@Article{CiCP-10-1184,
author = {Christophe Berthon, Martin Frank, Céline Sarazin and Rodolphe Turpault},
title = {Numerical Methods for Balance Laws with Space Dependent Flux: Application to Radiotherapy Dose Calculation},
journal = {Communications in Computational Physics},
year = {2011},
volume = {10},
number = {5},
pages = {1184--1210},
abstract = {<p style="text-align: justify;">The present work is concerned with the derivation of numerical methods
to approximate the radiation dose in external beam radiotherapy. To address this issue,
we consider a moment approximation of radiative transfer, closed by an entropy
minimization principle. The model under consideration is governed by a system of
hyperbolic equations in conservation form supplemented by source terms. The main
difficulty coming from the numerical approximation of this system is an explicit space
dependence in the flux function. Indeed, this dependence will be seen to be stiff and
specific numerical strategies must be derived in order to obtain the needed accuracy. A
first approach is developed considering the 1D case, where a judicious change of variables
allows to eliminate the space dependence in the flux function. This is not possible
in multi-D. We therefore reinterpret the 1D scheme as a scheme on two meshes, and
generalize this to 2D by alternating transformations between separate meshes. We call
this procedure projection method. Several numerical experiments, coming from medical
physics, illustrate the potential applicability of the developed method.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.020810.171210a},
url = {http://global-sci.org/intro/article_detail/cicp/7480.html}
}