Paper Info
Title
Computation of Interface Reflection and Regular or Diffuse Transmission of the Planar Symmetric Radiative Transfer Equation with Isotropic Scattering and Its Diffusion Limit
Abstract
In this paper, we develop a numerical scheme for the interface problem in the planar symmetric radiative transfer equation with isotropic scattering. Such problems arise in the modeling of the propagation of energy density for waves in heterogeneous media with weak random fluctuation in the high frequency regime. The idea, following the earlier work of Jin and Wen for regular transmission and reflection, is to build the interface condition, which characterizes the reflection and transmission, into the numerical flux. The new contribution of this article is to deal with the diffuse transmission at the interface. The positivity of the scheme is proven. Moreover, we show, via numerical examples, that this new scheme is able to capture the correct (regular or diffuse) transmission and reflection through the interface, and, as the mean free path goes to zero, capture the diffusion limit with the correct interface conditions.
Year
DOI
Venue
2008
10.1137/060676192
SIAM J. Scientific Computing
Keywords
Field
DocType
isotropic scattering,diffuse transmission,planar symmetric radiative transfer,correct interface condition,new contribution,interface reflection,regular transmission,numerical flux,numerical scheme,interface problem,new scheme,numerical example,interface condition,diffusion limit,specular reflection,radiative transfer equation,mean free path,high frequency
Mean free path,Mathematical analysis,Specular reflection,Diffusion limit,Isotropic scattering,Planar,Radiative transfer,Numerical analysis,Mathematics,Computation
Journal
Volume
Issue
ISSN
30
4
1064-8275
Citations 
PageRank 
References 
2
0.47
4
Authors
3
Name
Order
Citations
PageRank
Shi Jin157285.54
Xiaomei Liao220.47
Xu Yang3459.17