Grid generation for the solution of partial differential equations

A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given

Real-Time Noise Removal in Foveated Path Tracing

Path tracing is a method for rendering photorealistic two-dimensional images of three-dimensional scenes based on computing intersection between the scene geometry and light rays traveling through the scene. The rise in parallel computation resources in devices such as graphics processing units (GPUs) have made it more and more viable to do path tracing in real time. To achieve real-time performance, path tracing can be further optimized by using foveated rendering, where the properties of the human visual system are exploited to reduce the number of rays outside the central point of vision (fovea), where the human eye cannot discern fine detail. The reduction in the number of rays can, however, lead to several issues. Noise appears in the image as a result of an inadequate number of path tracing samples allocated to each pixel. Furthermore, the variation in the noise from one animation frame to the next appears as flicker. Finally, artifacts can appear when the spatially subsampled image is upsampled to a uniform resolution for display. In this thesis, solutions to the aforementioned issues are explored by implementing three noise removal methods into a foveated path tracing rendering system. The computational performance and the visual quality of the implemented methods is evaluated. Of the implemented methods, cross-bilateral filter provides the best quality, but its runtime doesn't scale well to large filter sizes. Large filter sizes are enabled by the À-Trous approximation of the cross-bilateral filter, at the cost of generating more artifacts in the result. Overall, while the implemented methods are able to provide visually pleasing results in some scenarios, improvements in the algorithms (e.g., local filter parameter selection) are needed to reach the quality seen in offline methods

Electrostatic Density Measurements in Green-State P/M Parts

The goal of this research is to show the feasibility of detecting density variations in green-state powder metallurgy (P/M) compacts from surface voltage measurements. By monitoring a steady electric current flow through the sample and recording the voltages over the surface, valu-able information is gathered leading to the prediction of the structural health of the compacts. Unlike prior research that concentrated on the detection of surface-breaking and subsurface de-fects, the results presented in this thesis target the density prediction throughout the volume of the sample. The detection of density variations is achieved by establishing a correlation between the conductivity and their respective density. The data obtained from the surface measurements is used as part of an inversion algorithm, calculating the conductivity distribution, and subse-quently the density within the compact. In a first step, the relationship between conductivity and density of green-state P/M com-pacts was investigated. Tests were conducted for a number of parts of various powder mixtures. In all cases a clear correlation between conductivity and density could be established, indicating that measurements of electric conductivity could indeed be exploited in an effort to render valid information about the density of the sample under test. We found a linear correlation for non-lubricated parts and a non-linear behavior for lubricated samples. Specifically, it was found that the conductivity increases with increasing density only up to a maximum value obtained at ap-proximately 6.9g/cm3. Interestingly, any additional density increase leads to a reduction of the conductivity. This behavior was confirmed to be inherent in all powder mixtures with lubricants. The thesis research is able to provide a physical model and a mathematical formulation describ-ing this counter-intuitive phenomenon. A finite element solver in conjunction with an inversion algorithm was then implemented to study arbitrarily shaped part geometries. Based on the principles of electric impedance imag-ing, the developed algorithm faithfully reconstructs the density distribution from surface voltage measurements. The feasibility of the instrumentation approach for both simple and complex parts can be demonstrated using a new sensor concept and measurement arrangement. Measurements were performed on both geometrically simple and complex parts

Future Computer Requirements for Computational Aerodynamics

Recent advances in computational aerodynamics are discussed as well as motivations for and potential benefits of a National Aerodynamic Simulation Facility having the capability to solve fluid dynamic equations at speeds two to three orders of magnitude faster than presently possible with general computers. Two contracted efforts to define processor architectures for such a facility are summarized

Investigation into the Accuracy and Practicality of Methods for Transforming Coordinates between Geodetic Datums

This thesis is a study of methods of transforming coordinates between geodetic datums, the methods being generally known as datum transformations. Direct methods are described and categorised as conformal, near-conformal and non-conformal. New variations on all three types are included in the direct methods: SMITSWAM (which avoids changes of coordinate-type), generalisations of Standard & Abridged Molodensky, and normalised generalisations of multiple regression equations (5 types). Reverse transformations are extensively covered, as are methods of derivation. In both cases, new algorithms are included. Direct methods, with the exception of multiple regression equations, do not capture distortions in datum transformations. The thesis therefore includes a review of composite methods which extract a trend model and apply a surface-fitting technique (SFT) to the residuals. Sometimes the SFT is used as a gridding method, producing regularly-spaced data that can be interpolated as a final stage of the composite process. The SFTs selected for detailed study include new variations on inverse-distance-to-a-power weighting and nearest-neighbour interpolation. These are called HIPFEAD and LIVONN respectively. In both cases, the variations are shown to have advantages in terms of accuracy of fit. Least-squares collocation and radial basis functions are shown to produce reusable vectors - described here as “revamped signals” – that enable interpolation without gridding. Where the composite methods are used for gridding, it is shown that geodetic coordinates can be used, avoiding the need for projected grid coordinates. The interpolation options applied are piecewise-bilinear and piecewise-bicubic, the latter being an algorithm (believed to be new) that uses up to 12 “grid” points. Case studies were considered using 6 datasets, two for Great Britain, one each for Western Australia, Ghana, Sweden and Slovenia. These showed beneficial properties of the new methods, both in the direct and composite categories. They also enabled comparisons of transformation methods generally

Aeronautical Engineering: a Continuing Bibliography with Indexes (Supplement 244)

This bibliography lists 465 reports, articles, and other documents introduced into the NASA scientific and technical information system in September 1989. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics