A Rigorous Treatment of Transverse Buckling Effects in Two-Dimensional Neutron Transport Computations

Abstract

The variational formulation of the even-parity form of the within-group neutron transport equation is generalized to include complex trial functions. The introduction of transverse leakage effects through the buckling term exp(iB·r) leads, in general, to a coupled set of Euler equations for the real and imaginary even-parity flux components. The coupling between real and imaginary flux components is retained in both discrete-ordinates and finite element angular approximations. Employment of the spherical harmonics approximations in angle, however, leads to an uncoupled set of Euler equations if an appropriate choice of axes is made. Hence, a rigorous buckling treatment of third-dimensional leakage can be incorporated into two-dimensional transport computations without solving for the imaginary flux component. The foregoing spherical harmonic formulation is combined with finite element discretization in space in the multigroup criticality code FESH. One- and multigroup results are presented to demonstrate the elimination of ray effects and to examine the errors introduced by the DB2 leakage correction used in conventional transport calculations.