Abstract
On the basis of the neutron transport equation, several neutron diffusion codes were developed in the past due to its simplified form and the limitations on computational power. Numerical schemes were developed to solve the diffusion equation with acceptable performance but still with problems in the regions where diffusion theory is not physically accurate. Nowadays, computational power has significantly increased and thus, new numerical schemes are being implemented to deal directly with neutron transport equation. The Simplified Spherical Harmonics approximation can be found among such methods. One of the interesting features of SPL is that, depending on the order of approximation, several diffusion-like equations are derived and thus, the same solvers that were developed to deal with diffusion equation can be used to solve the SPL equations with adaptations on the equation's coefficients. In Mexico, the AZNHEX code is being developed. AZNHEX is a neutron diffusion code for hexagonal geometry which employs the Raviart-Thomas-Nédélec of index zero for the space discretization of the scalar neutron flux and the multigroup theory for energy discretization. In this paper, a novel implementation of SPL in the AZNHEX code is presented. Due to the canonical representation of the solution of SPL equations, no changes in source code are necessary, instead, a pre-processor for input file is developed, and new coefficients and artificial energy mesh structure are considered on the implementation, which has been verified through the improvement of the numerical results of a practical example presented here.
Transport Equation with Nonlocal Velocity in Wasserstein Spaces: Convergence of Numerical Schemes
