In the present study, a fifth-order weighted essentially non-oscillatory (WENO) scheme was built for solving the surface-capturing level-set equation. Combined with the level-set equation, the three-dimensional Reynolds averaged Navier-Stokes (RANS) equations were employed for the prediction of nonlinear wave-interaction and wave-breaking phenomena over sloping beaches. In the level-set finite-analytic Navier-Stokes (FANS) method, the free surface is represented by the zero level-set function, and the flows are modeled as immiscible air-water two phase flows. The Navier-Stokes equations for air-water two phase flows are formulated in a moving curvilinear coordinate system and discretized by a 12-point finite-analytical scheme using the finite-analytic method on a multi-block over-set grid system. The Pressure Implicit with Splitting of Operators / Semi-Implicit Method for Pressure-Linked Equation Revised (PISO/SIMPLER) algorithm was used to determine the coupled velocity and pressure fields. The evolution of the level-set method was solved using the third-order total variation diminishing (TVD) Runge-Kutta method and fifth-order WENO scheme. The accuracy was confirmed by solving the Zalesak's problem. Two major subjects are discussed in the present study. First, to identify the WENO scheme as a more accurate scheme than the essentially non-oscillatory scheme (ENO), the characteristics of a nonlinear monochromatic wave were studied systematically and comparisons of wave profiles using the two schemes were conducted. To eliminate other factors that might produce wave profile fluctuation, different damping functions and grid densities were studied. To damp the reflection waves efficiently, we compared five damping functions. The free-surface elevation data collected from gauges distributed evenly in a numerical wave tank are analyzed to demonstrate the damping effect of the beach. Second, as a surface-tracking numerical method built on curvilinear coordinates, the level-set RANS model was tested for nonlinear bichromatic wave trains and breaking waves on a sloping beach with a complex free surface. As the wave breaks, the velocity of the fluid flow surface became more complex. Numerical modeling was performed to simulate the two-phase flow velocity and its corresponding surface and evolution when the wave passed over different sloping beaches. The breaking wave test showed that it is an efficient technique for accurately capturing the breaking wave free surface. To predict the breaking points, different wave heights and beach slopes are simulated. The results show that the dependency of wave shape and breaking characteristics to wave height and beach slope match the results provided by experiments.

In the present study, a fifth-order weighted essentially non-oscillatory (WENO) scheme was built for solving the surface-capturing level-set equation. Combined with the level-set equation, the three-dimensional Reynolds averaged Navier-Stokes (RANS) equations were employed for the prediction of nonlinear wave-interaction and wave-breaking phenomena over sloping beaches. In the level-set finite-analytic Navier-Stokes (FANS) method, the free surface is represented by the zero level-set function, and the flows are modeled as immiscible air-water two phase flows. The Navier-Stokes equations for air-water two phase flows are formulated in a moving curvilinear coordinate system and discretized by a 12-point finite-analytical scheme using the finite-analytic method on a multi-block over-set grid system. The Pressure Implicit with Splitting of Operators / Semi-Implicit Method for Pressure-Linked Equation Revised (PISO/SIMPLER) algorithm was used to determine the coupled velocity and pressure fields. The evolution of the level-set method was solved using the third-order total variation diminishing (TVD) Runge-Kutta method and fifth-order WENO scheme. The accuracy was confirmed by solving the Zalesak's problem. Two major subjects are discussed in the present study. First, to identify the WENO scheme as a more accurate scheme than the essentially non-oscillatory scheme (ENO), the characteristics of a nonlinear monochromatic wave were studied systematically and comparisons of wave profiles using the two schemes were conducted. To eliminate other factors that might produce wave profile fluctuation, different damping functions and grid densities were studied. To damp the reflection waves efficiently, we compared five damping functions. The free-surface elevation data collected from gauges distributed evenly in a numerical wave tank are analyzed to demonstrate the damping effect of the beach. Second, as a surface-tracking numerical method built on curvilinear coordinates, the level-set RANS model was tested for nonlinear bichromatic wave trains and breaking waves on a sloping beach with a complex free surface. As the wave breaks, the velocity of the fluid flow surface became more complex. Numerical modeling was performed to simulate the two-phase flow velocity and its corresponding surface and evolution when the wave passed over different sloping beaches. The breaking wave test showed that it is an efficient technique for accurately capturing the breaking wave free surface. To predict the breaking points, different wave heights and beach slopes are simulated. The results show that the dependency of wave shape and breaking characteristics to wave height and beach slope match the results provided by experiments.

In this thesis, Finite Volume Weighted Essentially Non-Oscillatory (FV-WENO) codes for one and two-dimensional discretised Euler equations are developed. The construction and application of the FV-WENO scheme and codes will be described. Also the effects of the grid coefficients as well as the effect of the Gaussian Quadrature on the solution have been tested and discussed. WENO schemes are high order accurate schemes designed for problems with piecewise smooth solutions containing discontinuities. The key idea lies at the high approximation level, where a convex combination of all the candidate stencils is used with certain weights. Those weights are used to eliminate the stencils, which contain discontinuity. WENO schemes have been quite successful in applications, especially for problems containing both shocks and complicated smooth solution structures. The applications tested in this thesis are the Diverging Nozzle, Shock Vortex Interaction, Supersonic Channel Flow, Flow over Bump, and supersonic Staggered Wedge Cascade. The numerical solutions for the diverging nozzle and the supersonic channel flow are compared with the analytical solutions. The results for the shock vortex interaction are compared with the Roe scheme results. The results for the bump flow and the supersonic staggered cascade are compared with results from literature.

