Numerical analysis of the neutron multigroup \(SP_N\) equations. (Analyse numérique des équations de la neutronique \(SP_N\) multigroupe.) (English. French summary) Zbl 1478.65086
Summary: The multigroup neutron \(SP_N\) equations, which are an approximation of the neutron transport equation, are used to model nuclear reactor cores. In their steady state, these equations can be written as a source problem or an eigenvalue problem. We study the resolution of those two problems with an \(H^1\)-conforming finite element method and a Discontinuous Galerkin method, namely the Symmetric Interior Penalty Galerkin method.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65N25 | Numerical methods for eigenvalue problems for boundary value problems involving PDEs |
| 35B45 | A priori estimates in context of PDEs |
| 82D75 | Nuclear reactor theory; neutron transport |
| 82M10 | Finite element, Galerkin and related methods applied to problems in statistical mechanics |
| 35Q49 | Transport equations |
| 35Q82 | PDEs in connection with statistical mechanics |
Keywords:
neutron multigroup equations; neutron transport equation; source problem; eigenvalue problem; conforming finite element method; discontinuous penalty Galerkin methodReferences:
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