A new and rigorous SPN theory for piecewise homogeneous regions

This new SPN theory is valid for the multi-group case as well and can be generalized to the case of anisotropic scattering. It may be a good candidate for practical applications to 3D pin-cell meshed whole core calculations, if the pin-cell meshes can be properly homogenized. The new interface and boundary conditions can be implemented in conventional SPN codes but require more work to revise the coupling equations, resulting in new SPN nodal equations. The discontinuity factors needed for using homogenized meshes can be generated without ambiguity by using the particular SPN angular flux solution as well. A physical interpretation for the SPN theory is suggested. It is believed that the missing steps are now filled to have a sound and complete SPN theory.