Spherical Harmonics and Discontinuous Galerkin Finite Element Methods for the Three-Dimensional Neutron Transport Equation: Application to Core and Lattice Calculation
Résumé
The spherical harmonics or P N method is intended to approximate the neutron angular flux by a linear combination of spherical harmonics of degree at most N. In this work, the P N method is combined with discontinuous Galerkin finite elements method and yield to a full discretization of the multigroup neutron transport equation. The employed method is able to handle all geometries describing the fuel elements without any simplification nor homogenisation. Moreover the use of a matrix assembly-free method avoids building large sparse matrices, which enables to produce high-order solutions in small computational time and less storage usage. The resulting transport solver called NYMO has a wide range of applications: it can be used for a core calculation as well as for a precise 281-groups lattice calculation accounting anisotropic scattering. To assess the accuracy of this numerical scheme, it was applied to 3D reactor core and fuel assembly calculations. These calculations point out that the proposed P N-DG method is capable of producing precise solutions while the developed solver is able to handle complex 3D core and assemblies geometries.
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