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Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/24762

Title: Accurate Residual-distribution Schemes for Accelerated Parallel Architectures
Authors: Guzik, Stephen Michael Jan
Advisor: Groth, Clinton P. T.
Department: Aerospace Science and Engineering
Keywords: residual distribution
parallel architectures
heterogeneous architectures
computational fluid dynamics
high order
partial differential equation
multi-dimensional upwind
multi-dimensional limiter
Issue Date: 12-Aug-2010
Abstract: 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.
URI: http://hdl.handle.net/1807/24762
Appears in Collections:Doctoral
Institute for Aerospace Studies - Doctoral theses

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