Buckled spherical harmonics solutions of neutron transport problems

The within-group even-parity neutron transport equation is formulated with complex angular and spatial trial functions and with a complex buckling approximation. Three angular trial functions are compared; finite elements, discrete ordinates, and complex spherical harmonics. When discrete ordinates or finite element basis functions are applied, the differential equations for the real and imaginary parts of the even-parity flux are coupled by the buckling vector. The spherical harmonics equations for the real and imaginary parts of the even-parity flux, however, uncouple when one particular transverse buckling direction is chosen for a two-dimensional problem. Bilinear rectangular finite elements are applied to the spatial variable, the buckled spherical harmonics angular treatment is generalized to arbitrary order, and the resulting formulation is incorporated into a multigroup formalism using a lumped source approximation. The finite element/buckled spherical harmonics multigroup neutron transport code, FESH, has been developed from these approximations, and treats either fixed source problems or criticality eigenvalue problems. The applicability of this method to problems with several thousand spatial nodes has been demonstrated by comparison of numerical results with another spherical harmonics code and with other computational methods. Buckled two-dimensional eigenvalue calculations reveal substantial improvements over the DB2 buckling method when transverse transport effects are important