High-Fidelity Simulation of Compressible Flows for Hypersonic Propulsion Applications

In the first part of this dissertation, the scalar filtered mass density function (SFMDF) methodology is implemented into the computer code US3D. The SFMDF is a subgrid scale closure and is simulated via a Lagrangian Monte Carlo solver. US3D is an Eulerian finite volume code and has proven very effective for compressible flow simulations. The resulting SFMDF-US3D code is employed for large eddy simulation (LES) of compressible turbulent flows on unstructured meshes. Simulations are conducted of subsonic and supersonic flows. The consistency and accuracy of the simulated results are assessed along with appraisal of the overall performance of the methodology. In the second part of this dissertation, a new methodology is developed for accurate capturing of discontinuities in multi-block finite difference simulations of hyperbolic partial differential equations. The fourth-order energy-stable weighted essentially non-oscillatory (ESWENO) scheme on closed domains is combined with simultaneous approximation term (SAT) weak interface and boundary conditions. The capability of the methodology is demonstrated for accurate simulations in the presence of significant and abrupt changes in grid resolution between neighboring subdomains. Results are presented for the solutions of linear scalar hyperbolic wave equations and the Euler equations in one and two dimensions. Strong discontinuities are passed across subdomain interfaces without significant distortions. It is demonstrated that the methodology provides stable and accurate solutions even when large differences in the grid-spacing exist, whereas strong imposition of the interface conditions causes noticeable oscillations

Low thrust viscous nozzle flow fields prediction

A Navier-Stokes code was developed for low thrust viscous nozzle flow field prediction. An implicit finite volume in an arbitrary curvilinear coordinate system lower-upper (LU) scheme is used to solve the governing Navier-Stokes equations and species transportation equations. Sample calculations of carbon dioxide nozzle flow are presented to verify the validity and efficiency of this code. The computer results are in reasonable agreement with the experimental data

Unequally spaced knot techniques for the numerical solution of partial differential equations.

Cubic spline approximations to time dependent partial differential equations, having both constant and variable coefficients, are developed in which the knot points may be chosen to be unequally spaced. Four methods are presented for obtaining 'optimal' knot positions, these being chosen so at to produce an increase in accuracy compared with methods based on equally spaced knots. Three of the procedures described produce knot partitions which are fixed throughout time. The fourth procedure yields differently placed 'optimal' knots on each time line, thus enabling us to better approximate the varying time nature characteristic of many partial differential equations. Truncation errors and stability criteria are derived and full numerical implementation procedures are given. Five case studies are presented to enable comparisons to be drawn between the knot placement methods and results found using equally spaced knots. Possible extensions of the work of this thesis are given

Computation of the inviscid supersonic flow about cones at large angles of attack by a floating discontinuity approach

The technique of floating shock fitting is adapted to the computation of the inviscid flowfield about circular cones in a supersonic free stream at angles of attack that exceed the cone half-angle. The resulting equations are applicable over the complete range of free-stream Mach numbers, angles of attack and cone half-angles for which the bow shock is attached. A finite difference algorithm is used to obtain the solution by an unsteady relaxation approach. The bow shock, embedded cross-flow shock, and vortical singularity in the leeward symmetry plane are treated as floating discontinuities in a fixed computational mesh. Where possible, the flowfield is partitioned into windward, shoulder, and leeward regions with each region computed separately to achieve maximum computational efficiency. An alternative shock fitting technique which treats the bow shock as a computational boundary is developed and compared with the floating-fitting approach. Several surface boundary condition schemes are also analyzed

Computational Hydraulics

Computational Hydraulics introduces the concept of modeling and the contribution of numerical methods and numerical analysis to modeling. It provides a concise and comprehensive description of the basic hydraulic principles, and the problems addressed by these principles in the aquatic environment. Flow equations, numerical and analytical solutions are included. The necessary steps for building and applying numerical methods in hydraulics comprise the core of the book and this is followed by a report of different example applications of computational hydraulics: river training effects on flood propagation, water quality modelling of lakes and coastal applications. The theory and exercises included in the book promote learning of concepts within academic environments.  Sample codes are made available online for purchasers of the book. Computational Hydraulics is intended for under-graduate and graduate students, researchers, members of governmental and non-governmental agencies and professionals involved in management of the water related problems.

Single freeform surface imaging design with unconstrained object to image mapping

An imaging design approach which is free of third-order astigmatism for one freeform optical surface and the image is presented in this paper. A set of differential equations is derived from generalized ray tracing. The solution of the above derived equations provides the anastigmatic freeform optical surface, the image surface and the object to image mapping. The obtained design can be used as a good starting point for optimization. As an example, a reflective freeform surface is designed for a single reflective Head Mounted Display (HMD). This example has a 3 mm pupil, 15mm eye clearance, 24-degree diagonal full field of view, and the final design yields an average MTF of 62.6% across 17 field points

Computational Hydraulics

Computational Hydraulics introduces the concept of modeling and the contribution of numerical methods and numerical analysis to modeling. It provides a concise and comprehensive description of the basic hydraulic principles, and the problems addressed by these principles in the aquatic environment. Flow equations, numerical and analytical solutions are included. The necessary steps for building and applying numerical methods in hydraulics comprise the core of the book and this is followed by a report of different example applications of computational hydraulics: river training effects on flood propagation, water quality modelling of lakes and coastal applications. The theory and exercises included in the book promote learning of concepts within academic environments.  Sample codes are made available online for purchasers of the book. Computational Hydraulics is intended for under-graduate and graduate students, researchers, members of governmental and non-governmental agencies and professionals involved in management of the water related problems.

Complex Mach reflection in shock diffraction problems

Numerical simulations of the interaction of a planar blast wave with a compression ramp are presented. The split coefficient matrix (SCM) method in conjunction with boundary shock and floating discontinuity-fitting procedures was employed to obtain the time-asymptotic solutions of the two-dimensional, unsteady Euler equations. The solutions were computed for the complex Mach reflection (CMR) regime of the shock diffraction problem is an attempt to explore the basic physical process governing the evolution of an incipient second Mach stem and the associated topological changes. Numerical results were obtained for shock diffraction over a 40(DEGREES) ramp with varying incident shock Mach numbers. The validity of the present approach has been substantiated by experimental observations and earlier numerical calculations

On the use of splines in the numerical solution of hyperbolic partial differential equations.

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