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Ougouag, Abderrafi M. Fitzpatrick, William Edward 2011-05-07T12:28:15Z 2011-05-07T12:28:15Z 10000-01-01 1995 A new nodal method for the solution of multigroup multidimensional diffusion problems in hexagonal geometry is developed and implemented into the FORTRAN code HEXPEDITE. The algorithm is adapted for modern computer features including vector and concurrent computations and demonstrates high efficiency and accuracy on many 2-D and 3-D problems. Two procedures consistent with the HEXPEDITE formalism to allow the modeling of mild intranodal heterogeneities due to depletion are outlined. Innovative solution techniques for the time-dependence of the diffusion equations are developed and are coupled to spatial nodal algorithms. In 1-D problems, an analytical solution based on linear and quadratic dependencies over discrete time intervals of the effective source are compared against finite-difference solutions. The quadratic interpolation allows much larger time steps than the other approaches on two problems. A new method, the moment integral method, for multidimensional nodal kinetic problems is introduced. This method solves analytically the time dependence of the flux spatial moments over discrete time intervals. The moment integral method, based on an exponential fit, shows better accuracy at large time steps than a finite-difference solution on 2-D rectangular and hexagonal problems. The completely analytical solution to the transient reactor physics equations is investigated with no approximations further than nodal diffusion theory. A formal solution is shown to be feasible and to be adaptable for a nodal algorithm in a modified form. The telegrapher's equation describing the true wave-like changes in the neutron flux of reactor media is studied. The new semi-analytical kinetic techniques with slight modifications are applied to a multigroup 1-D model. Made available in DSpace on 2011-05-07T12:28:15Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9522109.pdf: 4433192 bytes, checksum: 811973b3481b14e2256177166a4c3dfb (MD5) Previous issue date: 1995 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:41:26Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:17:56-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission ETDs are only available to UIUC Users without author permission U of I Only AAI9522109 (UMI)AAI9522109 http://hdl.handle.net/2142/20083 eng Copyright 1995 Fitzpatrick, William Edward Engineering, Nuclear Computer Science Developments in nodal reactor analysis tools for hexagonal geometry text Nuclear, Plasma, and Radiological Engineering Nuclear Engineering University of Illinois at Urbana-Champaign Dissertation Ph.D.