A numerical approach for a system of transport equations in the field of radiotherapy
Language
en
Article de revue
This item was published in
Communications in Computational Physics. 2018, vol. 25, n° 4, p. 1097-1126
Global Science Press
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Implicit scheme
Relaxation scheme
M1 model
Radiotherapy dose computation
Origin
Hal imported