[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.1016/j.net.2016.08.006

Sensitivity Analysis of the Galerkin Finite Element Method Neutron Diffusion Solver to the Shape of the Elements

Hosseini, Seyed Abolfazl (Department of Energy Engineering, Sharif University of Technology)

Publication Information

Nuclear Engineering and Technology / v.49, no.1, 2017 , pp. 29-42 More about this Journal

Abstract

The purpose of the present study is the presentation of the appropriate element and shape function in the solution of the neutron diffusion equation in two-dimensional (2D) geometries. To this end, the multigroup neutron diffusion equation is solved using the Galerkin finite element method in both rectangular and hexagonal reactor cores. The spatial discretization of the equation is performed using unstructured triangular and quadrilateral finite elements. Calculations are performed using both linear and quadratic approximations of shape function in the Galerkin finite element method, based on which results are compared. Using the power iteration method, the neutron flux distributions with the corresponding eigenvalue are obtained. The results are then validated against the valid results for IAEA-2D and BIBLIS-2D benchmark problems. To investigate the dependency of the results to the type and number of the elements, and shape function order, a sensitivity analysis of the calculations to the mentioned parameters is performed. It is shown that the triangular elements and second order of the shape function in each element give the best results in comparison to the other states.

Keywords

Galerkin Finite Element Method; Shape Function; Triangle; Quadrilateral; Linear; Second Approximation;

Citations & Related Records

Reference

1	B. Christensen, Three-dimensional Static and Dynamic Reactor Calculations by the Nodal Expansion Method, Riso National Laboratory, 1985.
2	C. Kang, K. Hansen, Finite element methods for reactor analysis, Nucl. Sci. Eng. 51 (1973) 456-495. DOI
3	E. Lewis, Finite element approximation to the even-parity transport equation, in: Advances in Nuclear Science and Technology, Springer, New York, 1981, pp. 155-225.
4	A. Hebert, A Raviart-Thomas-Schneider solution of the diffusion equation in hexagonal geometry, Ann. Nucl. Energy 35 (2008) 363-376. DOI
5	S. Cavdar, H. Ozgener, A finite element/boundary element hybrid method for 2-D neutron diffusion calculations, Ann. Nucl. Energy 31 (2004) 1555-1582. DOI
6	Y. Wang, W. Bangerth, J. Ragusa, Three-dimensional h-adaptivity for the multigroup neutron diffusion equations, Prog. Nucl. Energy 51 (2009) 543-555. DOI
7	S.A. Hosseini, N. Vosoughi, Development of two-dimensional, multigroup neutron diffusion computer code based on GFEM with unstructured triangle elements, Ann. Nucl. Energy 51 (2013) 213-226. DOI
8	K. Smith, An Analytical Nodal Method for Solving the Two-group, Multidimensional, Static and Transient Neutron Diffusion Equations, MIT Department of Nuclear Engineering, Cambridge (MA), 1979.
9	E. Varin, A. Hebert, R. Roy, J. Koclas, A User's Guide for DONJON, Technical Report IGE-208 Rev. 2, Ecole Polytechnique de Montreal, 2004.
10	J.J. Duderstadt, L.J. Hamilton, Nuclear Reactor Analysis, Wiley, Hoboken (NJ), 1976.
11	J.R. Lamarsh, Introduction to Nuclear Reactor Theory, Addison Wesley Publishing Company, Boston (MA), 1966.
12	M. Maiani, B. Montagnini, A Galerkin approach to the boundary element-response matrix method for the multigroup neutron diffusion equations, Ann. Nucl. Energy 31 (2004) 1447-1475. DOI
13	S. Gonzalez-Pintor, D. Ginestar, G. Verdu, High order finite element method for the lambda modes problem on hexagonal geometry, Ann. Nucl. Energy 36 (2009) 1450-1462. DOI