On the relevance of the scattering anisotropy for a low order transport method

The present paper is concerned with the extension of the treatment of the scattering anisotropy developed in the AN-SPN (or simply AN) method up to the approximation of the second order. To assess such extension, two 3D examples are considered: the first one is an axial piece of a 17×17 PWR MOX assembly containing the heads of control rods; while the second example is related to a 3D reactor core containing UO2 and MOX homogenized assemblies. It is shown that the passage from the isotropic to the linearly anisotropic approximation of the differential scattering cross section turns out into a remarkable improvement of the results, as regards the multiplication factor as well as the flux distribution. For the kind of problems like those here considered, less important is, on the contrary, the extension to the second order of the anisotropy, although such an upgrade may be included in the calculation with only an almost negligible effort, owing to the irrelevant impact on the computing time.