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In this paper, we present an accurate and robust scaling operator based onmaterial optical thickness (OT) for the least-squares spherical harmonics(LSP$_N$) method for solving neutron transport problems. LSP$_N$ without properscaling is known to be erroneous in highly scattering medium, if the opticalthickness of the material is large. A previously presented scaling developed byManteuffel, et al.\ does improve the accuracy of LSP$_N$, in problems where thematerial is optically thick. With the method, however, essentially no scalingis applied in optically thin materials, which can lead to an erroneous solutionwith presence of highly scattering medium. Another scaling approach, called thereciprocal-removal (RR) scaled LSP$_N$, which is equivalent to the self-adjointangular flux (SAAF) equation, has numerical issues in highly-scatteringmaterials due to a singular weighting. We propose a scaling based on opticalthickness that improves the solution in optically thick media while avoidingthe singularity in the SAAF formulation.

Accurate Least-Squares P$_N$ Scaling based on Problem Optical Thickness for solving Neutron Transport Problems