Solving Radiative Transfer Equation in Scattering Plane-Parallel Medium Using Wavelets Approximation

2002 ◽  
Author(s):  
Oguzhan Guven ◽  
Bryan Y. Wang ◽  
Yildiz Bayazitoglu
Keyword(s):  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Heat ◽  
Numerical Solutions ◽  
Radiative Transfer Equation ◽  
Anisotropic Scattering ◽  
Wavelet Approximation ◽  
Plane Parallel ◽  
Scattering Phase ◽  
Scattering Phase Function

Wavelet analysis is presented for solving the radiative transfer equation for a scattering medium in a one-dimensional plane-parallel geometry. Some properties of the wavelet transform for numerical approximation of radiative heat transfer are demonstrated. The governing equations are reduced to a system of first-order ordinary differential equations. Linear anisotropic scattering is assumed in order to compare the results with the previous researchers. The method of analysis is quite general since it only requires that the scattering phase function is square integrable. The numerical solutions indicate that wavelet approximation is promising.

Radiative Transfer in Axisymmetric, Finite Cylindrical Enclosures

1986 ◽  
Vol 108 (2) ◽  
pp. 271-276 ◽  
Author(s):  
M. P. Mengu¨c¸ ◽  
R. Viskanta
Keyword(s):  
Finite Element ◽  
Radiative Transfer ◽  
Numerical Solutions ◽  
Radiative Transfer Equation ◽  
Radiative Properties ◽  
Radiation Characteristics ◽  
Scattering Phase ◽  
Model Equations ◽  
Scattering Phase Function ◽  
Finite Element Schemes

A solution of the radiative transfer equation for an axisymmetric cylindrical enclosure containing radiatively participating gases and particles is presented. Nonhomogeneities of the radiative properties of the medium as well as of the radiation characteristics of the boundaries are allowed for, and the boundaries are assumed to be diffusely emitting and reflecting. The scattering phase function is represented by the delta-Eddington approximation to account for highly forward scattering by particulates. The model for radiative transfer is based on the P1 and P3-spherical harmonics approximations. Numerical solutions of model equations are obtained using finite-difference as well as finite-element schemes.

Completely Spectral Collocation Solution of Radiative Heat Transfer in an Anisotropic Scattering Slab With a Graded Index Medium

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Jing Ma ◽  
Ya-Song Sun ◽  
Ben-Wen Li
Keyword(s):  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Anisotropic Scattering ◽  
Discrete Ordinates ◽  
Spectral Collocation ◽  
Graded Index ◽  
Wide Range ◽  
Derivative Term ◽  
Scattering Phase Function

A completely spectral collocation method (CSCM) is developed to solve radiative transfer equation in anisotropic scattering medium with graded index. Different from the Chebyshev collocation spectral method based on the discrete ordinates method (SP-DOM), the CSCM is used to discretize both the angular domain and the spatial domain of radiative transfer equation. In this approach, the angular derivative term and the integral term are approximated by the high order spectral collocation scheme instead of the low order finite difference approximations. Compared with those available data in literature, the CSCM has a good accuracy for a wide range of the extinction coefficient, the scattering albedo, the scattering phase function, the gradient of refractive index and the boundary emissivity. The CSCM can provide exponential convergence for the present problem. Meanwhile, the CSCM is much more economical than the SP-DOM. Moreover, for nonlinear anisotropic scattering and graded index medium with space-dependent albedo, the CSCM can provide smoother results and mitigate the ray effect.

Finite Volume Solution of the Radiative Transfer Equation Using NVD and TVD Schemes in Unstructured Grids

2013 ◽  
Author(s):  
P. J. Coelho
Keyword(s):  
Radiative Transfer ◽  
Transfer Equation ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Unstructured Grids ◽  
Radiative Transfer Equation ◽  
Navier Stokes ◽  
Cartesian Grids ◽  
Tvd Schemes ◽  
Navier Stokes Equations

Discretization schemes based on the normalized variable diagram (NVD) and total variation diminishing (TVD) schemes are applied to the solution of the radiative transfer equation (RTE) in unstructured grids. The success of the application of these schemes to Cartesian grids has been previously demonstrated. However, their extension to unstructured grids is not straightforward. A few methods to overcome this difficulty have been proposed, and successfully applied to the solution of a scalar transport equation and to the Navier-Stokes equations. These methods are applied here to the solution of the RTE, along with a new one, recently proposed, for several test cases in which the analytical solution or other reliable numerical solutions are available for comparison. The results demonstrate that although the NVD and TVD schemes are much more accurate than the step and mean flux interpolation schemes, their order of accuracy in the case of unstructured grids is lower than in Cartesian grids. Moreover, in contrast to Cartesian grids, the NVD and TVD schemes are not strictly bounded in unstructured grids, and unphysical solutions may occur. The alternative method proposed to implement the NVD and TVD schemes is generally more accurate than previous ones, but also computationally more demanding.

scholarly journals Ray Effects and False Scattering in Improved Discrete Ordinates Method

Energies ◽  
2021 ◽  
Vol 14 (20) ◽  
pp. 6839
Author(s):  
Yong Cheng ◽  
Shuihua Yang ◽  
Zhifeng Huang
Keyword(s):  
Heat Flux ◽  
Radiative Transfer ◽  
Radiative Heat ◽  
Anisotropic Scattering ◽  
Radiative Heat Flux ◽  
Discrete Ordinates ◽  
Discrete Ordinates Method ◽  
Computation Efficiency ◽  
Scattering Phase ◽  
Ray Effects

The improved discrete ordinates method (IDOM) developed in our previous paper is extended to solve radiative transfer in three-dimensional radiative systems with anisotropic scattering medium. In IDOM, radiative intensities in a large number of new discrete directions are calculated by direct integration of the conventional discrete ordinates method (DOM) results, and radiative heat flux is obtained by integrating radiative intensities in these new discrete directions. Ray effects and false scattering, which tend to compensate each other, are investigated together in IDOM. Results show that IDOM can mitigate both of them effectively with high computation efficiency. Finally, the effect of scattering phase function on radiative transfer is studied. Results of radiative heat flux at boundaries containing media with different scattering phase functions are compared and analyzed. This paper indicates that the IDOM can overcome the shortages of the conventional DOM well while inheriting its advantages such as high computation efficiency and easy implementation.

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