Variational techniques for reactor physics calculations of heterogeneous reactor cores. Final report for April 15, 1993--April 14, 1995

Abstract

Variational coarse mesh techniques are developed for the solution of the one group neutron transport equation in one-dimensional reactor lattices. In contrast to conventional nodal lattice applications which discretize diffusion theory and use node homogenized cross sections, the authors retain the spatial dependence of the cross sections and instead employ an alternative flux representation. The initial form of this flux representation (trial function) for the angular flux was inspired by the leading order solution in the asymptotic expansion of the angular flux--namely, the slow modulation of a periodic pin cell flux. The authors called the variational technique based on this form of trial function the Spectral Element Asymptotic Method (SEAM); it is capable of achieving order of magnitude reductions of eigenvalue and pointwise scalar flux errors as compared with diffusion theory. A different trial function can be developed based on the leading order and first order correction terms in the asymptotic expansion of the angular flux. SuperSEAM, the method based on this new trial function, allows the neutron transport equation to be cast into a form whose solution has much slower spatial variation than the SEAM solution; thus, the SuperSEAM result can be accurately described with fewer variables. SuperSEAM is therefore capable of achieving the same high degree of accuracy as SEAM at a cost comparable with homogenized nodal diffusion theory.