Interface Angular Coupling Reductions in Variational Nodal Methods for Neutron Transport

Variational nodal methods for neutron transport are modified to reduce the angular coupling between spatial nodes without a commensurate loss of accuracy. In both one and two dimensions, the interface conditions of the variational principle allow near P_n accuracy to be obtained with only P_n−2 interface coupling. As a result, the dimension of the nodal response matrix is reduced by a factor of 2, and the number of arithmetic operations required for solution by a factor of 4. In the small spatial mesh limit, the resulting P_{n, n−2} approximation retains accuracy near the P_n approximation used within the node rather than reverting to the P_n−2 interface approximation. Two-dimensional P_3,1 transport calculations demonstrate that the variational nodal approximations are not subject to the flux depression suffered by other interface current nodal transport methods in problems dominated by streaming diagonal to the coordinate directions.