Indexed by:期刊论文
Date of Publication:2016-08-17
Journal:NUMERICAL HEAT TRANSFER PART A-APPLICATIONS
Included Journals:SCIE、EI、Scopus
Volume:70
Issue:4
Page Number:384-398
ISSN No.:1040-7782
Abstract:Taking the strongly nonlinear energy conservation equation and the transient diffusion equations as examples, the differences of solving procedure and the computation time are compared and discussed between the fast cosine transformation (FCT) and the matrix multiplication transformation (MMT) in the application of spectral methods. To compare the solving procedures for the energy equation, the temperature distribution in the fin with variable thermal conductivity, variable heat transfer coefficient, and internal heat generation are considered. To compare the computation time, the transient diffusion equations in 1D and 2D enclosures, which contain the Poisson operator and the source term, are analyzed. All variables are approximated by the Chebyshev polynomials and all equations are discretized by the Chebyshev-Gauss-Lobatto (CGL) collocation points in space. The comparisons indicate that the FCT can be adopted to solve the strongly nonlinear equation directly and it can provide the same accuracy as MMT does. The comparison of computation time indicates that the MMT is faster than the FCT when the grid number is small or moderate (less than 200), while, if the grid number is large (greater than 200), the FCT is more faster than the MMT.
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