Variational Nodal Methods for Neutron Transport

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Abstract
Nodal diffusion and transport methods are formulated variationally in terms of the even-parity form of the neutron transport equation and applied to problems in X-Y geometry. The resulting functional guarantees the satisfaction of nodal balance, regardless of the form of the space-angle trial function within the node or on its boundaries. Deletion of X-Y cross terms from the within-node flux approximations yields equations that are strikingly similar to conventional diffusion nodal methods; inclusion of the terms obviates ad hoc approximations to the transverse leakage. Transport and diffusion nodal methods differ only in the angular basis functions. In both cases the equations are first solved for partial current moments along nodal interfaces. Subsequently, the detailed flux distribution and the node-averaged scalar flux values are obtained from the spatial trial functions. Results are given for fixed-source two-dimensional problems in the P1 and P3 approximations. Code vectorization and general...