The continued research and development of high-order methods in Computational Fluid Dynamics (CFD) is primarily motivated by their potential to significantly reduce the computational cost and memory usage required to obtain a solution to a desired level of accuracy. In this work, a high-order Central Essentially Non-Oscillatory (CENO) finite-volume scheme is developed for the Euler and Navier-Stokes equations in three dimensions. The proposed CENO scheme is based on a hybrid solution reconstruction procedure using a fixed central stencil. A solution smoothness indicator facilitates the hybrid switching between a high-order k-exact reconstruction technique, and a monotonicity preserving limited piecewise linear reconstruction algorithm. The resulting scheme is applied to the compressible forms of the Euler and Navier-Stokes equations in three dimensions. The latter of which includes the application of this high-order work to the Large Eddy Simulation (LES) of turbulent non-reacting flows.

During endovascular aneurysm repair (EVAR), if the stent-graft device is too long for a given patient the redundant (extra) length adopts a convex configuration in the aneurysm. Based on clinical experience, we hypothesize that redundant stent-graft configurations increase the downward force acting on the device, thereby increasing the risk of device dislodgement and failure. This work numerically studies both steady-state and physiologic pulsatile blood flow in redundant stent-graft configurations. Computational fluid dynamics simulations predicted a peak downward displacement force for the zero-, moderate- and severe-redundancy configurations of 7.36, 7.44 and 7.81 N, respectively for steady-state flow; and 7.35, 7.41 and 7.85 N, respectively for physiologic pulsatile flow. These results suggest that redundant stent-graft configurations in EVAR do increase the downward force acting on the device, but the clinical consequence depends significantly on device-specific resistance to dislodgement.

The development of high-order solution methods remain a very active field of research in Computational Fluid Dynamics (CFD). These types of schemes have the potential to reduce the computational cost necessary to compute solutions to a desired level of accuracy. The goal of this thesis has been to develop a high-order Central Essentially Non Oscillatory (CENO) finite volume scheme for multi-block unstructured meshes. In particular, solutions to the compressible, inviscid Euler equations are considered. The CENO method achieves a high-order spatial reconstruction based on the k-exact method, combined with hybrid switching to limited piecewise linear reconstruction in non-smooth regions to maintain monotonicity. Additionally, fourth-order Runge-Kutta time marching is applied. The solver described has been validated through a combination of high-order function reconstructions, and solutions to the Euler equations. Cases have been selected to demonstrate high-orders of convergence, the application of the hybrid switching method, and the multi-block techniques which has been implemented.

A scramjet inlet was designed for use on a small scale, Mach six, ethylene-fuelled vehicle. The inlet used strut-based cantilevered fuel injectors and a well-defined mixing duct to mix fuel prior to the combustor. Designed using theoretical and numerical analyses, the resulting inlet configuration consisted of a single body shock inlet with vertical fuel injector struts and four cantilevered injectors per strut side. This inlet was 80 cm long and 42 cm high. Numerical analysis of the vehicle was conducted with computational fluid dynamics by solving the Favre-Averaged Navier-Stokes equations; turbulence was simulated using the Wilcox k-ω model. Multispecies simulations in two and three dimensions were used to evaluate the design. Analysis of the simulated flow features, thrust potential and mixing efficiency demonstrated favourable vehicle performance. In particular, the inlet allowed for complete combustion when lean equivalence ratios of less than 0.7 were used.

Increasing environmental concerns and fuel prices motivate the study of alternative, unconventional aircraft configurations. One such example is the blended-wing-body configuration, which has been shown to have several advantages over the conventional tube-and-wing aircraft configuration. In this thesis, a blended-wing-body aircraft is studied and optimized aerodynamically using a high-fidelity Euler-based flow solver, integrated geometry parameterization and mesh movement, adjoint-based gradient evaluation, and a sequential quadratic programming algorithm. Specifically, the aircraft is optimized at transonic conditions to minimize the sum of induced and wave drag. These optimizations are carried out with both fixed and varying airfoil sections. With varying airfoil sections and increased freedom, up to 52% drag reduction relative to the baseline geometry was achieved: at the target lift coefficient of 0.357, a drag coefficient of 0.01313 and an inviscid lift-to-drag ratio of 27.2 were obtained.

