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

Highlights: • The neutron transport equation is solved with a spherical harmonics-nodal collocation method. • The method is applied to the complex reactor seven group 2D NEA C5G7 MOX problem. • Results are consistent with the reference Monte Carlo solution. • First subcritical models are also computed for full reactor configuration. - 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 multi-dimensional 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 full reactor configuration.