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RICHARD SANCHEZ,IGOR ZMIJAREVIC,M. COSTE-DELCLAUX,EMILIANO MASIELLO,SIMONE SANTANDREA,EMANUELE MARTINOLLI,LAURENCE VILLATE,NADINE SCHWARTZ,NATHALIE GULER 한국원자력학회 2010 Nuclear Engineering and Technology Vol.42 No.5
This paper presents the most important developments implemented in the APOLLO2 spectral code since its last generalpresentation at the 1999 M&C conference in Madrid. APOLLO2 has been provided with new capabilities in the domain ofcross section self-shielding, including mixture effects and transfer matrix self-shielding, new or improved flux solvers (CPMfor RZ geometry, heterogeneous cells for short MOC and the linear-surface scheme for long MOC), improved accelerationtechniques (DP1), that are also applied to thermal and external iterations, and a number of sophisticated modules and tools tohelp user calculations. The method of characteristics, which took over the collision probability method as the main fluxsolver of the code, allows for whole core two-dimensional heterogeneous calculations. A flux reconstruction technique leadsto fast albeit accurate solutions used for industrial applications. The APOLLO2 code has been integrated (APOLLO2-A)within the ARCADIAreactor code system of AREVA as cross section generator for PWR and BWR fuel assemblies.APOLLO2 is also extensively used by Electricité de France within its reactor calculation chain. A number of numericalexamples are presented to illustrate APOLLO2 accuracy by comparison to Monte Carlo reference calculations. Results of thevalidation program are compared to the measured values on power plants and critical experiments.
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DIFFUSION PIECEWISE HOMOGENIZATION VIA FLUX DISCONTINUITY RATIOS
Sanchez, Richard,Dante, Giorgio,Zmijarevic, Igor Korean Nuclear Society 2013 Nuclear Engineering and Technology Vol.45 No.6
We analyze piecewise homogenization with flux-weighted cross sections and preservation of averaged currents at the boundary of the homogenized domain. Introduction of a set of flux discontinuity ratios (FDR) that preserve reference interface currents leads to preservation of averaged region reaction rates and fluxes. We consider the class of numerical discretizations with one degree of freedom per volume and per surface and prove that when the homogenization and computing meshes are equal there is a unique solution for the FDRs which exactly preserve interface currents. For diffusion submeshing we introduce a Jacobian-Free Newton-Krylov method and for all cases considered obtain an 'exact' numerical solution (eight digits for the interface currents). The homogenization is completed by extending the familiar full assembly homogenization via flux discontinuity factors to the sides of regions laying on the boundary of the piecewise homogenized domain. Finally, for the familiar nodal discretization we numerically find that the FDRs obtained with no submesh (nearly at no cost) can be effectively used for whole-core diffusion calculations with submesh. This is not the case, however, for cell-centered finite differences.
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Diffusion Piecewise Homogenization Via Flux Discontinuity Ratios
RICHARD SANCHEZ,Giorgio Dante,IGOR ZMIJAREVIC 한국원자력학회 2013 Nuclear Engineering and Technology Vol.45 No.6
We analyze piecewise homogenization with flux-weighted cross sections and preservation of averaged currents at theboundary of the homogenized domain. Introduction of a set of flux discontinuity ratios (FDR) that preserve reference interfacecurrents leads to preservation of averaged region reaction rates and fluxes. We consider the class of numerical discretizationswith one degree of freedom per volume and per surface and prove that when the homogenization and computing meshes areequal there is a unique solution for the FDRs which exactly preserve interface currents. For diffusion submeshing we introducea Jacobian-Free Newton-Krylov method and for all cases considered obtain an ‘exact’ numerical solution (eight digits for theinterface currents). The homogenization is completed by extending the familiar full assembly homogenization via fluxdiscontinuity factors to the sides of regions laying on the boundary of the piecewise homogenized domain. Finally, for thefamiliar nodal discretization we numerically find that the FDRs obtained with no submesh (nearly at no cost) can beeffectively used for whole-core diffusion calculations with submesh. This is not the case, however, for cell-centered finitedifferences. We analyze piecewise homogenization with flux-weighted cross sections and preservation of averaged currents at the boundary of the homogenized domain. Introduction of a set of flux discontinuity ratios (FDR) that preserve reference interface currents leads to preservation of averaged region reaction rates and fluxes. We consider the class of numerical discretizations with one degree of freedom per volume and per surface and prove that when the homogenization and computing meshes are equal there is a unique solution for the FDRs which exactly preserve interface currents. For diffusion submeshing we introduce a Jacobian-Free Newton-Krylov method and for all cases considered obtain an ‘exact’ numerical solution (eight digits for the interface currents). The homogenization is completed by extending the familiar full assembly homogenization via flux discontinuity factors to the sides of regions laying on the boundary of the piecewise homogenized domain. Finally, for the familiar nodal discretization we numerically find that the FDRs obtained with no submesh (nearly at no cost) can be effectively used for whole-core diffusion calculations with submesh. This is not the case, however, for cell-centered finite differences.
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Analysis of alpha modes in multigroup diffusion
Richard Sanchez,Daniele Tomatis,IGOR ZMIJAREVIC,주한규 한국원자력학회 2017 Nuclear Engineering and Technology Vol.49 No.6
The alpha eigenvalue problem in multigroup neutron diffusion is studied with particular attention to thetheoretical analysis of the model. Contrary to previous literature results, the existence of eigenvalue andeigenflux clustering is investigated here without the simplification of a unique fissile isotope or a singleemission spectrum. A discussion about the negative decay constants of the neutron precursors concentrationsas potential eigenvalues is provided. An in-hour equation is derived by a perturbationapproach recurring to the steady state adjoint and direct eigenvalue problems of the effective multiplicationfactor and is used to suggest proper detection criteria of flux clustering. In spite of the priorwork, the in-hour equation results give a necessary and sufficient condition for the existence of theeigenvalue-eigenvector pair. A simplified asymptotic analysis is used to predict bands of accumulation ofeigenvalues close to the negative decay constants of the precursors concentrations. The resolution of theproblem in one-dimensional heterogeneous problems shows numerical evidence of the predictedclustering occurrences and also confirms previous theoretical analysis and numerical results.
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