A Numerical Approach for a System of Transport Equations in the Field of Radiotherapy

A Numerical Approach for a System of Transport Equations in the Field of Radiotherapy

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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.