Numerical study of scattering Legendre moments and effect of anisotropic scattering on SN shielding calculation

In neutron and photon transport problems, anisotropic scattering is of great importance for the particle flux, especially when the angular flux has a strong forward peak in shielding analyses. The conventional Legendre expansion is widely used in discrete ordinates transport codes because of algebraic simplifications with spherical harmonics for the scattering source. However, negative cross sections caused by the finitely truncated expansion may give rise to a negative source and flux. A simple method is adopted, based on integrating functions of scattering moments, to evaluate anisotropy and convergence of expanded functions. A series of problems were designed with angular fluxes of different anisotropy, and numerical simulations were performed using the ARES transport code to study different treatments and algorithms for scattering. Results show that the diagonal transport approximation is more stable and obtains a similar accuracy with the extended approximation. A conservative fix-up for the negative source could ensure particle balance and improve computational accuracy significantly for photon transport. The effect of anisotropic scattering is problem-dependent, and no distinct differences among various methods are observed for volume source problems with a continuous energy source. For beam source problems, flux results are sensitive to negative scattering functions, and strictly nonnegative cross sections need to be implemented.