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3D Radiative Transfer Under Conditions of Non-local Thermodynamic Equilibrium: A Contribution to the Numerical Solution [chapter]

Doris Folini, Rolf Walder
1999 Hyperbolic Problems: Theory, Numerics, Applications  
We present the rst application of the generalized mean intensity approach, suggested by Turek 9], 10] for the solution of the radiative transfer equation, to NLTE problems.  ...  A new approach to the solution of the 3D NLTE optically thick radiative transfer problem for moving media is presented.  ...  The present approach takes up the idea of Turek for the solution of the radiative transfer equation. He suggested to solve for a generalized mean intensity instead of directed intensities.  ... 
doi:10.1007/978-3-0348-8720-5_33 fatcat:cnocvnhfufdp3nxmpd53hk3gka

On radiative transfer problems and their solution

Olga Atanackovic-Vukmanovic
2004 Serbian Astronomical Journal  
A survey of the main stages in the solution of radiative transfer (RT) problems is given with special emphasis on recent approaches and powerful numerical techniques developed to solve non-LTE RT problems  ...  Eduardo Simonneau for having introduced me the exciting field of radiative transfer and for his continued support through many years. I also thank Prof. Dr. Trajko Angelov for his valuable comments.  ...  This work has been realized within the project "Solar spectral irradiance variability" (No. 1951) supported by the Ministry of Science and Environmental Protection of the Republic of Serbia.  ... 
doi:10.2298/saj0469001a fatcat:5zg3wcssy5fdvdv7bmebnh2thq

Benchmark problems for wavelength dependent continuum radiative transfer [article]

Z. Ivezic, M. Groenewegen, A. Menshchikov, R. Szczerba
1997 arXiv   pre-print
When verifying a sophisticated numerical code, it is a usual practice to compare the results with reliable solutions obtained by other means.  ...  Results for the dust temperature and emerging spectra agree to better than 0.1%, and can be used as benchmark solutions for the verification of the dust radiative transfer codes.  ...  Knapp for their careful reading, A. Boss for his encouragement, and the referee C. Skinner for useful comments which helped improve the manuscript.  ... 
arXiv:astro-ph/9705154v1 fatcat:a3qgtf3ze5eljp53orubd5ydri

Page 42 of Astronomy and Astrophysics Vol. 108, Issue 1 [page]

1982 Astronomy and Astrophysics  
Furthermore, the numerical methods give little insight into the general behavior of the solution of the transfer equation.  ...  For a class of problems it solves the discretized transfer equation analytically by means of the calculus of difference equations (see e.g. Jordan, 1950).  ... 

Page 613 of Astronomy and Astrophysics Vol. 266, Issue 1 [page]

1992 Astronomy and Astrophysics  
Thus the radiative transfer problem has been simplified to searching for solutions J(r,t) of just this single equation.  ...  We demonstrate that this set of equations has solutions which fulfill the funda- mental physical requirements for approximations of radiative transfer.  ... 

Radiative transfer in layered media and its connection to the O'Doherty-Anstey formula

Matthew M. Haney, Kasper van Wijk, Roel Snieder
2005 Geophysics  
We examine radiative transfer theory, which accounts for the multiple scattering of waves, in a layered medium composed of randomly placed thin beds excited by a 1D source.  ...  At its most basic level, radiative transfer predicts that the wavefield separates into a coherent, or wavelike, part and an incoherent, or diffusive, flow after a length scale known as a mean free path  ...  In Figure 6 , the solution of the diffusion equation asymptotically approaches, with time, the numerical intensities of the experiment.  ... 
doi:10.1190/1.1852788 fatcat:dkoteqw3lzfvdgvreltnyd566m

Predictions of radiative transfer in two-dimensional nonhomogeneous participating cylindrical media

Jian-Min Zhang, William H. Sutton
1996 Journal of thermophysics and heat transfer  
solution meth- ods to the equation of radiative transfer remains a robust area in the study of heat transfer.  ...  In the present work, a solution method based on the S-type integral equation of transfer allowing for space-dependent radiative properties is developed, and anal- ysis for radiation in a nonhomogeneous  ... 
doi:10.2514/3.751 fatcat:i5auqqnytjgojfymju3iw3p2pe

Evaluation Of Participating Media Models For Fire Simulation

P. Cumber, M. Fairweather
2000 IAFSS - The International Association for Fire Safety Science : proceedings  
The models considered differ in their generality, sophistication, accuracy and computational cost, and are assessed in terms of their ability to predict radiative transfer in idealised situations, as well  ...  Use of models based on the banded grey gas, TTNH, wide and narrow band approaches yield satisfactory results for fire applications.  ...  ACKNOWLEDGEMENT This paper is published by permission of BG Technology  ... 
doi:10.3801/iafss.fss.6-337 fatcat:wg7nerw6k5etfkdwgzu24viqji

