Residual-distribution methods offer several potential benefits over classical methods, such as a means of applying upwinding in a multi-dimensional manner and a multi-dimensional positivity property. While it is apparent that residual-distribution methods also offer higher accuracy than finite-volume methods on similar meshes, few studies have directly compared the performance of the two approaches in a systematic and quantitative manner. In this study, comparisons between residual distribution and finite volume are made for steady-state smooth and discontinuous flows of gas dynamics, governed by hyperbolic conservation laws, to illustrate the strengths and deficiencies of the residual-distribution method. Deficiencies which reduce the accuracy are analyzed and a new nonlinear scheme is proposed that closely reproduces or surpasses the accuracy of the best linear residual-distribution scheme. The accuracy is further improved by extending the scheme to fourth order using established finite-element techniques. Finally, the compact stencil, arithmetic workload, and data parallelism of the fourth-order residual-distribution scheme are exploited to accelerate parallel computations on an architecture consisting of both CPU cores and a graphics processing unit. Numerical experiments are used to assess the gains to efficiency and possible monetary savings that may be provided by accelerated architectures.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OTU.1807/24762 |
| Date | 12 August 2010 |
| Creators | Guzik, Stephen Michael Jan |
| Contributors | Groth, Clinton P. T. |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
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