Parallel Jacobian-free Newton Krylov solution of the discrete ordinates method with flux limiters for 3D radiative transfer

2012 ◽  
Vol 231 (11) ◽  
pp. 4257-4278 ◽  
Author(s):  
William F. Godoy ◽  
Xu Liu
Keyword(s):  
Radiative Transfer ◽  
Discrete Ordinates ◽  
Discrete Ordinates Method ◽  
Flux Limiters

Transient Radiative Transfer in Anisotropically Scattering Media Using Monotonicity-Preserving Schemes

2000 ◽  
Author(s):  
M. Sakami ◽  
K. Mitra ◽  
P.-F. Hsu
Keyword(s):  
Radiative Transfer ◽  
Research Work ◽  
Discrete Ordinates ◽  
Scattering Media ◽  
Discrete Ordinates Method ◽  
Piecewise Parabolic ◽  
Phase Functions ◽  
Monotonicity Preserving ◽  
Made In ◽  
Thick Medium

Abstract This research work deals with the analysis of transient radiative transfer in one-dimensional scattering medium. The time-dependant discrete ordinates method was used with an upwind monotonic scheme: the piecewise parabolic scheme. This scheme was chosen over a total variation diminishing version of the Lax-Wendroff scheme. These schemes were originally developed to solve Eulerian advection problem in hydrodynamics. The capability of these schemes to handle sharp discontinuity in a propagating electromagnetic wave front was compared. The accuracy and the efficiency of the discrete ordinates method associated with the piecewise parabolic advection scheme were studied. Comparisons with Monte Carlo and integral formulation methods show the accuracy and the efficiency of this proposed method. Parametric study for optically thin and thick medium, different albedos and phase functions is then made in the unsteady state zone.

Analytical Delta-Four-Stream Doubling–Adding Method for Radiative Transfer Parameterizations

2013 ◽  
Vol 70 (3) ◽  
pp. 794-808 ◽  
Author(s):  
Feng Zhang ◽  
Zhongping Shen ◽  
Jiangnan Li ◽  
Xiuji Zhou ◽  
Leiming Ma
Keyword(s):  
Optical Properties ◽  
Radiative Transfer ◽  
Transfer Process ◽  
Solar Spectrum ◽  
Single Layer ◽  
Discrete Ordinates ◽  
Discrete Ordinates Method ◽  
Atmospheric Profile ◽  
Relative Errors ◽  
Transmission And Absorption

Abstract Although single-layer solutions have been obtained for the δ-four-stream discrete ordinates method (DOM) in radiative transfer, a four-stream doubling–adding method (4DA) is lacking, which enables us to calculate the radiative transfer through a vertically inhomogeneous atmosphere with multiple layers. In this work, based on the Chandrasekhar invariance principle, an analytical method of δ-4DA is proposed. When applying δ-4DA to an idealized medium with specified optical properties, the reflection, transmission, and absorption are the same if the medium is treated as either a single layer or dividing it into multiple layers. This indicates that δ-4DA is able to solve the multilayer connection properly in a radiative transfer process. In addition, the δ-4DA method has been systematically compared with the δ-two-stream doubling–adding method (δ-2DA) in the solar spectrum. For a realistic atmospheric profile with gaseous transmission considered, it is found that the accuracy of δ-4DA is superior to that of δ-2DA in most of cases, especially for the cloudy sky. The relative errors of δ-4DA are generally less than 1% in both the heating rate and flux, while the relative errors of δ-2DA can be as high as 6%.

Discrete ordinates method in the analysis of the radiative transfer in high intensity discharge lamps

2005 ◽  
Vol 38 (22) ◽  
pp. 4053-4065 ◽  
Author(s):  
Mohamed Bouaoun ◽  
Hatem Elloumi ◽  
Kamel Charrada ◽  
Mounir Ben El Hadj Rhouma ◽  
Mongi Stambouli
Keyword(s):  
Radiative Transfer ◽  
High Intensity ◽  
Discrete Ordinates ◽  
Discrete Ordinates Method

Angular False Scattering in Radiative Heat Transfer Analysis Using the Discrete-Ordinates Method With Higher-Order Quadrature Sets

2013 ◽  
Author(s):  
Brian Hunter ◽  
Zhixiong Guo
Keyword(s):  
Monte Carlo ◽  
Radiative Transfer ◽  
Phase Function ◽  
Radiative Heat ◽  
Higher Order ◽  
Heat Transfer Analysis ◽  
Discrete Ordinates ◽  
Equal Weight ◽  
Participating Media ◽  
Discrete Ordinates Method

The SN quadrature set for the discrete-ordinates method is limited in overall discrete direction number in order to avoid physically unrealistic negative directional weight factors. Such a limitation can adversely impact radiative transfer predictions. Directional discretization results in errors due to ray effect, as well as angular false scattering error due to distortion of the scattering phase function. The use higher-order quadrature schemes in the discrete-ordinates method allows for improvement in discretization errors without an overall directional limitation. In this analysis, four higher-order quadrature sets (Legendre-Equal Weight, Legendre-Chebyshev, Triangle Tessellation, and Spherical Ring Approximation) are implemented for determination of radiative transfer in a 3-D cubic enclosure containing participating media. Radiative heat fluxes, calculated at low direction number, are compared to the SN quadrature and Monte Carlo predictions to gauge quadrature accuracy. Additionally, investigation into the reduction of angular false scattering with sufficient increase in direction number using higher-order quadrature, including heat flux accuracy with respect to Monte Carlo and computational efficiency, is presented. While higher-order quadrature sets are found to effectively minimize angular false scattering error, it is found to be much more computationally efficient to implement proper phase function normalization for accurate radiative transfer predictions.

Hybrid SN-PN Solution of the Radiative Transfer Equation in Multi-Dimensional Media

2011 ◽  
Author(s):  
Maathangi Sankar ◽  
Sandip Mazumder
Keyword(s):  
Radiative Transfer ◽  
Transfer Equation ◽  
Complex Geometry ◽  
Radiative Transfer Equation ◽  
Discrete Ordinates ◽  
Differential Approximation ◽  
Discrete Ordinates Method ◽  
Surface Exchange ◽  
New Formulation ◽  
Ray Effects

The Modified Differential Approximation (MDA) was originally proposed for solution of the radiative transfer equation (RTE) in order to remove the shortcomings of the P1 approximation in scenarios where the radiation intensity is strongly directionally dependent. In the original MDA approach, the wall-emitted component of the intensity is determined using a surface-to-surface exchange formulation that makes use of geometric viewfactors. Such an approach is computationally very expensive for complex geometry and/or inhomogeneous media. This article presents a new formulation in which the wall-emitted component is solved using the Discrete Ordinates Method (SN approximation), while the medium-emitted component is solved using the P1 approximation, resulting in a hybrid SN-PN RTE solver. Results show that the hybrid Discrete Ordinates-P1 method (DOM-P1) is computationally very efficient, but its accuracy is poor in optically thin situations where ray effects, inherent in the Discrete Ordinates Method, are pronounced. To circumvent this problem, the control-angle Discrete Ordinates Method (CADOM) is finally employed, and the accuracy of the hybrid CADOM-P1 method is found to be far superior to the hybrid DOM-P1 method.

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