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Piecewise-Constant Method for Angular Approximation for the Second-Order Multidimensional Neutron Transport Equations  

Noh, Tae-Wan (Applied Mathematics, Hongik University)
Publication Information
Journal of Energy Engineering / v.16, no.1, 2007 , pp. 46-52 More about this Journal
Abstract
The piecewise constant angular approximation is developed to replace the conventional angular quadrature sets in the solution of the second-order, multi-dimensional $S_{N}$ neutron transport equations. The newly generated quadrature sets by this method substantially mitigate ray effects and can be used in the same manner as the conventional quadrature sets are used. The discrete-ordinates and the piecewise-constant approximations are applied to both the first-order Boltzmann and the second-order form of neutron transport equations in treating angular variables. The result is that the mitigation of ray effects is only achieved by the piecewise-constant method, in which new angular quadratures are generated by integrating angle variables over the specified region. In other sense, the newly generated angular quadratures turn out to decrease the contribution of mixed-derivative terms in the even-parity equation that is one of the second-order neutron transport equation. This result can be interpreted as the entire elimination or substantial mitigation of ray effect are possible in the simplified even-parity equation which has no mixed-derivative terms.
Keywords
Neutron transport; Discrete-ordinates method; Piecewise-constant method; Ray effects; Scalar flux; Angular flux;
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1 Miller, Jr. W.F.; Noh, T.W. 'Finite-Differences versus Finite elements in Slab Geometry, Even-Parity Transport Theory', Transport Theory and Statistical Physics, 1993, 22
2 Noh, T.W., Miller, Jr. W.F.; Morel, J.E. 'The Even- Parity and Simplified Even-Parity Transport Equation in Two-Dimensional X-Y Geometry', Nucl. Sci. Eng., 1996, 123, 38   DOI
3 Lewis, E.E.; Miller, Jr. W.F. Computational Methods of Neutron Transport, John Wiley & Sons, 1993
4 Azmy, Y.Y.; 'Multidimensional Nodal Transport Methods for Multiple-Instruction Multiple-Data, Distributed Memory Machines', Trans. Am. Nucl. Soc., 1988, 56, 292
5 Lawrence, R.D. 'Progress in Nodal Methods for the Solution of the Neutron Diffusion and Transport Equations', Prog. Nucl. Energy, 1986, 17, 271   DOI   ScienceOn
6 Haghighat, A.; Azmy, Y.Y. 'Parallelization of a Spherical SN Algorithm Based on the Spatial Domain Decomposition', Proceedings of the Conference on Advances in Mathematics, Computation, and Reactor Physics, Pittsburgh, PA, 1991, April 28-May 1
7 Lathrop, K.D. 'Ray Effects in Discrete Ordinates Equations', Nucl. Sci. Eng., 1968, 32, 357   DOI
8 Lathrop, K.D. 'Remedies for Ray effects', Nucl. Sci. Eng., 1971, 45, 255   DOI
9 Noh, T.W.; Miller, Jr. W.F.; Morel, J.E. 'Improved Approximations Applied to the $S_N$ Even-Parity Trasport Equations', Trans. Am. Nucl. Soc., 1993, 69, 214
10 Larsen, E.W.; McGhee, J.M.; Morel, J.E. 'The Simplified PN Equations as an Asymptotic Limit of the Transport Equation', Trans. Am. Nucl. Soc., 1992, 66, 231
11 Morel, J.E.; McGhee, J.M. 'A Self-Adjoint Angular Flux Equation', Nucl. Sci. Eng., 1999, 132, 312-325   DOI