Discrete Ordinates Solutions for Highly Forward Peaked Scattering

The limitations of asymptotic methods for numerically solving highly forward peaked scattering (HFPS) problems are reviewed before resorting to a discrete ordinates solution for such problems based on biased angular quadrature formulas to increase the precision of the angular representation and on source evaluation from cell-averaged angular fluxes to reduce memory requirements. Also, a twice-collided source is introduced to avoid numerical representation of singularities in the solution. As an example the propagation and spreading of a collimated particle beam in an HFPS medium has been calculated with a discrete ordinates diamond-differenced numerical solution of the transport equation in two-dimensional curvilinear cylindrical coordinates. The calculation was carried out for a strongly forward peaked Henyey-Greenstein scattering law for which Fokker-Planck asymptotic models are not valid. The results show promise for numerically calculated reference solutions based on accurate spatial representations for checking the accuracy of standard asymptotic models for these types of problems.