skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Extension of modified power method to two-dimensional problems

Abstract

In this study, the generalized modified power method was extended to two-dimensional problems. A direct application of the method to two-dimensional problems was shown to be unstable when the number of requested eigenmodes is larger than a certain problem dependent number. The root cause of this instability has been identified as the degeneracy of the transfer matrix. In order to resolve this instability, the number of sub-regions for the transfer matrix was increased to be larger than the number of requested eigenmodes; and a new transfer matrix was introduced accordingly which can be calculated by the least square method. The stability of the new method has been successfully demonstrated with a neutron diffusion eigenvalue problem and the 2D C5G7 benchmark problem. - Graphical abstract:.

Authors:
 [1];  [2];  [3];  [3]
  1. School of Power and Mechanical Engineering, Wuhan University, Bayilu 299, Wuchang Dist., Wuhan, Hubei, 430072 (China)
  2. (Korea, Republic of)
  3. Ulsan National Institute of Science and Technology, 50 UNIST-gil, Ulsan 44919 (Korea, Republic of)
Publication Date:
OSTI Identifier:
22572344
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 320; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BENCHMARKS; EIGENVALUES; INSTABILITY; LEAST SQUARE FIT; MATRICES; NEUTRON DIFFUSION EQUATION; NEUTRONS; STABILITY; TWO-DIMENSIONAL CALCULATIONS

Citation Formats

Zhang, Peng, Ulsan National Institute of Science and Technology, 50 UNIST-gil, Ulsan 44919, Lee, Hyunsuk, and Lee, Deokjung, E-mail: deokjung@unist.ac.kr. Extension of modified power method to two-dimensional problems. United States: N. p., 2016. Web. doi:10.1016/J.JCP.2016.05.024.
Zhang, Peng, Ulsan National Institute of Science and Technology, 50 UNIST-gil, Ulsan 44919, Lee, Hyunsuk, & Lee, Deokjung, E-mail: deokjung@unist.ac.kr. Extension of modified power method to two-dimensional problems. United States. doi:10.1016/J.JCP.2016.05.024.
Zhang, Peng, Ulsan National Institute of Science and Technology, 50 UNIST-gil, Ulsan 44919, Lee, Hyunsuk, and Lee, Deokjung, E-mail: deokjung@unist.ac.kr. 2016. "Extension of modified power method to two-dimensional problems". United States. doi:10.1016/J.JCP.2016.05.024.
@article{osti_22572344,
title = {Extension of modified power method to two-dimensional problems},
author = {Zhang, Peng and Ulsan National Institute of Science and Technology, 50 UNIST-gil, Ulsan 44919 and Lee, Hyunsuk and Lee, Deokjung, E-mail: deokjung@unist.ac.kr},
abstractNote = {In this study, the generalized modified power method was extended to two-dimensional problems. A direct application of the method to two-dimensional problems was shown to be unstable when the number of requested eigenmodes is larger than a certain problem dependent number. The root cause of this instability has been identified as the degeneracy of the transfer matrix. In order to resolve this instability, the number of sub-regions for the transfer matrix was increased to be larger than the number of requested eigenmodes; and a new transfer matrix was introduced accordingly which can be calculated by the least square method. The stability of the new method has been successfully demonstrated with a neutron diffusion eigenvalue problem and the 2D C5G7 benchmark problem. - Graphical abstract:.},
doi = {10.1016/J.JCP.2016.05.024},
journal = {Journal of Computational Physics},
number = ,
volume = 320,
place = {United States},
year = 2016,
month = 9
}
  • The analytic function expansion nodal (AFEN) method has been successfully applied to two-group neutron diffusion problems. However, the current AFEN method cannot treat complex eigenmodes, which appear in the general multigroup equations. The AFEN method is extended such that complex eigenmodes are treated within the framework of the original AFEN method for any type of geometry. Also, a suite of new nodal codes based on the extended AFEN theory is developed for hexagonal-z geometry and applied to several benchmark problems. Numerical results obtained attest to their accuracy and applicability to practical problems.
  • The variable-flux-weighting method has been shown to largely eliminate numerical diffusion at saturation discontinuities in two-phase flow in two-dimensional problems. The method has been extended to multidimensional problems including gravity and capillarity. The method is derived from fractional flow theory and involves the computation of a variable weighting factor for the interface fractional flow between grid blocks. In order to eliminate numerical diffusion at shocks, the appropriate weighting has been found to be downstream weighting just ahead of the shock and upstream weighting otherwise. In one-dimension, the saturation distribution for two-phase flow including gravity has been solved and compared withmore » the analytical solution. The comparison is very good with no numerical diffusion apparent at the saturation discontinuity. Problems including capillarity have also been solved. In this case there is no saturation discontinuity, but the method introduces downstream weighting at the upstream edge of the capillary fringe which effectively eliminates any significant numerical diffusion. Two- and three-dimensional problems have also been solved which demonstrate the accuracy of the method. For three-dimensional problems, the current implementation of the VFW method is ten times slower than an upstream-weighting IMPES method.« less
  • An extension to 1D relativistic hydrodynamics of the piecewise parabolic method (PPM) of Colella and Woodward using an exact relativistic Riemann solver is presented. Results of several tests involving ultrarelativistic flows, strong shocks and interacting dis- continuities are shown. A comparison with Godunov`s method demonstrates that the main features of PPM are retained in our relativistic version.
  • We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition (SLC) is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear and polynomial time convergence properties, while achieving practical performance. It either successfully solves the problem, or concludes that the SLC is not satisfied. When compared with the mature software package MOSEK (barrier solver version 6.0.0.106), iOptimize solves convex quadraticmore » programming problems, convex quadratically constrained quadratic programming problems, and general convex programming problems in fewer iterations. Moreover, several problems for which MOSEK fails are solved to optimality. In addition, we also find that iOptimize detects infeasibility more reliably than the general nonlinear solvers Ipopt (version 3.9.2) and Knitro (version 8.0).« less