Computation of the C5G7 neutron transport benchmark using a spherical harmonics-nodal collocation method

Abstract

[EN] The spherical harmonics method is applied to the angular dependence of the neutron transport equation, obtaining a finite approximation known as the PL equations, that are rewritten as a vector-valued second order differential equation. Marshak vacuum boundary conditions are also considered. We have developed a nodal collocation method to spatially discretize the multi-dimensional PL equations, for arbitrary odd order L, on a rectilinear mesh, based on the expansion of the neutronic fluxes in terms of orthonormal Legendre polynomials. In this work, the capability of the method to treat advanced reactor problems is verified with the 2D C5G7 MOX Fuel Assembly Benchmark, that is a criticality calculation proposed by NEA/NSC for testing the ability of modern deterministic transport methods and codes to treat heterogeneous reactor core problems without spatial homogenization. The large sparse generalized eigenvalue problem that arises is numerically solved on parallel computers using the software library SLEPc. The solution of this problem is obtained for different types of spatial meshes, for various PL expansion orders and for different Legendre polynomial orders. We show that our results are consistent with the reference Monte Carlo solution.