Improvement in Computational Fluid Dynamics Through Boundary Verification and Preconditioning

This thesis provides improvements to computational fluid dynamics accuracy and ef- ficiency through two main methods: a new boundary condition verification procedure and preconditioning techniques. First, a new verification approach that addresses boundary conditions was developed. In order to apply the verification approach to a large range of arbitrary boundary condi- tions, it was necessary to develop unifying mathematical formulation. A framework was developed that allows for the application of Dirichlet, Neumann, and extrapolation bound- ary condition, or in some cases the equations of motion directly. Verification of boundary condition techniques was performed using exact solutions from canonical fluid dynamic test cases. Second, to reduce computation time and improve accuracy, preconditioning algorithms were applied via artificial dissipation schemes. A new convective upwind and split pressure (CUSP) scheme was devised and was shown to be more effective than traditional precon- ditioning schemes in certain scenarios. The new scheme was compared with traditional schemes for unsteady flows for which both convective and acoustic effects dominated. Both boundary conditions and preconditioning algorithms were implemented in the context of a strand grid solver. While not the focus of this thesis, strand grids provide automatic viscous quality meshing and are suitable for moving mesh overset problems