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Title: An optimally diffusive Coarse Mesh Finite Difference method to accelerate neutron transport calculations

Authors:
; ; ; ; ;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1326418
Grant/Contract Number:
AC05-00OR22725
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Annals of Nuclear Energy (Oxford)
Additional Journal Information:
Journal Name: Annals of Nuclear Energy (Oxford); Journal Volume: 95; Journal Issue: C; Related Information: CHORUS Timestamp: 2017-10-04 16:06:32; Journal ID: ISSN 0306-4549
Publisher:
Elsevier
Country of Publication:
United Kingdom
Language:
English

Citation Formats

Zhu, Ang, Jarrett, Michael, Xu, Yunlin, Kochunas, Brendan, Larsen, Edward, and Downar, Thomas. An optimally diffusive Coarse Mesh Finite Difference method to accelerate neutron transport calculations. United Kingdom: N. p., 2016. Web. doi:10.1016/j.anucene.2016.05.004.
Zhu, Ang, Jarrett, Michael, Xu, Yunlin, Kochunas, Brendan, Larsen, Edward, & Downar, Thomas. An optimally diffusive Coarse Mesh Finite Difference method to accelerate neutron transport calculations. United Kingdom. doi:10.1016/j.anucene.2016.05.004.
Zhu, Ang, Jarrett, Michael, Xu, Yunlin, Kochunas, Brendan, Larsen, Edward, and Downar, Thomas. Thu . "An optimally diffusive Coarse Mesh Finite Difference method to accelerate neutron transport calculations". United Kingdom. doi:10.1016/j.anucene.2016.05.004.
@article{osti_1326418,
title = {An optimally diffusive Coarse Mesh Finite Difference method to accelerate neutron transport calculations},
author = {Zhu, Ang and Jarrett, Michael and Xu, Yunlin and Kochunas, Brendan and Larsen, Edward and Downar, Thomas},
abstractNote = {},
doi = {10.1016/j.anucene.2016.05.004},
journal = {Annals of Nuclear Energy (Oxford)},
number = C,
volume = 95,
place = {United Kingdom},
year = {Thu Sep 01 00:00:00 EDT 2016},
month = {Thu Sep 01 00:00:00 EDT 2016}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/j.anucene.2016.05.004

Citation Metrics:
Cited by: 8works
Citation information provided by
Web of Science

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  • Modern nodal methods have been successfully used for conventional light water reactor core analyses where the homogenized, node average cross section (XSs) and the flux discontinuity factors (DFs) based on equivalence theory can reliably predict core behavior. For other types of cores and other geometries characterized by tightly coupled, heterogeneous core configurations, the intranodal flux shapes obtained from a homogenized nodal problem may not accurately portray steep flux gradients near fuel assembly interfaces or various reactivity control elements. This may require extreme values of DFs (either very large, very small, or even negative) to achieve a desired solution accuracy. Extrememore » values of DFs, however, can disrupt the convergence of the iterative methods used to solve for the node average fluxes and can lead to difficulty in interpolating adjacent DF values. Several attempts to remedy the problem have been made, but nothing has been satisfactory. A new coarse-mesh nodal scheme called the diffusive-mesh finite difference (DMFD) technique, as contrasted with the coarse-mesh finite difference (CMFD) technique, has been developed to resolve this problem. This new technique and the development of a few-group, multidimensional kinetics computer program are described in this paper.« less
  • This study has been undertaken to evaluate an uncertainty in a finite difference method for two-dimensional neutron diffusion calculations and to provide a simple method to eliminate the uncertainty from k/sub eff/, control rod worth, and peak power density. An effect of a condensation of the energy groups is also studied. It is found that errors in k/sub eff/, control rod worth, and peak power density have linear relationships with the square of mesh spacing, and an extrapolation to zero mesh spacing, by using the linear relationships, is possible, eliminating the uncertainties of 0.7 percent ..delta..k/k in k/sub eff/, approximatelymore » 8 percent in control rod worth and approximately 2 percent in peak power density in a case of a mesh calculation as coarse as one mesh point per subassembly. When a basic multigroup cross-section set is condensed into a few-group cross-section set, the errors due to the condensation of the cross sections on k/sub eff/ and on control rod worth are shown to have linear relationships with the inverse square of the number of the condensed energy group. These relationships have been confirmed analytically with the application of perturbation theory.« less
  • In order to take into account in a more effective and accurate way the intranodal heterogeneities in coarse-mesh finite-difference (CMFD) methods, a new equivalent parameter generation methodology has been developed and tested. This methodology accounts for the dependence of the nodal homogeneized two-group cross sections and nodal coupling factors, with interface flux discontinuity (IFD) factors that account for heterogeneities on the flux-spectrum and burnup intranodal distributions as well as on neighbor effects.The methodology has been implemented in an analytic CMFD method, rigorously obtained for homogeneous nodes with transverse leakage and generalized now for heterogeneous nodes by including IFD heterogeneity factors.more » When intranodal mesh node heterogeneity vanishes, the heterogeneous solution tends to the analytic homogeneous nodal solution. On the other hand, when intranodal heterogeneity increases, a high accuracy is maintained since the linear and nonlinear feedbacks on equivalent parameters have been shown to be as a very effective way of accounting for heterogeneity effects in two-group multidimensional coarse-mesh diffusion calculations.« less
  • A reconstruction method has been developed for recovering pin powers from Canada deuterium uranium (CANDU) reactor core calculations performed with a coarse-mesh finite difference diffusion approximation and single-assembly lattice calculations. The homogeneous intranodal distributions of group fluxes are efficiently computed using polynomial shapes constrained to satisfy the nodal information approximated from the node-average fluxes. The group fluxes of individual fuel pins in a heterogeneous fuel bundle are determined using these homogeneous intranodal flux distributions and the form functions obtained from the single-assembly lattice calculations. The pin powers are obtained using these pin fluxes and the pin power cross sections generatedmore » by the single-assembly lattice calculation. The accuracy of the reconstruction schemes has been estimated by performing benchmark calculations for partial core representation of a natural uranium CANDU reactor. The results indicate that the reconstruction schemes are quite accurate, yielding maximum pin power errors of less than {approx}3%. The main contribution to the reconstruction error is made by the errors in the node-average fluxes obtained from the coarse-mesh finite difference diffusion calculation; the errors due to the reconstruction schemes are <1%.« less
  • The convergence rates of the nonlinear coarse-mesh finite difference (CMFD) method and the coarse-mesh rebalance (CMR) method are derived analytically for one-dimensional, one-group solutions of the fixed-source diffusion problem in a nonmultiplying infinite homogeneous medium. The derivation was performed by linearizing the nonlinear algorithm and by applying Fourier error analysis to the linearized algorithm. The mesh size measured in units of the diffusion length is shown to be a dominant parameter for the convergence rate and for the stability of the iterative algorithms. For a small mesh size problem, the nonlinear CMFD is shown to be a more effective accelerationmore » method than CMR. Both CMR and two-node CMFD algorithms are shown to be unconditionally stable. However, the one-node CMFD becomes unstable for large mesh sizes. To remedy this instability, an underrelaxation of the current correction factor for the one-node CMFD method is successfully introduced, and the domain of stability is significantly expanded. Furthermore, the optimum underrelaxation parameter is analytically derived, and the one-node CMFD with the optimum relaxation is shown to be unconditionally stable.« less