Theoretical Convergence Rate Lower Bounds for Variants of Coarse Mesh Finite Difference to Accelerate Neutron Transport Calculations

References

• S. PALMTAG et al., “Coupled Neutronics and Thermal-Hydraulic Solution of a Full Core PWR Using VERA-CS,” Proc. Int. Topl. Mtg. Advances in Reactor Physics (PHYSOR), Kyoto, Japan, 2014.
   Google Scholar
• A. ZHU et al., “A Multilevel Quasi-Static Kinetics Method for Pin-Resolved Transport Transient Reactor Analysis,” Nucl. Sci. Eng., 182, 4, 435 (2016); http://dx.doi.org/10.13182/NSE15-39.
   Web of Science ®Google Scholar
• A. ZHU et al., “Stability Analysis of the Backward Euler Time Discretization for the Pin-Resolved Transport Transient Reactor,” Ann. Nucl. Energy, 87, 2, 252 (2016); http://dx.doi.org/10.1016/j.anucene.2015.09.004.
   Web of Science ®Google Scholar
• M. ADAMS and E. LARSEN, “Fast Iterative Methods for Discrete Ordinates Particle Transport Calculations,” Prog. Nucl. Energy, 40, 3 (2002); http://dx.doi.org/10.1016/S0149-1970(01)00023-3.
   Google Scholar
• L. LI, “A Low Order Acceleration Scheme for Solving the Neutron Transport Equation,” Masters Dissertation, Massachusetts Institute of Technology (2013).
   Google Scholar
• K. SMITH, “Nodal Method Storage Reduction by Nonlinear Iteration,” Trans. Am. Nucl. Soc., 44, 265 (1983).
   Google Scholar
• T. DOWNAR, Y. XU, and V. SEKER, “PARCS V3.0 U.S. NRC Core Neutronics Simulator User/Theory Manual,” University of Michigan Department of Nuclear Engineering and Radiological Sciences, Ann Arbor, Michigan (2009).
   Google Scholar
• MPACT TEAM, “MPACT Theory Manual, Version 1.0,” University of Michigan, Ann Arbor, Michigan ( Oct. 2013).
   Google Scholar
• A. ZHU et al., “Transient Methods for Pin-Resolved Whole Core Transport Using the 2D-1D Methodology in MPACT,” Proc. M&C 2015, Nashville, Tennessee, April 19–23, 2015, American Nuclear Society (2015).
   Google Scholar
• J. CHO et al., “Transient Capability for a MOC-Based Whole Core Transport Code DeCART,” Trans. Am. Nucl. Soc., 92, 721 (2005).
   Google Scholar
• S. SHANER, B. FORGET, and K. SMITH, “Sensitivity Analysis and Performance of the Adiabatic, Theta, and Multigrid Amplitude Function Kinetics Methods in 2D MOC Neutron Transport,” Proc. M&C 2013, Sun Valley, Idaho, May 5–9, 2013, American Nuclear Society (2013).
   Google Scholar
• M. JARRETT et al., “Stabilization Methods for CMFD Acceleration,” Proc. M&C 2015, Nashville, Tennessee, April 19–23, American Nuclear Society (2015).
   Google Scholar
• K. KEADY and E. LARSEN, “Stability of SN K-Eigenvalue Iterations Using CMFD Acceleration,” Proc. M&C 2015, Nashville, Tennessee, April 19–23, American Nuclear Society (2015).
   Google Scholar
• D. LEE, T. DOWNAR, and Y. KIM, “Convergence Analysis of the Nonlinear Coarse-Mesh Finite Difference Method for One-Dimensional Fixed-Source Neutron Diffusion Problem,” Nucl. Sci. Eng., 147, 127 (2004); http://dx.doi.org/10.13182/NSE03-64.
   Google Scholar
• S. HONG, K. KIM, and J. SONG, “Fourier Convergence Analysis of the Rebalance Methods for Discrete Ordinates Transport Equations in Eigenvalue Problems,” Nucl. Sci. Eng., 164, 33 (2010); http://dx.doi.org/10.13182/NSE09-18.
   Google Scholar
• N. CHO et al., “Partial Current-Based CMFD Acceleration of the 2D/1D Fusion Method for 3D Whole-Core Transport Calculations,” Trans. Am. Nucl. Soc., 88, 594 (2003).
   Google Scholar
• N. CHO “Partial Current-Based CMFD (P-CMFD) Method Revisited,” Trans. Korea Nucl. Soc. Autumn Meeting, Gyeongju, Korea, October 25–26, 2012.
   Google Scholar
• M. JARRETT et al., “Analysis of Stabilization Techniques for CMFD Acceleration of Neutron Transport Problems,” Nucl. Sci. Eng., 184, 2, 208 (2016); http://dx.doi.org/10.13182/NSE16-51.
   Web of Science ®Google Scholar
• A. ZHU et al., “An Optimally Diffusive Coarse Mesh Finite Difference Method to Accelerate Neutron Transport Calculations,” Ann. Nucl. Energy, 95, 116 (2016); http://dx.doi.org/10.1016/j.anucene.2016.05.004.
   Google Scholar
• A. YAMAMOTO, “Generalized Coarse-Mesh Rebalance Method for Acceleration of Neutron Transport Calculations,” Nucl. Sci. Eng., 151, 3, 274 (2005); http://dx.doi.org/10.13182/NSE151-274.
   Web of Science ®Google Scholar
• L. LI, “Techniques for Stabilizing Coarse-Mesh Finite Difference (CMFD) in Methods of Characteristics (MOC),” Proc. M&C 2015, Nashville, Tennessee, April 19–23, American Nuclear Society (2015).
   Google Scholar