Title: Iterative methods for solving space-time one dimensional multigroup diffusion equations

Authors: Y. Yulianti, Z. Su'ud, A. Waris, S.N. Khotimah

Addresses: Department of Physics, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology (ITB), c/ Campus Jl, Ganesha 10 Bandung, Indonesia. ' Department of Physics, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology (ITB), c/ Campus Jl, Ganesha 10 Bandung, Indonesia. ' Department of Physics, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology (ITB), c/ Campus Jl, Ganesha 10 Bandung, Indonesia. ' Department of Physics, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology (ITB), c/ Campus Jl, Ganesha 10 Bandung, Indonesia

Abstract: The numerical methods of Successive Overrelaxation (SOR), Successive-Line Overrelaxation (SLOR) and Alternating Direction Implicit (ADI) are used in this research to solve space-time one-dimensional diffusion equations. The results of this research have been compared with the ANL-Benchmark Problem BSS-6-A2. In general, the results are in agreement with the Argonne National Laboratory Benchmark Source Situation (BSS-6-A2). However, there is very little difference between SOR and ANL-BSS-6-A2 because of inner iterations in the SOR method. This research shows that the SLOR and ADI methods are more accurate and more efficient than the SOR method in solving space-time diffusion equations. SLOR is the most efficient in the case of a big number of mesh elements; however, the ADI method is the most efficient in the case of a small number of mesh elements.

Keywords: iterative method; successive overrelaxation; SOR; successive-line overrelaxation; SLOR; alternating direction implicit; ADI; space-time diffusion equations; multigroup diffusion equations; mathematical modelling; reactor behaviour; nuclear reactors; nuclear energy; nuclear power; nuclear accidents.

DOI: 10.1504/IJNEST.2010.030553

International Journal of Nuclear Energy Science and Technology, 2010 Vol.5 No.2, pp.114 - 126

Available online: 21 Dec 2009 *

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