The finite-element method for multigroup neutron transport: anisotropic scattering in 1-D slab geometry

Proof-tests on 1-D multigroup neutron transport problems are reported for strong anisotropic scattering. These tests have been undertaken as part of the validation of the 3-D multigroup finite-element transport code FELTRAN for anisotropic scattering media. To illustrate the treatment of within-group and intergroup anisotropic scattering in the finite-element method the relevant theory is outlined. Ingroup scattering is checked using the backward-forward-isotropic (BFI) scattering law for source and eigenvalue problems. With this law anisotropic scattering problems can be transformed into equivalent isotropic scattering problems. In this way the well-validated isotropic scattering version of FELTRAN is used to validate the anisotropic version. Intergroup scattering effects are checked by solving few-group source problems for P1 and P3 scattering and the BFI scattering law. For P1 and P3 scattering checks are made with the discrete-ordinate finite-difference code ANISN and the spherical harmonics finite-difference code MARC/PN. For the BFI scattering law comparison is made with two-group exact solutions of Williams (1985) for 1-D systems. (author)