TED-AJ03-254 An Approximate Spectral Method for Accurate Solution of Fourier and Non-Fourier Heat Conduction Problems
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概要
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A new form of the pseudo-spectral method is presented, which has attractive features of being theoretically simple yet robust enough to produce very accurate solutions to a wide variety of hyperbolic and parabolic partial differential equations (PDE's). It accomplishes this while avoiding the effects of Gibb's phenomenon, and using a relatively small amount of computational memory. The method is based on the observation that an analytical function may be well represented in a set of small neighborhoods, which share common boundaries, by low order Chebyshev polynomials. As the solution is marched forward in time the Chebyshev expansion coefficients of the highest order terms are monitored. If these coefficients grow beyond a specified small size, then the function must have changed so much that the current subdomains are not valid. The new sub-domains are then redefined so that the function is again well represented by Chebyshev polynomial expansions. In this paper, after a brief review of Chebyshev polynomials, the method of finding computational subdomains of the physical domain is discussed and the strategy for solving the PDE's is presented. The method is then applied to Fourier and non-Fourier heat conduction.
- 一般社団法人日本機械学会の論文
著者
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Russell Cottam
Senior Research Associate Ohio Aerospace Institute Nasa Glenn Research Center
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Ramin Khosravi
Department of Mechanical, Industrial and Manufacturing Engineering, University of Toledo
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Keith Theo
Distinguished University Professor, ASME Fellow Department of Mechanical, Industrial and Manufacturi
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Keith Theo
Distinguished University Professor Asme Fellow Department Of Mechanical Industrial And Manufacturing
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Ramin Khosravi
Department Of Mechanical Industrial And Manufacturing Engineering University Of Toledo