Direct collocation meshless method for vector radiative transfer in scattering media

2015 ◽  
Vol 163 ◽  
pp. 50-62 ◽  
Author(s):  
Xun Ben ◽  
Hong-Liang Yi ◽  
Xun-Bo Yin ◽  
He-Ping Tan
Keyword(s):  
Radiative Transfer ◽  
Meshless Method ◽  
Scattering Media ◽  
Direct Collocation

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.

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.

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