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.

<p>This thesis project addresses the need for an interactive, real-time water animation tech-<br> nique that can showcase visually convincing effects such as splashes and breaking waves while<br> being computationally inexpensive. Our method couples SPH and wave equations in a one-<br> way manner to simulate the behavior of water in real-time, leveraging OpenGL’s Compute<br> Shaders for interactive performance and a novel Uniform Grid implementation. Through a<br> review of related literature on real-time simulation methods of fluids, and water animation,<br> this thesis presents a feasible algorithm, animations to showcase interesting water effects,<br> and a comparison of computational costs between SPH, wave equations, and the coupled<br> approach. The program renders a water body with a planar surface and discrete particles.<br> This project aims to provide a solution that can meet the needs of various water animation<br> use-cases, such as games, and movies, by offering a computationally efficient technique that<br> can animate water to behave plausibly and showcase essential effects in real-time.</p>

Mobile technology is improving in quality and capability faster now than ever before. When first introduced, cell phones were strictly used to make voice calls; now, they play satellite radio, MP3s, streaming television, have GPS and navigation capabilities, and have multi-megapixel video cameras. In the near future, cell phones will have programmable graphics processing units (GPU) that will allow users to play games similar to those currently available for top-of-the-line game consoles. Personal digital assistants enable users with full email, scheduling, and internet browsing capabilities in addition to those features offered on cell phones. Underlying all this mobile technology and entertainment is a battery whose technology has just barely tripled in the past 15 years, compared to available disk capacity that has increased over 1,000-fold. Ray tracing is a rendering technique used to generate photorealistic images that include reflections, refraction, participating media, and can fairly easily be extended to include photon mapping for indirect illumination and caustics. In recent years, ray tracing has been implemented on the GPU using various acceleration structures to facilitate rendering. Until now, all studies have used build time and achievable frame rates to determine which acceleration structure is best for ray tracing. We present the very first results comparing both CPU and GPU raytracing using various acceleration structures in terms of energy consumption. By exploring per-pixel costs, we provide insight on the energy consumption and frame rates that can be experienced on cell phones and other mobile devices based on currently available screen resolutions. Our results show that the choice in processing unit has the greatest affect on energy and time costs of ray tracing, followed by the size of the viewport used, and the choice of acceleration structure has the least impact on efficiency. For mobile devices enabled with a programmable GPU, whether it is a cell phone, PDA, or laptop computer, a bounding volume hierarchy implemented on the GPU is the most energy-efficient acceleration structure for ray tracing. Ray tracing on cellular phones with smaller screen resolutions is most energy-efficient using a CPU-based Kd-Tree implementation.

The primary concern of this work is real-time fluid simulation on modern programmable graphics hardware. It starts by introducing fundamental fluid simulation principles with focus on Smoothed particle hydrodynamics technique. The following discussion then provides a brief introduction to OpenCL as well as contemporary GPU hardware and outlines their programming specifics in comparison with CPUs. Finally, the last two chapters of this work, detail the problem analysis and its implementation.

Zoomable user interfaces (ZUIs) have been studied for a long time and many applications are built upon them. Most applications, however, only use two dimensions to express the content. This report presents a solution using all three dimensions where the base features are built as a framework with uniform grids and scene graphs as primary data structures. The purpose of these data structures is to improve performance while maintaining flexibility when creating and handling three-dimensional objects. A 3D-ZUI is able to represent the view of the world and its objects in a more lifelike manner. It is possible to interact with the objects much in the same way as in real world. By developing a prototype framework as well as some example applications, the usefulness of 3D-ZUIs is illustrated. Since the framework relies on abstraction and object-oriented principles it is easy to maintain and extend it as needed. The currently implemented data structures are well motivated for a large scale 3D-ZUI in terms of accelerated collision detection and picking and they also provide a flexible base when developing applications. It is possible to further improve performance of the framework, for example by supporting different types of culling and levels of detail

Subject of this thesis is acceleration of the photon mapping method on a graphic card. The photon mapping is a method for computing almost realistic global illumination of the scene. The computation itself is relatively time-consuming, so the acceleration of it is a hot issue in the field of computer graphics. The photon mapping is described in detail from photon tracing to rendering of the scene. The thesis is then focused on spatial subdivision structures, especially to the uniform grid. The design and the implementation of the application computing the photon mapping on GPU, which is achieved by OpenGL and CUDA interoperability, is described in the next part of the thesis. Lastly, the application is tested properly. The achieved results are reviewed in the conclusion of the thesis.