PICHARD, Teddy; BRULL, Stéphane; DUBROCA, Bruno

doi:10.4208/cicp.OA-2017-0245

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PICHARD, Teddy

BRULL, Stéphane
Institut de Mathématiques de Bordeaux [IMB]

DUBROCA, Bruno
Laboratoire des Composites Thermostructuraux [LCTS]

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Communications in Computational Physics. 2019, vol. 25, n° 4, p. 1097-1126

Global Science Press

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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 M1 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.< Réduire

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Implicit scheme

relaxation scheme

M 1 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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