Three-dimensional transport with variational nodal methods

The development of the variational nodal method contained in the three-dimensional transport code VARIANT is reviewed. This Argonne National Laboratory code treats two- and three- dimensional multigroup problems with anisotropic scattering in hexagonal and Cartesian geometries. The methodology couples hybrid finite elements in space, which enforce nodal balance, with spherical harmonics expansions in angle. The resulting response matrix equations are solved by red-black or four-color iterations. Several enhancements to VARIANT are discussed: The simplified spherical harmonics option provides near spherical harmonic accuracy for many problems at a fraction of the cost. Adjoint and perturbation calculations are performed without the physical- and mathematical adjoint dichotomy appearing in other nodal methods. Heterogeneous node methods extend the problem classes to which the method may be applied. Computational strategies and trade-offs are discussed and possible future research directions are outlined