Spectral element mesh generation and improvement methods

Meshing tools for finite element meshes have been studied extensively over the last few decades. However, relatively less attention has been paid to spectral element meshes. This thesis focuses on mesh generation and mesh improvement methods for spectral element meshes. A mesh smoother, based on a combination of Laplacian smoothing and optimization, has been developed and implemented in Nek5000, an open-source spectral element method based incompressible flow solver. The smoother takes a valid mesh as an input and outputs an improved mesh. Comparison of the original and smoothed mesh has shown that mesh smoothing decreases the iteration count of iterative solvers. This reduction is anticipated from an observed decrease in the ratio of the maximum to minimum eigenvalues of the upper Hessenberg matrix generated by the GMRES method. The mesh smoother was tested on various meshes for complicated geometries, and was found to improve the computational efficiency of calculations by up to 20% which is helping save 100,000s of cpu-hours on high-performance computing machines. A mesh skinning tool has also been developed which adds boundary layer resolving elements of user-specified thickness at user-specified surfaces in an existing mesh. This translates into savings in terms of human time and effort since the user can now robustly add boundary layer resolving elements instead of manually meshing the geometry to add these elements. Additionally, tools have been developed that generate meshes for geometries like turbine blades and random-array of cylinders (to simulate flow in vegetated channels), in a matter of seconds. Finally, a tetrahedral (tet) to hexahedron (hex) mesh converter has been implemented, that generates spectral element meshes for any complicated geometry by taking an all-tet mesh and converting it to an all-hex spectral element mesh. This tool has been developed to quickly generate all-hex meshes with minimal user intervention.