Application of Walsh Functions to Neutron Transport Problems—I. Theory

An approximation to the neutron transport equation is made by representing the angular flux with an expansion of the angular dependence in the orthogonal, complete, and binary valued sets of Walsh function. The Walsh approximation is applied to the one-speed, isotropic-scattering, rectangular-geometry form of the neutron transport equation. Sets of partial differential equations for the expansion coefficients are derived along with appropriate boundary conditions for their solution. The sets of equations and boundary conditions resulting from the application of the Walsh expansion to one-and two-dimensional forms of the transport equation are also obtained. The two-dimensional expansion coefficient equations are shown to be not only hyperbolic but also transformable to a set of S_N-like equations that are coupled only through the scattering term. Such transformal sets of equations are termed Walsh-derived quadrature sets.