Numerical solution of static and spatial kinetics self-adjoint angular flux neutron transport equation
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
This paper elucidates a comprehensive derivation of the variational formulation pertaining to the static and spatial kinetics self-adjoint angular flux (SAAF) neutron transport equation. The methodology employed for discretization of the spatial variable is the finite element method, while the energy group discretization is executed via the group method, and the directional discretization is conducted using the discrete ordinates method. Analytic expressions for the discretization to variable separation under both vacuum and reflective boundary conditions are furnished. Constructed upon the MOOSE framework, a code designated as SAAFCGSN has been developed for the resolution of the SAAF neutron transport equation. The zero-order scattering matrix within this computational framework is managed through an innovative "decoupling" method, thereby enhancing the computational efficiency significantly. The functionality and robustness of the SAAFCGSN code are corroborated through meticulous evaluation involving seven distinct steady-state scenarios as well as two transient states. Empirical outcomes verify the compatibility of the SAAFCGSN code with both structured and unstructured mesh, inclusive of their amalgamations, thus facilitating maintenance and ensuring elevated computational accuracy. In addition, a performance analysis benchmarked against IAEA standards reveals that the adoption of the scattering matrix "decoupling" method propels a computational speed increase exceeding 30 %, signifying a notable advancement in calculation efficiency.
Abstract
This paper elucidates a comprehensive derivation of the variational formulation pertaining to the static and spatial kinetics self-adjoint angular flux (SAAF) neutron transport equation. The methodology employed for discretization of the spatial variable is the finite element method, while the energy group discretization is executed via the group method, and the directional discretization is conducted using the discrete ordinates method. Analytic expressions for the discretization to variable separation under both vacuum and reflective boundary conditions are furnished. Constructed upon the MOOSE framework, a code designated as SAAFCGSN has been developed for the resolution of the SAAF neutron transport equation. The zero-order scattering matrix within this computational framework is managed through an innovative "decoupling" method, thereby enhancing the computational efficiency significantly. The functionality and robustness of the SAAFCGSN code are corroborated through meticulous evaluation involving seven distinct steady-state scenarios as well as two transient states. Empirical outcomes verify the compatibility of the SAAFCGSN code with both structured and unstructured mesh, inclusive of their amalgamations, thus facilitating maintenance and ensuring elevated computational accuracy. In addition, a performance analysis benchmarked against IAEA standards reveals that the adoption of the scattering matrix "decoupling" method propels a computational speed increase exceeding 30 %, signifying a notable advancement in calculation efficiency.
참고문헌 (33)
- Solution of the Transport Equation by Sn ApproximationsLA-1599, "B. G. Carlson", Los Alamos Scientific Laboratory, ~ (1953)
- Brody Bassett, "Meshless local Petrov-Galerkin solution of the neutron transport equation with streamline-upwind Petrov-Galerkin stabilization", J. Comput. Phys, 377, pp.1~73 (2019)
- G. Zhang, "A parallel tetrahedral discontinuous finite element code for the solution of the discrete ordinates neutron transport equation", Ann. Nucl. Energy, 196, pp.110242~ (2024)
- J. A. Welch, "A geometry preserving, conservative, mesh-to-mesh isogeometric interpolation algorithm for spatial adaptivity of the multigroup, second-order even-parity form of the neutron transport equation", J. Comput. Phys, 347, pp.129~146 (2017)
