DISCRETE ORDINATES SOLUTION OF RADIATIVE TRANSFER IN SCATTERING MEDIA WITH COLLIMATED IRRADIATION

2016 ◽  
Author(s):  
Pedro J. Coelho
Keyword(s):  
Radiative Transfer ◽  
Discrete Ordinates ◽  
Scattering Media

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.

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.

Least-Squares Finite Element Analysis for Transient Radiative Transfer in Absorbing and Scattering Media

2005 ◽  
Vol 128 (5) ◽  
pp. 499-503 ◽  
Author(s):  
W. An ◽  
L. M. Ruan ◽  
H. P. Tan ◽  
H. Qi
Keyword(s):  
Finite Element ◽  
Radiative Transfer ◽  
Least Squares ◽  
Present Model ◽  
Element Model ◽  
Discrete Ordinates ◽  
Scattering Media ◽  
Element Analysis ◽  
Volume Method ◽  
Transfer Problems

In some radiative transfer processes, the time scales are usually on the order of 10−9-10−15s, so the transient effect of radiation should be considered. In present research, a finite element model, which is based on the discrete ordinates method and least-squares variational principle, is developed to simulate the transient radiative transfer in absorbing and scattering media. The numerical formulations and detailed steps are given. Moreover, two transient radiative transfer problems are investigated and the results are compared with those by integral method and finite volume method. It indicates that the present model can simulate the transient radiative transfer effectively and accurately.

scholarly journals Variational Iteration Method for Infrared Radiative Transfer in a Scattering Medium

2017 ◽  
Vol 74 (2) ◽  
pp. 419-430 ◽  
Author(s):  
Feng Zhang ◽  
Yi-Ning Shi ◽  
Jiangnan Li ◽  
Kun Wu ◽  
Hironobu Iwabuchi
Keyword(s):  
Radiative Transfer ◽  
Iteration Method ◽  
Climate Models ◽  
Single Layer ◽  
Variational Iteration Method ◽  
Discrete Ordinates ◽  
Scattering Medium ◽  
Scattering Media ◽  
First Order ◽  
Variational Iteration

Abstract A new scheme is proposed for using the variational iteration method (VIM) to solve the problem of infrared radiative transfer in a scattering medium. This scheme allows the zeroth-order solution to be identified as the absorption approximation and the scattering effect is included in the first-order iteration. The upward and downward intensities are calculated separately in VIM, which simplifies the calculation process. By applying VIM to two single-layer scattering media and a full radiation algorithm with gaseous transmission, it is found that VIM is generally more accurate than the discrete-ordinates method (DOM), especially for cirrostratus. Computationally, VIM is slightly faster than DOM in the two-stream case but more than twice as fast in the four-stream case. In view of its high overall accuracy and computational efficiency, VIM is well suited to solving infrared radiative transfer in climate models.

An Acceleration Technique for the Computation of Participating Radiative Heat Transfer

2009 ◽  
Author(s):  
Sanjay R. Mathur ◽  
Jayathi Y. Murthy
Keyword(s):  
Heat Transfer ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Radiation Heat Transfer ◽  
Solution Procedure ◽  
Discrete Ordinates ◽  
Average Intensity ◽  
Scattering Media ◽  
Acceleration Techniques

It is known that the finite volume and discrete ordinates methods for computing participating radiation are slow to converge when the optical thickness of the medium becomes large. This is a result of the sequential solution procedure usually employed to solve the directional intensities, which couples the ordinate directions and the energy equation loosely. Previously published acceleration techniques have sought to employ a governing equation for the angular-average of the radiation intensity to promote inter-directional coupling. These techniques have not always been successful, and even where successful, have been found to destroy the conservation properties of the radiative transfer equation. In this paper, we develop an algorithm called Multigrid Acceleration using Global Intensity Correction (MAGIC) which employs a multigrid solution of the average intensity and energy equations to significantly accelerate convergence, while ensuring that the conservative property of the radiative transfer equation is preserved. The method is shown to perform well for radiation heat transfer problems in absorbing, emitting and scattering media, both and without radiative equilibrium, and across a range of optical thicknesses.

Finite Element Simulation for Short Pulse Light Radiative Transfer in Homogeneous and Nonhomogeneous Media

2006 ◽  
Vol 129 (3) ◽  
pp. 353-362 ◽  
Author(s):  
W. An ◽  
L. M. Ruan ◽  
H. P. Tan ◽  
H. Qi ◽  
Y. M. Lew
Keyword(s):  
Finite Element ◽  
Optical Properties ◽  
Radiative Transfer ◽  
Short Pulse ◽  
Continuous Light ◽  
Ultrashort Pulses ◽  
Discrete Ordinates ◽  
Scattering Media ◽  
Nonhomogeneous Media ◽  
Pulse Light

With the rapid progress on ultrashort pulse laser, the transient radiative transfer in absorbing and scattering media has attracted increasing attention. The temporal radiative signals from a medium irradiated by ultrashort pulses offer more useful information which reflects the internal structure and properties of media than that by the continuous light sources. In the present research, a finite element model, which is based on the discrete ordinates method and least-squares variational principle, is developed to simulate short-pulse light radiative transfer in homogeneous and nonhomogeneous media. The numerical formulations and detailed steps are given. The present models are verified by two benchmark cases, and several transient radiative transfer cases in two-layer and three-layer nonhomogeneous media are investigated and analyzed. The results indicate that the reflected signals can imply the break of optical properties profile and their location. Moreover, the investigation for uniqueness of temporal reflected and transmitted signals indicate that neither of these two kinds of signals can be solely taken as experimental measurements to predict the optical properties of medium. They should be measured simultaneously in the optical imaging application. The ability of the present model to deal with multi-dimensional problems is proved by the two cases in the two-dimensional enclosure.

Least-Squares Radial Point Interpolation Collocation Meshless Method for Radiative Heat Transfer

2006 ◽  
Vol 129 (5) ◽  
pp. 669-673 ◽  
Author(s):  
J. Y. Tan ◽  
L. H. Liu ◽  
B. X. Li
Keyword(s):  
Radiative Transfer ◽  
Least Squares ◽  
Meshless Method ◽  
Solution Method ◽  
Approximate Solutions ◽  
Discrete Ordinates ◽  
Scattering Media ◽  
Radial Point Interpolation ◽  
Point Interpolation ◽  
Transfer Problems

A least-squares radial point interpolation collocation meshless method based on the discrete ordinates equation is developed for solving the radiative transfer in absorbing, emitting, and scattering media, in which compact support radial basis functions augmented with polynomial basis are employed to construct the trial functions. In addition to the collocation nodes, a number of auxiliary points are also adopted to form the total residuals of the problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of residuals of all collocation and auxiliary points. Three typical examples of radiative transfer in semitransparent media are examined to verify this new solution method. The numerical results are compared with other benchmark approximate solutions in references. By comparison, the results show that the least-squares radial point interpolation collocation meshless method has good accuracy in solving radiative transfer problems within absorbing, emitting, and scattering media.

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