A new spectral nodal method based on Larsen’s extended diamond approach

In this article, we describe a new spectral nodal method for solving discrete ordinates (SN) neutron transport problems with anisotropic scattering for arbitrary order N of angular quadrature. The key to our new spectral nodal method is a consistent derivation of nonstandard auxiliary equations that relate angular neutron fluxes only in the upwind directions. These nonstandard equations are angularly coupled extensions of very basic auxiliary equations proposed by Edward W. Larsen in his extended diamond scheme of solving S2 problems in the presence of scattering and free from spatial truncation error. The resulting method here is also free from spatial truncation error and, in contrast to previously developed spectral nodal methods, it is compatible with an efficient use of iteration on the scattering source and is free from the storage of cell-edge angular fluxes.