Nuclear Engineering and Technology

Korean Nuclear Society (한국원자력학회)
권호 표지

A New Acceleration Method of Additive Angular Dependent Rebalance with Extrapolation for Discrete Ordinates Transport Equation

  • Park, Chang-Je (Korea Advanced Institute of Science and Technology) ;
  • Cho, Nam-Zin (Korea Advanced Institute of Science and Technology)
  • Published : 2002.08.01
Download PDF
⟨ Previous Next ⟩

Abstract

A new extrapolation method is developed and applied to the additive angular dependent rebalance (AADR) acceleration for discrete ordinates neutron transport calculations. With this extrapolation, the convergence of AADR solution for distinct discretizations between the high- order and low-order equations is remarkably improved and thus the “inconsistent discretization problem” is resolved. Fourier analysis is also performed to find the optimal extrapolation and weighting parameters, which give the smallest spectral radius. The numerical tests demonstrate that the AADR with extrapolation works well as predicted by the Fourier analysis.

Keywords

References

  1. R.E. Alcouffe, 'Diffusion Synthetic Acceleration Methods for the Diamond-Differenced Discrete-Ordinates Equations,' Nucl. Sci. Eng., 64, 344 (1977) https://doi.org/10.13182/NSE77-1
  2. C.J. Park and N.Z. Cho, 'A Linear Multiple Balance Method with High Order Accuracy for Discrete Ordinates Neutron Transport Equations,' Annals of Nuclear Energy, 28, 1499 (2001) https://doi.org/10.1016/S0306-4549(00)00140-7
  3. C.J. Park and N.Z. Cho, 'Additive Angular Dependent Acceleration Method of the Discrete Ordinates Transport Calculations,' ANS International Meeting on Mathematical Methods for Nuclear Applications (M&C 2001), September 2001, Salt Lake City, U.S.A. (CD-ROM)
  4. N.Z. Cho and C.J. Park, 'An Additive Angular-Dependent Rebalance Method for Neutron Transport Equations,' Trans. Am. Nucl. Soc., 84, 222 (2001)
  5. S.G. Hong and N.Z. Cho, 'A Rebalance Approach to Nonlinear Iteration for Solving the Neutron Transport Equations,' Annals of Nuclear Energy, 24, 147 (1997) https://doi.org/10.1016/0306-4549(96)00054-0
  6. S.G. Hong and N.Z. Cho, 'Angle-Dependent Rebalance Factor Method for Nodal Transport Problems in X-V Geometry,' Trans. Am. Nucl. Soc., 79, 139 (1998)
  7. W.F. Miller, Jr. and E.W. Larsen, 'Modified Diffusion Synthetic Acceleration Algorithms,' Nucl. Sci. Eng., 93, 403 (1986) https://doi.org/10.13182/NSE86-A18475
  8. C.J. Park and N.Z. Cho, 'A New Acceleration Method of Additive Angular Dependent Rebalance with Extrapolation for Discrete Ordinates Transport Equation,' Proceeding of the Korean Nuclear Society Autumn Meeting, October 2001. Suwon (CD-ROM)
  9. W.H. Reed, 'The Effectiveness of Acceleration Techniques for Iterative Methods in Transport Theory,' Nucl. Sci. Eng., 125, 257 (1997) https://doi.org/10.13182/NSE97-A24274
  10. R.E. Alcouffe, et. al., 'DANTSYS: A Diffusion Accelerated Neutral Particle Transport Code System,' LA-12069-M, Los Alamos National Laboratory (1995)