Relaxation Schemes for the $M_1$ Model with Space-Dependent Flux: Application to Radiotherapy Dose Calculation
Year: 2016
Author: Teddy Pichard, Denise Aregba-Driollet, Stéphane Brull, Bruno Dubroca, Martin Frank
Communications in Computational Physics, Vol. 19 (2016), Iss. 1 : pp. 168–191
Abstract
Because of stability constraints, most numerical schemes applied to hyperbolic systems of equations turn out to be costly when the flux term is multiplied by some very large scalar. This problem emerges with the $M_1$ system of equations in the field of radiotherapy when considering heterogeneous media with very disparate densities. Additionally, the flux term of the $M_1$ system is non-linear, and in order for the model to be well-posed the numerical solution needs to fulfill conditions called realizability. In this paper, we propose a numerical method that overcomes the stability constraint and preserves the realizability property. For this purpose, we relax the $M_1$ system to obtain a linear flux term. Then we extend the stencil of the difference quotient to obtain stability. The scheme is applied to a radiotherapy dose calculation example.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.121114.210415a
Communications in Computational Physics, Vol. 19 (2016), Iss. 1 : pp. 168–191
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24