An analytical nodal method for solving the SN transport equation in 2-D Cartesian geometry

Abstract

A novel Analytical Nodal Discrete Ordinates (ANDO) method for the solution of the discrete ordinates (SN) neutron transport equation in Cartesian geometry with isotropic scattering and constant neutron source is presented. A nodal method approximates the multi-dimensional transport equation as a system of coupled one-dimensional transport equations along each coordinate axis through transverse integration. The resulting transverse-integrated equations are then solved separately using a one-dimensional solution technique. The one-dimensional solution utilized in the new ANDO method is based on a recent closed-form analytical solution in slab geometry (WANG and BYAMBAAKHUU, 2017). The novel solution approach allows for a compact closed-form solution on each computational cell. Results for constant and linear transverse leakage approximations are presented. The ANDO method possesses a number of favorable properties, demonstrated with numerical results, such as high accuracy, rapid convergence, asymptotic preserving, positivity preserving, near linear computational complexity, and local-hp adaptivity. The ANDO method can also be easily extended to higher-order transverse leakage approximations, to three-dimensional Cartesian geometry, and to multi-group.