@Article{CiCP-25-4,
author = {},
title = {A Numerical Approach for a System of Transport Equations in the Field of Radiotherapy},
journal = {Communications in Computational Physics},
year = {2019},
volume = {25},
number = {4},
pages = {1097--1126},
abstract = {<p style="text-align: justify;">Numerical schemes for systems of transport equations are commonly constrained by a stability condition of Courant-Friedrichs-Lewy (CFL) type. We consider
a system modeling the steady transport of photons and electrons in the field of radiotherapy. Naive discretizations of such a system are commonly constrained by a
very restrictive CFL condition. This issue is circumvented by constructing an implicit
scheme based on a relaxation approach.<br/>We use an entropy-based moment model, namely the $M_1$ model. Such a system
of equations possesses the non-linear flux terms of a hyperbolic system but no time
derivative. The flux terms are well-defined only under a condition on the unknowns,
called realizability, which corresponds to the positivity of an underlying kinetic distribution function.<br/>The present numerical approach is applicable to non-linear systems which possess no hyperbolic operator, and it preserves the realizability property. However, the
discrete equations are non-linear, and we propose a numerical method to solve such
non-linear systems.<br/>Our approach is tested on academic and practical cases in 1D, 2D, and 3D and it is
shown to require significantly less computational power than reference methods.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2017-0245},
url = {https://global-sci.com/article/79913/a-numerical-approach-for-a-system-of-transport-equations-in-the-field-of-radiotherapy}
}