Semi-analytical equation-solving RDFIEM method for radiative transfer in a plane-parallel anisotropic scattering medium

2021 ◽  
Vol 166 ◽  
pp. 106946
Author(s):  
Bao-Hai Gao ◽  
Hong Qi ◽  
Zhi-Qiang Yu ◽  
Jian-Ping Sun ◽  
Ya-Tao Ren ◽  
...  
Keyword(s):  
Radiative Transfer ◽  
Anisotropic Scattering ◽  
Analytical Equation ◽  
Scattering Medium ◽  
Plane Parallel ◽  
Equation Solving

The SKN Approximation for Solving Radiative Transfer Problems in Absorbing, Emitting, and Linearly Anisotropically Scattering Plane-Parallel Medium: Part 2

2002 ◽  
Vol 124 (4) ◽  
pp. 685-695 ◽  
Author(s):  
Zekeriya Altac¸
Keyword(s):  
Radiative Transfer ◽  
Incident Energy ◽  
Radiative Heat ◽  
Isotropic Scattering ◽  
Benchmark Problems ◽  
Scattering Medium ◽  
Second Order Differential Equations ◽  
Plane Parallel ◽  
Kernel Approximation ◽  
Transfer Problems

The SKN (Synthetic Kernel) approximation is proposed for solving radiative transfer problems in linearly anisotropically scattering homogeneous and inhomogeneous participating plane-parallel medium. The radiative integral equations for the incident energy and the radiative heat flux using synthetic kernels are reduced to a set of coupled second-order differential equations for which proper boundary conditions are established. Performance of the three quadrature sets proposed for isotropic scattering medium are further tested for linearly anisotropically scattering medium. The method and its convergence with respect to the proposed quadrature sets are explored by comparing the results of benchmark problems using the exact, P11, and S128 solutions. The SKN method yields excellent results even for low orders using appropriate quadrature set.

Parametric Study of Simultaneous Radiative Transfer in Plane-Parallel Scattering Medium With Variable Refractive Index by Spectral Collocation Method

2013 ◽  
Author(s):  
Jing Ma ◽  
Yasong Sun ◽  
Benwen Li
Keyword(s):  
Refractive Index ◽  
Radiative Transfer ◽  
Collocation Method ◽  
Spectral Collocation Method ◽  
Scattering Medium ◽  
Spectral Collocation ◽  
Plane Parallel ◽  
Derivative Term ◽  
Scattering Phase Function ◽  
Angular Domains

In this work, a spectral collocation method is developed to simulate radiative transfer in a refractive planar medium. The space and angular domains of radiative intensity are discretized by Chebyshev polynomials, and the angular derivative term and the integral term of radiative transfer equation are approximated by spectral collocation method. The spectral collocation method can provide exponential convergence and obtain high accuracy even using few nodes. There is a very satisfying correspondence between the spectral collocation results and available data in literatures. Influence of the extinction coefficient, the scattering albedo, the scattering phase function, the gradient of refractive index and the emissivity of boundary are investigated for the plane-parallel scattering medium with variable refractive index.

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