Numerical analysis of the 2D C5G7 MOX benchmark using PL equations and a nodal collocation method

Abstract

A classical discretization for the angular dependence of the neutron transport equation is based on a truncated spherical harmonics expansion. The resulting system of equations are the P L equations. We review the multidimensional P L equations, for arbitrary odd order L, and then we proceed to the spatial discretization of these equations, for rectangular geometries, using a nodal collocation method based on the expansion of the spatial dependence of the fields in terms of orthonormal Legendre polynomials. The validity of the method to deal with complex reactor problems is then studied with the seven-group 2D NEA C5G7 MOX fuel assembly benchmark problem. The solution is computed for different spatial meshes, showing that the P L results are consistent with the reference Monte Carlo solution. Additionally, the first subcritical modes are also computed for the the full reactor configuration.

Validation of the SHNC time-dependent transport code based on the spherical harmonics method for complex nuclear fuel assemblies

“…, 7, of an isolated pin cell, with reflecting boundary conditions, and spatial mesh given by a 7 × 7 nodes as described in Fig. 4 of [57]. 2.…”

Contributions to solve the Multi-group Neutron Transport equation with different Angular Approaches

“…Other power comparison results show good agreement with respect to the benchmark results. Furthermore, the sub-critical modes have been compared in table 3.11, where it can be seen that the result is independent of the any kind of angular discretization [Capilla et al, 2018], because the modes are the same for the Spherical Harmonics method as for the Discrete ordinates method. Fig.…”