Numerical Simulations of High-Speed Flows Over Complex Geometries

The effects of surface roughness on the stability of hypersonic flow are of great importance to hypersonic vehicles. Surface roughness can greatly alter boundary-layer flow and cause transition to turbulence to occur much earlier compared to a smooth wall, which will result in a significant increase of wall heating and skin friction drag. The work presented in this dissertation was motivated by a desire to study the effects of isolated roughness elements on the stability of hypersonic boundary layers. A new code was developed which can perform high-order direct numerical simulations of high-speed flows over arbitrary geometries. A fifth-order hybrid weighted essentially non-oscillatory scheme was implemented to capture any steep gradients in the flow created by the geometries. The simulations are carried out on Cartesian grids with the geometries imposed by a third-order cut-cell method. A multi-zone refinement method is also implemented to provide extra resolution at locations with expected complex physics. The combination results in a globally fourth-order scheme.;Results for two-dimensional and three-dimensional test cases show good agreement with previous results and will be presented. Results confirming the code's high order of convergence will also be shown. Two-dimensional simulations of flow over complex geometries will be presented to demonstrate the code's capabilities. Results for Mach 6 flow over a three-dimensional cylindrical roughness element will also be presented. The results will show that the code is a promising tool for the study of hypersonic roughness-induced transition.