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

Sparse Tensor Product Approximation for Radiative Transfer

2007 ◽  
Author(s):  
Gisela Widmer ◽  
Ralf Hiptmair
Keyword(s):  
Radiative Transfer ◽  
Tensor Product ◽  
Degrees Of Freedom ◽  
Convergence Result ◽  
Superior Performance ◽  
Discrete Ordinates ◽  
Strong Regularity ◽  
Scattering Media ◽  
Translation Invariant ◽  
Tensor Product Approximation

The stationary monochromatic radiative transfer equation is stated in five dimensions, with the intensity depending on both a position in a three-dimensional domain as well as a direction. In order to overcome the high dimensionality of the problem, we propose and analyse a new multiscale Galerkin Finite Element discretizaton that, under strong regularity assumptions on the solution, reduces the complexity of the problem to the number of degrees of freedom in space only (up to logarithmic terms). The sparse tensor product approximation adapts the idea of so-called ‘Sparse Grids’ for the product space of functions on the physical domain and the unit sphere. We present some details of the sparse tensor product construction including a convergence result that shows that, assuming strong regularity of the solution, the method converges with essentially optimal asymptotic rates while its complexity grows essentially only as that for a linear transport problem. Numerical experiments in a translation invariant setting in non-scattering media agree with predictions of theory and demonstrate the superior performance of the sparse tensor product method compared to the discrete ordinates method.

Sign in / Sign up

Export Citation Format

Share Document