PICHARD, Teddy; AREGBA-DRIOLLET, Denise; BRULL, Stéphane; DUBROCA, Bruno; FRANK, Martin

doi:10.4208/cicp.121114.210415a

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PICHARD, Teddy
Centre d'Etudes Lasers Intenses et Applications [CELIA]

AREGBA-DRIOLLET, Denise
Institut de Mathématiques de Bordeaux [IMB]

BRULL, Stéphane
Institut de Mathématiques de Toulouse UMR5219 [IMT]

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Communications in Computational Physics. 2016, vol. 19, n° 1, p. 168-191

Global Science Press

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Because of stability constraints, most numerical schemes applied to hyper-bolic 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.< Réduire

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Radiotherapy

Moments models

relaxation models

method of characteristics

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Relaxation schemes for the M 1 model with space-dependent flux: application to radiotherapy dose calculation

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