On the Analytical Solution of the SNRadiative Transport Equation in a Slab for a Space-dependent Albedo Coefficient

Rubem M F Vargas, Cynthia F Segatto, Marco Túllio Vilhena
2012 Journal of Physics, Conference Series  
In this work, we report a genuine general analytical solution for the linearized SN radiative-conductive transfer problem in a heterogeneous plane parallel atmosphere with the albedo coefficient depending  ...  By general solution, we mean that the solution is valid for an arbitrary albedo coefficient continuous functions of the spatial variable having the property of fulfill the requirements of existence and  ...  Motivated by the task of extending this of sort solution for heterogeneous media, in this work, we report a genuine general analytical solution for the linearized S N radiative-conductive transfer problem  ... 
doi:10.1088/1742-6596/369/1/012018 fatcat:tqy4hxfocvhplm2kgztajzanmq

An Assessment of and Solution to the Intensity Diffusion Error Intrinsic to Short-characteristic Radiative Transfer Methods

C. L. Peck, S. Criscuoli, M. P. Rast
2017 Astrophysical Journal  
In this paper, we quantify the effect of the numerical diffusion on the spatial resolution of synthesize emergent intensity images, and derive a closed form analytical model of the diffusion error as a  ...  We also show that the diffusion error is readily avoided by interpolating the simulation solution on a viewing-angle aligned grid prior to computing the radiative transfer.  ...  A reliable solution of the radiative transfer equation is required to both determine the radiative heating rate in the solution of the energy equation and synthesize spectra for comparison with observations  ... 
doi:10.3847/1538-4357/aa9178 fatcat:7udk442elzelzkni62sv3u53pe

Milne–Eddington Solutions for Relativistic Plane-Parallel Flows

Jun Fukue
2008 Nippon Tenmon Gakkai obun kenkyu hokoku  
Under the assumption of a constant flow speed, for the relativistically moving atmosphere we analytically obtain generalized Milne-Eddington solutions of radiative moment equations; the radiation energy  ...  Using the analytical solutions, we analytically integrate the relativistic transfer equation to obtain the specific intensity.  ...  The analytical approach in the present work as well as the numerical approach would help us to understand the relativistic radiative transfer.  ... 
doi:10.1093/pasj/60.3.627 fatcat:kriokd3xebbnbblczbicrv6eiy

A Concept of Discretization Error Indicator for Simulating Thermal Radiation by Finite Volume Method Based on an Entropy Generation Approach [chapter]

H. C., Y. Y., H. P., Y. Li
2012 Finite Volume Method - Powerful Means of Engineering Design  
The general equation to describe TR transport is the Radiative Transfer Equation (RTE), and several computational algorithms were proposed for solution of the RTE, which have achieved great advancement  ...  Generally, a relationship should be derived to correlate the radiative intensities in the face of the control volume and the intensities at the centre of the control volume, which constitute a kind of  ...  A Concept of Discretization Error Indicator for Simulating Thermal Radiation by Finite Volume Method Based on an Entropy Generation Approach, Finite Volume Method -Powerful Means of Engineering Design,  ... 
doi:10.5772/37765 fatcat:2owyrvevqraxtdmlhpioevvhay

Two-dimensional radiative heat-transfer calculations for nonequilibrium flows

Gregory J. Elbert, Pasquale Cinella
1995 Journal of Spacecraft and Rockets  
°~"” The solution to the equation of radiative transfer (9) will give the specific intensity at a given angle (direction of propagation) for a given frequency.  ...  Truly two-dimensional algorithms are developed for the radiative source term in the governing equations, whereby the determination of the specific intensity field is obtained by means of a numerical integration  ... 
doi:10.2514/3.26601 fatcat:2nshia4zjndzpcs2n5b43b7kue

Page 108 of Astronomy and Astrophysics Vol. 284, Issue 1 [page]

1994 Astronomy and Astrophysics  
In either case the frequency integration in Eq. (18) is performed before the solution of the transfer equation (19).  ...  Since the flow field comprises optically thin regions, the numerical treatment of the radiative transfer has to account for its non-local character.  ... 

Page 512 of Astronomy and Astrophysics Vol. 301, Issue 2 [page]

1995 Astronomy and Astrophysics  
The general approach of this paper is similar to that of Unno & Kondo (1976) and Masaki & Unno (1978).  ...  With these assumptions, the basic equation for spherical radiative problems is the frequency-integrated equation of ra- diative transfer, a partial differential equation for the frequency- integrated specific  ... 
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