of higher fidelity simulations with a view of industrial application [81]. The current state of the art in high-order mesh generation does not provide a reliable and efficient approach which would be required in an industrial setting.
This thesis investigates the generation of high-order curvilinear meshes for CFD applications. It focuses around the design and algorithms of an open-source high- order mesh generator, NekMesh, which has been created as part of this project and is part of the Nektar++ high-order CFD suite. The program aims to create high-order meshes directly from CAD as automatically and robustly as possible. This means that all parts of the high-order meshing problem must be addressed including CAD handling and linear mesh generation.
A significant contribution of this thesis to high-order mesh generation is the work on a variational approach to the generation of curved meshes. This has been encompassed in a framework within NekMesh. It has been shown to be able to apply several high-order mesh generation methods found throughout the literature and unify them in one context. In addition to this the algorithms used within this framework mitigate a significant amount of the high computational cost associated with high-order mesh generation and attempts to address robustness issues.
In addition to the work on NekMesh this thesis also explores using a semi- structured approach to linear mesh generation which can address several robustness issues. It also applies several the methods created to industrially relevant examples.