Positive and asymptotic preserving approximation of the radiation transport equation. (English) Zbl 1447.65142
This paper discusses numerical approximation methods for the radiation transport equation that are both positive and asymptotic preserving in the diffusion limit. The method is linear in space discretization and in compliance with Godunov’s theorem. It is observed a \(\mathcal{O}(h)\) convergence in the \(L^2\)-norm on manufactured solutions, and a \(\mathcal{O}(h^2)\) in the diffusion regime. Numerical experiments are also included.
Reviewer: Marius Ghergu (Dublin)
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N22 | Numerical solution of discretized equations for boundary value problems involving PDEs |
| 82D75 | Nuclear reactor theory; neutron transport |
| 35Q20 | Boltzmann equations |
| 35B09 | Positive solutions to PDEs |
Keywords:
finite element method; radiation transport; diffusion limit; asymptotic-preserving; positivity-preservingReferences:
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