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A theoretical study on a convergence problem of nodal methods

Conference ·
OSTI ID:22039702
;  [1];  [2]
  1. Shanghai Jiao Tong Univ., 1954 Hua Shan Road, Shanghai, 200030 (China)
  2. Westinghouse Electric Company, P. O. Box 355, Pittsburgh, PA 15230-0355 (United States)

The effectiveness of modern nodal methods is largely due to its use of the information from the analytical flux solution inside a homogeneous node. As a result, the nodal coupling coefficients depend explicitly or implicitly on the evolving Eigen-value of a problem during its solution iteration process. This poses an inherently non-linear matrix Eigen-value iteration problem. This paper points out analytically that, whenever the half wave length of an evolving node interior analytic solution becomes smaller than the size of that node, this non-linear iteration problem can become inherently unstable and theoretically can always be non-convergent or converge to higher order harmonics. This phenomenon is confirmed, demonstrated and analyzed via the simplest 1-D problem solved by the simplest analytic nodal method, the Analytic Coarse Mesh Finite Difference (ACMFD, [1]) method. (authors)

Research Organization:
American Nuclear Society, 555 North Kensington Avenue, La Grange Park, IL 60526 (United States)
OSTI ID:
22039702
Country of Publication:
United States
Language:
English