A finite subelement generalization of the variational nodal method

The variational nodal method is generalized by dividing each spatial node into a number of triangular finite elements designated as subelements. The finite subelement trial functions allow for explicit geometry representations within each node, thus eliminating the need for nodal homogenization. The method is implemented within the Argonne National Laboratory code VARIANT and applied to two-dimensional multigroup problems. Eigenvalue and pin-power results are presented for a four-assembly Organization for Economic Cooperation and Development/Nuclear Energy Agency benchmark problem containing enriched UO₂ and mixed oxide fuel pins. Our seven-group model combines spherical or simplified spherical harmonic approximations in angle with isoparametric linear or quadratic subelement basis functions, thus eliminating the need for fuel-coolant homogenization. Comparisons with reference seven-group Monte Carlo solutions indicate that in the absence of pin-cell homogenization, high-order angular approximations are required to obtain accurate eigenvalues, while the results are substantially less sensitive to the refinement of the finite subelement grids.