Homogeneity and Isotropy Restoration Theory for Derivation of Multigroup Transport Equations

In this paper, we propose a new way of deriving multigroup transport equation that maintains angle independence in the total cross section and homogeneity in the material region (originally each material region is usually homogeneous). As a byproduct, only isotropic scattering term remains, which also relieves the computational burden significantly. In this Homogeneity and Isotropy REstoration (HIRE) theory, we introduce a discontinuity factor in the form of partial current discontinuity factor (PCDF) at material interface. The homogeneity and isotropy restoration (HIRE) theory described in this paper removes the angle dependency of the group condensed total cross section in the multigroup transport equation. For a pin-cell problem with all reflective boundary conditions, the method has been successfully tested. It is noted again that the multigroup transport equation thus derived can be solved by a deterministic method well-known in the literature or by a simple MC method