- J. E. Morel, "A self-adjoint angular flux equation", Nucl. Sci. Eng, 132, pp.312~325 (1999)
- G. C. Pomraning, "The variational method applied to the monoenergetic Boltzmann equation. Part II", Nucl. Sci. Eng, 16, pp.155~ (1963)
- R. T. Ackroyd, "Least-squares derivation of extremum and weighted-residual methods for equations of reactor physics", Ann. Nucl. Energy, 10, pp.65~ (1983)
- Jennifer Liscum-Powell, "Finite Element Numerical Solution of a Self-Adjoint Transport Equation for Coupled Electron-Photon problems", pp.2000
- L. Cao, "Simplified spherical harmonics method for self-adjoint angular flux transport equation in unstructured geometry", Nucl. Power Eng, 27(3), pp.6~10 (2006)
- Q. Ye, "Spherical harmonics method for neutron transport equation in twodimensional cylindrical(R-Z)geometry", Nucl. Power Eng, 29(4), pp.19~23 (2008)
- Schunert Sebastian, "A new mathematical adjoint for the modified SAAF-SN equations", Ann. Nucl. Energy, 75, pp.340~352 (2015)
- Y. Wang, "Convergence study of Rattlesnake solutions for the two-dimensional C5G7 MOX benchmark", ANS MC2015 -International Conference on Mathematics and Computation (M&C), Supercomputing in Nuclear Applications (SNA) and the Monte Carlo (MC) Method (2015)
- Rattlesnake Theory Manual, "Y. Wang", Idaho National Laboratory, ~ (2018)
- C. Latimer, "A geometry conforming isogeometric method for the self-adjoint angular flux(SAAF)form of the neutron transport equation with a discrete ordinate(SN)angular discretization", Ann. Nucl. Energy, 136, pp.1~16 (2020)
- A. Sood, "Analytical benchmark test set for criticality code verification", Prog. Nucl. Energy, 42(1), pp.55~106 (2003)
- J. G. Issa, "3-Dimensions and R-Z Problems", Prog. Nucl. Energy, 18(1–2), pp.251~264 (1986)
- Z. Zheng, "Coupled PN-DPN method for solving the neutron transport equation of planar geometry", Nucl. Power Eng, 31(S2), pp.29~33 (2010)
- Y. Hirao, "Development of a connection-method calculation utility for the DORT–TORT code", Radiat. Protect. Dosim, 116(1–4), pp.19~23 (2005)
- "Calculation of four thermal reactor benchmark problems in X-Y geometry, EPRI NP-2855" (1983)[URL]
- L. Deng, "Multigroup Monte Carlo calculation coupled of transport and burnup", Chin. J. Comput. Phys, 20(1), pp.65~70 (2003)
- H. Wu, "Transmission probability method based on triangle meshes for solving unstructured geometry neutron transport problem", Nucl. Eng. Des, 237(1), pp.28~37 (2007)
- L. Deng, "MCMG : a 3-D multigroup P3 Monte Carlo code and its benchmarks", J. Nucl. Sci. Technol, 37(7), pp.608~614 (2000)
- S. G. Hong, "CRX : a code for rectangular and hexagonal lattices based on the method of characteristics", Ann. Nucl. Energy, 25(8), pp.547~565 (1998)
- Paul K. Romano, "OpenMC : a state-of-the-art Monte Carlo code for research and development", Ann. Nucl. Energy, 82, pp.90~97 (2015)
- A User Guide for DRAGON 3.06, Report IGE-174Rev. 7, "G. Marleau", Institut de g´enie nucl´eaire, Ecole ´ Polytechnique de Montr´eal, ~ (2008)
- X. Yang, "MOCUM : a two-dimensional method of characteristics code based on constructive solid geometry and unstructured meshing for general geometries", Ann. Nucl. Energy, 46, pp.20~28 (2012)
- T. Mazumdar, "Solution of neutron transport equation by Method of Characteristics", Ann. Nucl. Energy, 77, pp.522~535 (2015)
- Toshikazu Takeda, "3-D neutron transport benchmarks", J. Nucl. Sci. Technol, 28(7), pp.656~669 (1991)
- Benchmark Problem Book, "Arogonne Code Center", Argonne National Laboratory, ~, pp.ANL-7416, Supplement No. 3 (1985)
- Rattlesnake: User Manual, "Y. Wang", Idaho National Laboratory, ~, pp.Technical Report INL (2015), EXT-15-37337
- Deterministic Time-dependent Neutron Transport Benchmark without Spatial Homogenization(C5G7-TD), "V. Boyarinov", Nuclear Energy Agency Organisation for Economic Co-operation and Development, ~ (2016)
- Q. Shen, "Transient analysis of C5G7-TD benchmark with MPACT", Ann. Nucl. Energy, 125, pp.107~120 (2019)
- Preliminary Results for the OECD, "NEA Time Dependent Benchmark Using Rattlesnake, Rattlesnake-IQS and TDKENO", M. D. DeHart, 2016, Technical Report INL[DOI]