An efficient equation-solving method for calculating radiative transfer in isotropic scattering medium

2021 ◽  
Vol 174 ◽  
pp. 121298
Author(s):  
Bao-Hai Gao ◽  
Hong Qi ◽  
Ying Zhao ◽  
Ya-Tao Ren ◽  
Ming-Jian He
Keyword(s):  
Radiative Transfer ◽  
Isotropic Scattering ◽  
Scattering Medium ◽  
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.

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