Spectral element lattice calculations based on an asymptotic flux representation.

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, we 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. We called the variational technique based on this form of trial function the Spectral Element Asymptotic Method (SEAM) and demonstrated it to be capable of achieving order of magnitude reductions of eigenvalue and pointwise scalar flux errors as compared with diffusion theory. In spite of SEAM's accuracy, we later determined the SEAM trial function to be an inefficient flux representation and developed a new trial function based on the leading order and first order correction terms in the asymptotic expansion of the angular flux. SuperSEAM, the method based on the new trial function, allowed the neutron transport equation to be cast into a form whose solution had much slower spatial variation than the SEAM solution; thus, the SuperSEAM result could be accurately described with fewer variables. SuperSEAM proved capable of achieving the same high degree of accuracy as SEAM at a cost comparable with homogenized nodal diffusion theory.Ph.D.Nuclear EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/104722/1/9542985.pdfDescription of 9542985.pdf : Restricted to UM users only