Year: 2019
Communications in Computational Physics, Vol. 25 (2019), Iss. 4 : pp. 1097–1126
Abstract
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.
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.
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.
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2017-0245
Communications in Computational Physics, Vol. 25 (2019), Iss. 4 : pp. 1097–1126
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Implicit scheme relaxation scheme $M_1$ model radiotherapy dose computation.