Schur-decomposition for 3D matrix equations and its application in solving radiative discrete ordinates equations discretized by Chebyshev collocation spectral method

2010 ◽  
Vol 229 (4) ◽  
pp. 1198-1212 ◽  
Author(s):  
Ben-Wen Li ◽  
Shuai Tian ◽  
Ya-Song Sun ◽  
Zhang-Mao Hu
Keyword(s):  
Spectral Method ◽  
Discrete Ordinates ◽  
Matrix Equations ◽  
Schur Decomposition ◽  
Chebyshev Collocation ◽  
3D Matrix ◽  
Collocation Spectral Method

Chebyshev Collocation Spectral Method for Three-Dimensional Transient Coupled Radiative–Conductive Heat Transfer

2012 ◽  
Vol 134 (9) ◽  
Author(s):  
Ya-Song Sun ◽  
Jing Ma ◽  
Ben-Wen Li
Keyword(s):  
Heat Transfer ◽  
Spectral Method ◽  
Three Dimensional ◽  
Conservation Equation ◽  
Conductive Heat Transfer ◽  
Discrete Ordinates ◽  
Conductive Heat ◽  
Chebyshev Collocation ◽  
Energy Conservation Equation ◽  
Collocation Spectral Method

Abstract A Chebyshev collocation spectral method (CSM) is presented to solve transient coupled radiative and conductive heat transfer in three-dimensional absorbing, emitting, and scattering medium in Cartesian coordinates. The walls of the enclosures are considered to be opaque, diffuse, and gray and have specified temperature boundary conditions. The CSM is adopted to solve both the radiative transfer equation (RTE) and energy conservation equation in spatial domain, and the discrete ordinates method (DOM) is used for angular discretization of RTE. The exponential convergence characteristic of the CSM for transient coupled radiative and conductive heat transfer is studied. The results using the CSM show very satisfactory calculations comparing with available results in the literature. Based on this method, the effects of various parameters, such as the scattering albedo, the conduction–radiation parameter, the wall emissivity, and the optical thickness, are analyzed.

Chebyshev Collocation Spectral Methods for Coupled Radiation and Conduction in a Concentric Spherical Participating Medium

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Ben-Wen Li ◽  
Ya-Song Sun ◽  
Da-Wei Zhang
Keyword(s):  
Spectral Method ◽  
Spectral Methods ◽  
Discrete Ordinates ◽  
Conductive Heat ◽  
Discrete Ordinates Method ◽  
Chebyshev Collocation ◽  
Collocation Points ◽  
Collocation Spectral Method ◽  
Space Dependence ◽  
Very High

The Chebyshev collocation spectral method for coupled radiative and conductive heat transfer in concentric spherical participating medium is introduced and formulated. The angular dependence of the problem is discretized by conventional discrete ordinates method, and the space dependence is expressed by Chebyshev polynomial and discretized by collocation spectral method. Due to the exponential convergence of the spectral methods, very high accuracy can be obtained even using a small resolution (i.e., number of collocation points) for present problems. Comparisons between the solutions from Chebyshev collocation spectral–discrete ordinates method (SP-DOM) with available numerical or exact solutions in references indicate that the SP-DOM for the combination of radiation and conduction in concentric spherical participating medium is accurate and efficient.

scholarly journals A novel Chebyshev-collocation spectral method for solving the transport equation

2017 ◽  
Vol 13 (5) ◽  
pp. 0-0
Author(s):  
Zhonghui Li ◽  
◽  
Xiangyong Chen ◽  
Jianlong Qiu ◽  
Tongshui Xia ◽  
...  
Keyword(s):  
Transport Equation ◽  
Spectral Method ◽  
Chebyshev Collocation ◽  
Collocation Spectral Method
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