Nuclear Engineering and Technology

  • 제55권4호
  • /
  • Pages.1428-1438
  • /
  • 2023
  • /
  • 1738-5733(pISSN)
  • /
  • 2234-358X(eISSN)
한국원자력학회 (Korean Nuclear Society)
권호 표지
DOI QR코드

DOI QR Code

A hybrid neutronics method with novel fission diffusion synthetic acceleration for criticality calculations

  • Jiahao Chen (North Carolina State University, Department of Nuclear Engineering) ;
  • Jason Hou (North Carolina State University, Department of Nuclear Engineering) ;
  • Kostadin Ivanov (North Carolina State University, Department of Nuclear Engineering)
  • 투고 : 2022.11.12
  • 심사 : 2022.12.17
  • 발행 : 2023.04.25
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

A novel Fission Diffusion Synthetic Acceleration (FDSA) method is developed and implemented as a part of a hybrid neutronics method for source convergence acceleration and variance reduction in Monte Carlo (MC) criticality calculations. The acceleration of the MC calculation stems from constructing a synthetic operator and solving a low-order problem using information obtained from previous MC calculations. By applying the P1 approximation, two correction terms, one for the scalar flux and the other for the current, can be solved in the low-order problem and applied to the transport solution. A variety of one-dimensional (1-D) and two-dimensional (2-D) numerical tests are constructed to demonstrate the performance of FDSA in comparison with the standalone MC method and the coupled MC and Coarse Mesh Finite Difference (MC-CMFD) method on both intended purposes. The comparison results show that the acceleration by a factor of 3-10 can be expected for source convergence and the reduction in MC variance is comparable to CMFD in both slab and full core geometries, although the effectiveness of such hybrid methods is limited to systems with small dominance ratios.

키워드

참고문헌

  1. T.J. Urbatsch, Iterative Acceleration Methods for Monte Carlo and Deterministic Criticality Calculations," LA-13052-T, Los Alamos National Lab., Los Alamos, NM (United States), 1995.
  2. F.B. Brown, S.E. Carney, B.C. Kiedrowski, W.R. Martin, Fission Matrix Capability for MCNP, Part I-Theory," M&C 2013 Conference, ID, Sun Valley, 2013.
  3. S. Carney, F. Brown, B. Kiedrowski, W. Martin, Theory and applications of the fission matrix method for continuous-energy Monte Carlo, Annals of Nuclear Energy 73 (2014) 423.
  4. J.C. Wagner, A. Haghighat, Automated variance reduction of Monte Carlo shielding calculations using the discrete ordinates adjoint function, Nuclear Science and Engineering 128 (2) (1998) 186.
  5. J.C. Wagner, D.E. Peplow, S.W. Mosher, FW-CADIS method for global and regional variance reduction of Monte Carlo radiation transport calculations, Nuclear Science and Engineering 176 (1) (2014) 37.
  6. K.S. Smith, Nodal method storage reduction by nonlinear iteration, Transactions of the American Nuclear Society (1983) 44.
  7. D.Y. Anistratov, V.Y. Gol'Din, Nonlinear methods for solving particle transport problems, Transport Theory and Statistical Physics 22 (2-3) (1993) 125.
  8. M.-J. Lee, H.G. Joo, D. Lee, K. Smith, Investigation of CMFD accelerated Monte Carlo eigenvalue calculation with simplified low dimensional multigroup formulation, Proc. PHYSOR (2010) 9-14, 2010.
  9. M.J. Lee, H.G. Joo, D. Lee, K. Smith, Coarse mesh finite difference formulation for accelerated Monte Carlo eigenvalue calculation, Annals of Nuclear Energy 65 (2014) 101.
  10. S. Yun, N.Z. Cho, Acceleration of source convergence in Monte Carlo k-eigenvalue problems via anchoring with a p-CMFD deterministic method, Annals of Nuclear Energy 37 (12) (2010) 1649.
  11. E.W. Larsen, J. Yang, A functional Monte Carlo method for k-eigenvalue problems, Nuclear Science and Engineering 159 (2) (2008) 107.
  12. H. Dong, M. Ravishankar, P. Sathre, M.B. Sullivan, W. Taitano, J. Willert, T. Germann, D. Knoll, B. Lally, P. McCormick, et al., Quasi Diffusion Accelerated Monte Carlo, Los Alamos National Laboratory, 2011.
  13. E.R. Wolters, E.W. Larsen, W.R. Martin, Generalized Hybrid Monte Carlo-CMFD Methods for Fission Source Convergence, 2011.
  14. R.E. Alcouffe, Diffusion synthetic acceleration methods for the diamond-differenced discrete-ordinates equations, Nuclear Science and Engineering 64 (2) (1977) 344.
  15. E.W. Larsen, Unconditionally stable diffusion-synthetic acceleration methods for the slab geometry discrete ordinates equations. Part I: Theory, Nuclear Science and Engineering 82 (1) (1982) 47.
  16. J. Chen, J. Hou, K. Ivanov, A hybrid Monte Carlo method for k-eigenvalue problem, in: The International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M&C 2023), vols. 220-229, Citeseer, 2021.
  17. J. Chen, A Novel Fission Diffusion Synthetic Acceleration Method for Criticality Calculations,, PhD Thesis, North Carolina State University, 2014.
  18. R. Haberman, Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, Pearson Higher, 2012.
  19. A. Hebert, Applied Reactor Physics, Presses inter Polytechnique, 2009.
  20. B.R. Herman, Monte Carlo and Thermal Hydraulic Coupling Using Low-Order Nonlinear Diffusion Acceleration,, PhD Thesis, Massachusetts Institute of Technology, 2014.
  21. P.K. Romano, N.E. Horelik, B.R. Herman, A.G. Nelson, B. Forget, K. Smith, OpenMC: a state-of-the-art Monte Carlo code for research and development, Annals of Nuclear Energy 82 (2015) 90.
  22. E. Lewis, M. Smith, N. Tsoulfanidis, G. Palmiotti, T. Taiwo, R. Blomquist, Benchmark specification for Deterministic 2-D/3-D MOX fuel assembly transport calculations without spatial homogenization (C5G7 MOX), NEA/NSC 280 (2001) 2001.
  23. F.B. Brown, On the Use of Shannon Entropy of the Fission Distribution for Assessing Convergence of Monte Carlo Criticality Calculations," ANS Topical Meeting on Reactor Physics (PHYSOR 2006), Canadian Nuclear Society, Canada, 2006.
  24. F.B. Brown, A Review of Best Practices for Monte Carlo Criticality Calculations, 2009.
  25. J. Park, P. Zhang, H. Lee, S. Choi, J. Yu, D. Lee, Performance evaluation of CMFD on inter-cycle correlation reduction of Monte Carlo simulation, Computer Physics Communications 235 (2019) 111.