A multilevel acceleration method for the multigroup SP(3) approximation to the neutron transport equation
Abstract
The factors introducing error in the solution of the Boltzmann transport equation, such as spatial discretization, spatial homogenization, group collapsing, and transport, are qualitatively and quantitatively evaluated for solution of core neutronics problems in static and transient LWRs. In order to minimize these errors, the multigroup transport equation for heterogeneous core configurations is formulated within a framework of a multi-level acceleration which enhances the computational efficiency for both eigenvalue and fixed source problems. The simplified P3 approximation (SP3) is used as a transport solver because of its favorable characteristics in terms of accuracy and computing time. The heterogeneous configuration with pin-homogenized cross sections is also adopted to minimize the spatial homogenization error and improve estimates of pin powers. In order to provide flexibility on the choice of method for adaptive methods, the multigroup nodal expansion method for SP3 has also been developed within a framework of the “one-node” scheme. The homogeneous and heterogeneous, diffusion and SP3 methods are implemented at a time using an adaptive method, which enables the use of solvers with different levels of complexity in the same core calculation. The work here is verified for steady-state and transient calculations using the OECD L336 benchmark and the modified KAIST benchmark problems which have multigroup pin-homogenized cross sections. The results show that the multi-level (global/local) acceleration method for the SP3 approximation is successful in the steady-state and transient conditions in terms of accuracy and computation time. In addition, the nodal expansion method for SP 3 turned out to be somewhat efficient at relatively mild change of neutron spectrum, and the adaptive method has been tested and shown to provide good performance for practical range of conditions.
Degree
Ph.D.
Advisors
Downar, Purdue University.
Subject Area
Nuclear physics
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