An Integral Form of the Variational Nodal Method

Abstract

An integral form of the variational nodal method is formulated, implemented, and tested. The method combines an integral transport treatment of the even-parity flux within the spatial node with an odd-parity spherical harmonics expansion of the Lagrange multipliers at the node interfaces. The response matrices that result from this formulation are compatible with those in the VARIANT code at Argonne National Laboratory. Spatial discretization within each node allows for accurate treatment of homogeneous or heterogeneous node geometries. The integral method is implemented in Cartesian x-y geometry and applied to three benchmark problems. The method’s accuracy is compared to that of the standard spherical harmonic formulation of the variational nodal method, and the CPU and memory requirements of the two approaches are compared and contrasted. In general, for calculations requiring higher-order angular approximations, the integral method yields solutions with comparable accuracy while requiring substantially less CPU time and memory than the spherical harmonics approach.