Large-eddy simulation (LES) is emerging as a promising computational tool for reacting flows. High-order schemes for LES are desirable to achieve improved solution accuracy with reduced computational cost. In this study, a parallel, block-based, three-dimensional high-order central essentially non-oscillatory (CENO) finite-volume scheme for LES of premixed turbulent combustion is developed for Cartesian mesh. This LES formulation makes use of the flame surface density (FSD) for subfilter-scale reaction rate modelling. An algebraic model is used to approximate the FSD. A detailed explanation of the governing equations for LES and the mathematical framework for CENO schemes are presented. The CENO reconstruction is validated and is also applied to three-dimensional Euler equations prior to its application to the equations governing LES of reacting flows.

During endovascular aneurysm repair (EVAR), if the stent-graft device is too long for a given patient the redundant (extra) length adopts a convex configuration in the aneurysm. Based on clinical experience, we hypothesize that redundant stent-graft configurations increase the downward force acting on the device, thereby increasing the risk of device dislodgement and failure. This work numerically studies both steady-state and physiologic pulsatile blood flow in redundant stent-graft configurations. Computational fluid dynamics simulations predicted a peak downward displacement force for the zero-, moderate- and severe-redundancy configurations of 7.36, 7.44 and 7.81 N, respectively for steady-state flow; and 7.35, 7.41 and 7.85 N, respectively for physiologic pulsatile flow. These results suggest that redundant stent-graft configurations in EVAR do increase the downward force acting on the device, but the clinical consequence depends significantly on device-specific resistance to dislodgement.

The development of high-order solution methods remain a very active field of research in Computational Fluid Dynamics (CFD). These types of schemes have the potential to reduce the computational cost necessary to compute solutions to a desired level of accuracy. The goal of this thesis has been to develop a high-order Central Essentially Non Oscillatory (CENO) finite volume scheme for multi-block unstructured meshes. In particular, solutions to the compressible, inviscid Euler equations are considered. The CENO method achieves a high-order spatial reconstruction based on the k-exact method, combined with hybrid switching to limited piecewise linear reconstruction in non-smooth regions to maintain monotonicity. Additionally, fourth-order Runge-Kutta time marching is applied. The solver described has been validated through a combination of high-order function reconstructions, and solutions to the Euler equations. Cases have been selected to demonstrate high-orders of convergence, the application of the hybrid switching method, and the multi-block techniques which has been implemented.

A scramjet inlet was designed for use on a small scale, Mach six, ethylene-fuelled vehicle. The inlet used strut-based cantilevered fuel injectors and a well-defined mixing duct to mix fuel prior to the combustor. Designed using theoretical and numerical analyses, the resulting inlet configuration consisted of a single body shock inlet with vertical fuel injector struts and four cantilevered injectors per strut side. This inlet was 80 cm long and 42 cm high. Numerical analysis of the vehicle was conducted with computational fluid dynamics by solving the Favre-Averaged Navier-Stokes equations; turbulence was simulated using the Wilcox k-ω model. Multispecies simulations in two and three dimensions were used to evaluate the design. Analysis of the simulated flow features, thrust potential and mixing efficiency demonstrated favourable vehicle performance. In particular, the inlet allowed for complete combustion when lean equivalence ratios of less than 0.7 were used.

Increasing environmental concerns and fuel prices motivate the study of alternative, unconventional aircraft configurations. One such example is the blended-wing-body configuration, which has been shown to have several advantages over the conventional tube-and-wing aircraft configuration. In this thesis, a blended-wing-body aircraft is studied and optimized aerodynamically using a high-fidelity Euler-based flow solver, integrated geometry parameterization and mesh movement, adjoint-based gradient evaluation, and a sequential quadratic programming algorithm. Specifically, the aircraft is optimized at transonic conditions to minimize the sum of induced and wave drag. These optimizations are carried out with both fixed and varying airfoil sections. With varying airfoil sections and increased freedom, up to 52% drag reduction relative to the baseline geometry was achieved: at the target lift coefficient of 0.357, a drag coefficient of 0.01313 and an inviscid lift-to-drag ratio of 27.2 were obtained.