The extension of the 2-D finite element/boundary element hybrid method to general multigroup neutron diffusion theory
-
B. Ozgener
Abstract
The finite element-boundary element hybrid method developed previously for reflected systems and restricted to one or two group neutron diffusion theory has been extended to the general multigroup neutron diffusion theory by using the boundary integral equation of multigroup neutron diffusion theory. A linear or bilinear 2-D FEM formulation in the core combined with a 2-D linear BEM formulation in the reflector constitute the basic discretization procedure. Use of the boundary integral equation of multigroup diffusion theory transforms all group-to-group scattering domain integrals into surface integrals in the reflector. Hence the need for a reflector domain mesh is completely eliminated. Via comparisons with pure FEM and BEM solutions of the reflected systems within the context of three and four group diffusion theories, the present formulation is validated and assessed.
Kurzfassung
Die Finite Elemente und Randelemente Hybridmethode wurde für reflektierte Systeme entwickelt und blieb auf Ein- oder Zweigruppen Neutrondiffusionstheorie beschränkt. Diese Arbeit erweitert die obengenannte Methode mit Hilfe der Randintegralgleichung der Mehrgruppendiffusionstheorie zu Mehrgruppendiffusiongleichungen. Eine lineare oder bilineare zweidimensionale Finite Elemente Formulierung für den Reaktorkern, die mit einer linearen zwei-dimensionale Randelemente Formulierung für den Reflektor kombiniert wird, stellt das grundlegende Diskretisierungverfahren dar. Da die Benutzung der Randintegralgleichung der Mehrgruppendiffusionstheorie alle Streuungvolumenintegrale zu Oberflächeintegralen in dem Reflektor transformiert, wird eine Reflektorvolumenmasche überflüssig. Durch Vergleiche mit reinen Finite Elemente und Randelemente Lösungen für die reflektierten Systeme in Kontext der Drei- und Viergruppen Theorien wird die präsentierte Formulierung validiert und bewertet.
References
1 Semenza, L. A.; Rossow, E. C.; Lewis, E. E.: Application of finite element method to multigroup neutron diffusion equation. Nucl. Sci. Eng.47 (1972) 302Suche in Google Scholar
2 Itagaki, M.: Boundary element methods applied to two-dimensional neutron diffusion problems. J. Nucl. Sci. Technol.22 (1985) 565Suche in Google Scholar
3 Lewis, E. E.: Finite element approximations to the even-parity transport equation. Adv. Nucl. Sci. Technol.13 (1981) 155Suche in Google Scholar
4 Ozgener, B.; Ozgener, H. A.: The solution of the criticality eigenvalue problems in the application of the boundary element method to the neutron diffusion equation. Ann. Nucl. Energy20 (1993) 503Suche in Google Scholar
5 Ozgener, B.; Ozgener, H. A.: The application of the multiple reciprocity method to the boundary element formulation of the neutron diffusion equation. Ann. Nucl. Energy21 (1994) 711Suche in Google Scholar
6 Purwadi, M. D.; Tsuji, M.; Narita, M.; Itagaki, M.: The application of the domain decomposition method into the boundary element method for solving the multiregion neutron diffusion equation. Eng. Anal. Boundary Elements20 (1998) 197Suche in Google Scholar
7 Ozgener, H. A.; Ozgener, B.: A multiregion boundary element method for multigroup neutron diffusion calculations. Ann. Nucl. Energy28 (2001) 585Suche in Google Scholar
8 Purwadi, M. D.; Tsuji, M.; Narita, M.; Itagaki, M.: A hierarchical domain decomposition boundary element method applied to the multiregion problems of neutron diffusion equations. Nucl. Sci. Eng.129 (1998) 88Suche in Google Scholar
9 Chiba, G.; Tsuji, M.; Shimazo, Y.: A hierarchical domain decomposition boundary element method with a higher order polynomial expansion for solving 2-D multiregion neutron diffusion equations. Ann. Nucl. Energy28 (2001) 89510.1016/S0306-4549(00)00100-6Suche in Google Scholar
10 Chiba, G.; Tsuji, M.; Shimazo, Y.: Development of the hierarchical domain decomposition boundary element method for solving the three-dimensional multiregion neutron diffusion equations. J. Nucl. Sci. Technol38 (2001) 664Suche in Google Scholar
11 Maiani, M.; Montagnini, B.: A boundary element-response matrix method for the multigroup neutron diffusion equations. Ann. Nucl. Energy26 (1999) 1341Suche in Google Scholar
12 Cavdar, S.; Ozgener, H. A.: A finite element/boundary element hybrid method for 2-D neutron diffusion calculations. Ann. Nucl. Energy31 (2004) 155510.1016/j.anucene.2004.04.006Suche in Google Scholar
13 Maiani, M.; Montagnini, B.: A Galerkin approach to the boundary element-response matrix method for the multigroup neutron diffusion equations. Ann. Nucl. Energy31 (2004) 1447Suche in Google Scholar
14 Ozgener, B.: A boundary integral equation for boundary element applications in multigroup neutron diffusion theory. Ann. Nucl. Energy25 (1998) 347Suche in Google Scholar
15 Ozgener, B.; Kabadayi, Y.: The acceleration of the finite element solutions of the diffusion theory criticality eigenvalue problems by Chebyshev polynomial extrapolation (in Turkish). In: Proceedings of the Seventh National Meetings on Nuclear Sciences and Technology, Burses Turkey (1993)Suche in Google Scholar
© 2007, Carl Hanser Verlag, München
Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- Effect of fuel particles' size and position variations on multiplication factor in pebble-bed nuclear reactors
- Axial flux harmonics affecting the parallel channel instabilities in boiling water reactors
- Uncontrolled withdrawal of a control rod without SCRAM
- Modelling of Carbon-14, Iodine-129 and Cesium-137 releases from near surface radioactive waste disposal and their impact on environment and humans
- Investigation of nuclear model predictions for proton induced reaction cross-sections up to 150 MeV
- The extension of the 2-D finite element/boundary element hybrid method to general multigroup neutron diffusion theory
- Extension of the HN method for solving radiation transfer problems in plane geometry for general anisotropic scattering
- The albedo problem for pure-triplet scattering
- Studies on the transmission and processing of pulse-shaped signals from nuclear radiation detectors using methods of systems theory
- The preignition problem in nuclear explosive devices (NEDs) for a sigmoidal Rossi-α and a high neutron background
- Comparison of economy and emissions of nuclear power plants and combined gas and wind electricity generators
Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- Effect of fuel particles' size and position variations on multiplication factor in pebble-bed nuclear reactors
- Axial flux harmonics affecting the parallel channel instabilities in boiling water reactors
- Uncontrolled withdrawal of a control rod without SCRAM
- Modelling of Carbon-14, Iodine-129 and Cesium-137 releases from near surface radioactive waste disposal and their impact on environment and humans
- Investigation of nuclear model predictions for proton induced reaction cross-sections up to 150 MeV
- The extension of the 2-D finite element/boundary element hybrid method to general multigroup neutron diffusion theory
- Extension of the HN method for solving radiation transfer problems in plane geometry for general anisotropic scattering
- The albedo problem for pure-triplet scattering
- Studies on the transmission and processing of pulse-shaped signals from nuclear radiation detectors using methods of systems theory
- The preignition problem in nuclear explosive devices (NEDs) for a sigmoidal Rossi-α and a high neutron background
- Comparison of economy and emissions of nuclear power plants and combined gas and wind electricity generators
