PICHARD, Teddy; BRULL, Stéphane; DUBROCA, Bruno

doi:10.4208/cicp.OA-2017-0245

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PICHARD, Teddy
Laboratoire Jacques-Louis Lions [LJLL]

BRULL, Stéphane
Institut de Mathématiques de Bordeaux [IMB]

DUBROCA, Bruno
Laboratoire des Composites Thermostructuraux [LCTS]

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Communications in Computational Physics. 2018, vol. 25, n° 4, p. 1097-1126

Global Science Press

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Numerical schemes for the systems of transport equations are commonly constrained by a stability condition of Courant-Friedrichs-Lewy (CFL) type. We consider here a system modeling the steady transport of photons and electrons in the field of radiotherapy, which leads to very stiff CFL conditions at the discrete level. We circumvent this issue by constructing an implicit scheme based on a relaxation approach. The physics is modeled by an entropy-based moment system, namely the M 1 model. This model is non-linear, possesses potentially no hy-perbolic operator. It is furthermore only valid under a condition 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 potentially 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.< Réduire

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Implicit scheme

Relaxation scheme

M1 model

Radiotherapy dose computation

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A numerical approach for a system of transport equations in the field of radiotherapy

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