| An engineering design tool is developed to streamline the process of creating, verifying, and using complex computational meshes for use with numerical simulations. A fully three-dimensional high order finite element code is developed and verified with several different types of physics equations including anisotropic thermal conduction, and magnetohydrodynamcis (MHD). A multi-block framework and CAD/mesh generator interface is developed such that complex, non-axisymmetric, and non-simply connected topologies are possible with minimal complexity for the user. An a priori error estimation technique is developed using mesh quality metrics and is included as a step in the engineering design tool. One can assess a mesh's quality prior to numerical simulation and determine if it will yield acceptable results. It is found that the mesh quality analysis can predict the global error norms in the solution and therefore can be used as an a priori guide to improving computational meshes.;The multi-block framework is verified by solving a m = 1 kink mode in a Z-pinch and comparing to a linear stability analysis, yielding a positive agreement. Further studies of the Z-pinch include wall stabilization in a cylindrical geometry, and subsequently, a study of wall stabilization in a non-axisymmetric geometry made possible by the multi-block framework. The mesh deformation analysis is applied to the Z-pinch meshes and previous results are confirmed.;A non-axisymmetric and non-simply connected geometry representing the HIT-SI experiment is created using the CAD and mesh generator interface and multi-block framework. A mesh deformation analysis is applied to identify degenerate and poor mesh regions during mesh creation. Methods for repairing the mesh from degeneracies and further improvement for more accurate simulations is demonstrated. A spheromak MHD solution is computed on the HIT-SI mesh as a demonstration of the practicality of using the developments in this dissertation as an engineering design tool. |
