An Approximate Spectral Method for Accurate Solution of Fourier and Non-Fourier Heat Conduction Problems(<Special Issue>Emerging Fields in Thermal Engineering)
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概要
- 論文の詳細を見る
In this paper a new form of the pseudo-spectral method is presented. The method is theoretically simple yet robust enough to produce very accurate solutions to hyper-bolic and parabolic PDE's while avoiding the effects of Gibb's phenomenon. Moreover the method uses 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 that share common boundaries, called sub-domains, by low order Chebyshev polynomials. A collocation solution scheme is used in each subdomain to march facilitate a time. Throughout this process the Chebyshev expansion coefficients of the highest order terms are monitored. If these coefficients grow beyond a specified small size, the new sub-domains are then redefined so that the function is again well represented by Chebyshev polynomial expansions. An approach for the determination of computational sub-domains of the physical domain for the special case of a discontinuous function is discussed. The strategy for solving the PDE's is presented. The method is then applied to Fourier and non-Fourier heat conduction problems.
- 一般社団法人日本機械学会の論文
- 2003-11-15
著者
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Cottam Russell
Ohio Aerospace Institute Nasa Glenn Research Center
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Keith T
Univ. Toledo Ohio Usa
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Keith Theo
Department Of Mechanical Industrial And Manufacturing Engineering The University Of Toledo
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RAHMANI Ramin
Department of Mechanical, Industrial and Manufacturing Engineering, University of Toledo
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Rahmani Ramin
Department Of Mechanical Industrial And Manufacturing Engineering University Of Toledo
関連論文
- An Approximate Spectral Method for Accurate Solution of Fourier and Non-Fourier Heat Conduction Problems(Emerging Fields in Thermal Engineering)
- Application of the Conservation Element and Solution Element Method in Numerical Modeling of Axisymmetric Heat Conduction with Melting and/or Freezing