Vectorization of the time-dependent Boltzmann transport equation: Application to deep penetration problems
| Autor: | Agustín C. Cobos, Ana Lucía Poma, Darío Esteban Sanz, Guillermo Daniel Alvarez |
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| Rok vydání: | 2016 |
| Předmět: |
Physics
Radiation Discretization 010308 nuclear & particles physics Courant–Friedrichs–Lewy condition Monte Carlo method Monte Carlo method for photon transport 01 natural sciences Boltzmann equation 030218 nuclear medicine & medical imaging 03 medical and health sciences 0302 clinical medicine Quantum mechanics Phase space 0103 physical sciences Convergence (routing) Applied mathematics Convection–diffusion equation |
| Zdroj: | Radiation Physics and Chemistry. 127:102-114 |
| ISSN: | 0969-806X |
| Popis: | We introduce an alternative method to calculate the steady state solution of the angular photon flux after a numerical evolution of the time-dependent Boltzmann transport equation (BTE). After a proper discretization the transport equation was converted into an ordinary system of differential equations that can be iterated as a weighted Richardson algorithm. As a different approach, in this work the time variable regulates the iteration process and convergence criteria is based on physical parameters. Positivity and convergence was assessed from first principles and a modified Courant-Friedrichs-Lewy condition was devised to guarantee convergence. The Penelope Monte Carlo method was used to test the convergence and accuracy of our approach for different phase space discretizations. Benchmarking was performed by calculation of total fluence and photon spectra in different one-dimensional geometries irradiated with 60 Co and 6 MV photon beams and radiological applications were devised. |
| Databáze: | OpenAIRE |
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