The purpose of this thesis is to implement Finite Volume Weighted Essentially Non-Oscillatory (FV-WENO) scheme to solution of one and two-dimensional discretised Euler equations with different flux algorithms. The effects of the different fluxes on the solution have been tested and discussed. Beside, the effect of the grid on these fluxes has been investigated. Weighted Essentially Non-Oscillatory (WENO) schemes are high order accurate schemes designed for problems with piecewise smooth solutions that involve discontinuities. WENO schemes have been successfully used in applications, especially for problems containing both shocks and complicated smooth solution structures. Fluxes are used as building blocks in FV-WENO scheme. The efficiency of the scheme is dependent on the fluxes used in scheme The applications tested in this thesis are the 1-D Shock Tube Problem, Double Mach Reflection, Supersonic Channel Flow, and supersonic Staggered Wedge Cascade. The numerical solutions for 1-D Shock Tube Problem and the supersonic channel flow are compared with the analytical solutions. The results for the Double Mach Reflection and the supersonic staggered cascade are compared with results from literature.

This thesis is concerned with experimental and computational studies on pulse detonation engine (PDE) that has been envisioned as a new concept engine. These engines use the high pressure generated by detonation wave for propulsion. The cycle efficiency of PDE is either higher in comparison to conventional jet engines or at least has similar high performance with much greater simplicity in terms of components. The first part of the work consists of an experimental study of the performance of PDE under choked flame and partial fill conditions. Detonations used in classical PDEs create conditions of Mach numbers of 4-6 and choked flames create conditions in which flame achieves Mach numbers near-half of detonation wave. While classical concepts on PDE's utilize deflagration-to-detonation transition and are more intensively studied, the working of PDE under choked regime has received inadequate attention in the literature and much remains to be explored. Most of the earlier studies claim transition to detonation as success in the working of the PDE and non-transition as failure. After exploring both these regimes, the current work brings out that impulse obtained from the wave traveling near the choked flame velocity conditions is comparable to detonation regime. This is consistent with the understanding from the literature that CJ detonation may not be the optimum condition for maximum specific impulse. The present study examines the details of working of PDE close to the choked regime for different experimental conditions, in comparison with other aspects of PDEs. The study also examines transmission of fast flames from small diameter pipe into larger ducts. This approach in the smaller pipe for flame acceleration also leading to decrease in the time and length of transition process. The second part of the study aims at elucidating the features of deflagration-to-detonation transition with direct numerical simulation (DNS) accounting for and the choice of full chemistry and DNS is based on two features: (a) the induction time estimation at the conditions of varying high pressure and temperature behind the shock can only be obtained through the use of full chemistry, and (b) the complex effects of fine scale of turbulence that have sometimes been argued to influence the acceleration phase in the DDT cannot be captured otherwise. Turbulence in the early stages causes flame wrinkling and helps flame acceleration process. The study of flame propagation showed that the wrinkling of flame has major effect on the final transition phase as flame accelerates through the channel. Further, flame becomes corrugated prior to transition. This feature was investigated using non-uniform initial conditions. Under these conditions the pressure waves emanating from corrugated flame interact with the shock moving ahead and transition occurs in between the flame and the forward propagating shock wave. The primary contributions of this thesis are: (a) Elucidating the phenomenology of choked flames, demonstrating that under partial fill conditions, the specific impulse can be superior to detonations and hence, allowing for the possibility of choked flames as a more appropriate choice for propulsive purposes instead of full detonations, (b) The use of smaller tube to enhance the flame acceleration and transition to detonation. The comparison with earlier experiments clearly shows the enhancements achieved using this method, and (c) The importance of the interaction between pressure waves emanating from the flame front with the shock wave which leads to formation of hot spots finally transitioning to detonation wave.

Minimizing numerical dissipation without compromising the robust shock-capturing attributes remains an outstanding challenge in the design of numerical methods for high-speed compressible flows. The conflicting requirements of low and high numerical dissipation for accurate resolution of discontinuous and smooth flow features, respectively, are the principal reason behind this challenge. In this work we pursue a recently proposed novel strategy of combining adaptive mesh redistribution with conservative high-order shock-capturing finite-volume discretization methodology to overcome this challenge. In essence, we perform high-order finite-volume WENO (weighted essentially non oscillatory) reconstruction on a continuously moving grid the nodes of which are repositioned adaptively in such a way that maximum spatial resolution is achieved in regions associated with sharpest flow gradients. Moreover, to reduce computational expense, the finite-volume WENO discretization strategy is combined with the midpoint quadrature so that only one reconstruction along each intercool location is necessary. To estimate a monotone upwind flux, a rotated HLLC (Harten-Lax-vanLeer-contact resolving) Riemann solver is employed at each intercool location with the state variables estimated from the high-order WENO reconstruction procedure. The effectiveness of this adaptive high-order discretization methodology is assessed on the well-known double Mach reflection test case for reconstruction orders ranging from five to eleven. We find that the resolution of the intricate flow features such as the wall-jet improves progressively with the reconstruction order, which is indicative of the reduced dissipation level of the adaptive high-order WENO discretization. The adaptive discretization methodology is applied to simulate a flow configuration consisting of a Mach 3 supersonic jet injected in a Mach 2 supersonic crossflow of similar ideal gas. It is found that the flow characteristics and especially features that are formed as a result of the Kelvin-Helmholtz instability are strongly influenced by the reconstruction order. The influence of the jet inclination angle on the overall flow features is analyzed.