Application of a nodal collocation approximation for the multidimensional PL equations to the 3D Takeda benchmark problems

PL equations are classical approximations to the neutron transport equations, which are obtained expanding the angular neutron flux in terms of spherical harmonics. These approximations are useful to study the behavior of reactor cores with complex fuel assemblies, for the homogenization of nuclear cross-sections, etc., and most of these applications are in three-dimensional (3D) geometries. In this work, we review the multi-dimensional PL equations and describe a nodal collocation method for the spatial discretization of these equations for arbitrary odd order L, which is based on the expansion of the spatial dependence of the fields in terms of orthonormal Legendre polynomials. The performance of the nodal collocation method is studied by means of obtaining the keff and the stationary power distribution of several 3D benchmark problems. The solutions are obtained are compared with a finite element method and a Monte Carlo method.

► The multidimensional PL approximation to the nuclear transport equation is reviewed.
► A nodal collocation method is developed for the spatial discretization of PL equations.
► Advantages of the method are lower dimension and good characterists of the associated algebraic eigenvalue problem.
► The PL nodal collocation method is implemented into the computer code SHNC.
► The SHNC code is verified with 2D and 3D benchmark eigenvalue problems from Takeda and Ikeda, giving satisfactory results.