Abstract
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.
Highlights
The neutron transport equation describes the neutron flux density in a reactor core
The geometry of the core is three-dimensional and the domain is {(x, y, z) ∈ R3, 0 ≤ x ≤ 140 cm; 0 ≤ y ≤ 140 cm; 0 ≤ z ≤ 150 cm}. This test is defined with 4 energy groups, isotropic scattering and vacuum boundary conditions
Since the scattering is isotropic, the SP3 formulation can be reformulated as a multigroup diffusion problem with 8 energy groups and an isotropic albedo boundary condition [3]
Summary
The neutron transport equation describes the neutron flux density in a reactor core It depends on 7 variables: 3 for the space, 2 for the motion direction, 1 for the energy (or the speed), and 1 for the time. Concerning the motion direction, the PN transport equations are obtained by developing the neutron flux on the spherical harmonics from order 0 to order N. We will denote by φ = ( (φmg )m∈Ie )g ∈IG ∈ RN×G the set of functions containing, for all energy group g , the even moments of the neutron flux.
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