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[en] The 3-D steady-state SN neutron-gamma transport theory code ATES3 developed at BARC can be utilized for external source problems such as shielding analysis. A brief description on the use of ATES3 and its validation for international shielding type benchmarks problems is presented in the paper. (author)
[en] Highlights: • Multi-level acceleration including MOC/NEM, Multigroup CMFD and One Group CMFD. • Generalized equivalence theory for the consistencies between 3 levels. • In-house developed linear solver and a innovated efficient Preconditioner for large scale parallel computing. - Abstract: A new 2D/1D method with multi-level generalized equivalence theory (GET) based coarse mesh finite difference (CMFD) acceleration was proposed for the whole core transport calculation in this paper. Fouressential features of this new 2D/1D methods are as follows: (1) Two new defined factors, nodal discontinuity factor (NDF) and modified diffusion coefficient factor (MDF), were defined in this new GET based CMFD method to achieve equivalence between CMFD and the transport solutions and especially insure that only positive coupling coefficients would occur in the CMFD linear system; (2) For accelerating the convergence of the CMFD, a multi-level acceleration scheme was implemented and an innovative self-developed RSILU preconditioned GMRES solver was developed to solve the CMFD linear system; (3) Within the new CMFD framework, 2D MOC and 1D two-node nodal expansion solvers were developed for 3D whole core transport calculation and the sub-plane technique was applied to minimize the nodal error successfully while maintain a reasonable computing time; (4) For implementation, transverse leakage splitting technique was applied to avoid the total source to become negative, and domain decomposition method based on MPI was implemented to take advantages of high performance clusters. The accuracy of this 2D/1D method via multi-level GET based CMFD and the effectiveness and acceleration performance of the multi-level CMFD method were examined for the well-known C5G7 benchmarks problems. The numerical results demonstrate that superior accuracy is achievable and the multi-level acceleration schemeis efficient and enhances the converge speed of both the GET based CMFD acceleration and the MOC calculation.
[en] A CMFD (Coarse-Mesh-Finite-Difference) formulation of the HEXNEM3 nodal expansion method for solving the neutron transport equation in two-group diffusion approximation is developed. One- and two-dimensional versions are created which can be used to solve three-dimensional problems through transverse integration. The CMFD formulation is constructed directly for the node-averaged scalar fluxes. The resulting balance equations are cast in the standard form of a nonhomogeneous system of linear algebraic equations, with a full freedom of choosing an appropriate solution method. In time-dependent applications this offers an important advantage over the partial current coupling approach employed in the original HEXNEM3 method which is restricted to stationary iteration only, with the corresponding limitation on the choice of acceleration techniques. Results from solving several steady-state test problems are presented. In the one-dimensional case they are compared with a corresponding fine-mesh finite difference solution, and in the two-dimensional – with solutions of appropriate modifications of standard WWER-1000 and WWER-440 benchmark problems produced using the original partial current coupling technique of HEXNEM3. Key words: two-group diffusion nodal methods, HEXNEM, CMFD, WWER-1000, WWER-440
[en] Highlights: • Conventional Monte Carlo α-k iteration methods are improved in this paper. • A direct physical relation to adjust the α-eigenvalue is also derived. • Besides variance reduction, the need for a proper initial α is alleviated. • The proposed automatic shifting method highly improves the convergence rate. • A comparative analysis on the performance of α-adjusting techniques is presented. - Abstract: The α-k iteration method is a common approach for calculating the fundamental α- or time-eigenvalue. The bottleneck of the method lies in how to estimate or adjust the amount of α value in each iteration. Prolonged convergence as well as the need for a proper initial guess for the α-eigenvalue are two main deficiencies of commonly employed α adjusting techniques. This article proposes a direct physical relation to adjust the α-eigenvalue in the Monte Carlo (MC) α-k iteration method, lifting the need for an initial guess along with an improved convergence rate. To do that, a link is established between the actual physical parameters of the system and the α-eigenvalue in each iteration. Also, it is shown that the combination of currently used methods and our proposed algorithm would end to a reduced variance in the final result. The MC3 Monte Carlo code is empowered via several modules enabling us to perform a comparative analysis on the performance of α adjusting techniques. Several test cases are examined for the assessment of suggested scheme proving efficiency and robustness of the approach.
[en] The Consortium for Advanced Simulation of Light Water Reactors Virtual Environment for Reactor Applications (VERA) neutronic simulator MPACT is being developed by Oak Ridge National Laboratory and the University of Michigan for various reactor applications. The MPACT and simplified MPACT 51- and 252-group cross section libraries have been developed for the MPACT neutron transport calculations by using the AMPX and Standardized Computer Analyses for Licensing Evaluations (SCALE) code packages developed at Oak Ridge National Laboratory. It has been noted that the conventional AMPX/SCALE procedure has limited applications for fast-spectrum systems such as boiling water reactor (BWR) fuels with very high void fractions and fast reactor fuels because of its poor accuracy in unresolved and fast energy regions. This lack of accuracy can introduce additional error sources to MPACT calculations, which is already limited by the Bondarenko approach for resolved resonance self-shielding calculation. To enhance the prediction accuracy of MPACT for fast-spectrum reactor analyses, the accuracy of the AMPX/SCALE code packages should be improved first. The purpose of this study is to identify the major problems of the AMPX/SCALE procedure in generating fast-spectrum cross sections and to devise ways to improve the accuracy. For this, various benchmark problems including a typical pressurized water reactor fuel, BWR fuels with various void fractions, and several fast reactor fuels were analyzed using the AMPX 252-group libraries. Isotopic reaction rates were determined by SCALE multigroup (MG) calculations and compared with continuous energy (CE) Monte Carlo calculation results. This reaction rate analysis revealed three main contributors to the observed differences in reactivity and reaction rates: (1) the limitation of the Bondarenko approach in coarse energy group structure, (2) the normalization issue of probability tables, and (3) neglect of the self-shielding effect of resonance-like cross sections at high energy range such as (n,p) cross section of Cl35. The first error source can be eliminated by an ultra-fine group (UFG) structure in which the broad scattering resonances of intermediate-weight nuclides can be represented accurately by a piecewise constant function. A UFG AMPX library was generated with modified probability tables and tested against various benchmark problems. The reactivity and reaction rates determined with the new UFG AMPX library agreed very well with respect to Monte Carlo Neutral Particle (MCNP) results. To enhance the lattice calculation accuracy without significantly increasing the computational time, performing the UFG lattice calculation in two steps was proposed. In the first step, a UFG slowing-down calculation is performed for the corresponding homogenized composition, and UFG cross sections are collapsed into an intermediate group structure. In the second step, the lattice calculation is performed for the intermediate group level using the condensed group cross sections. A preliminary test showed that the condensed library reproduces the results obtained with the UFG cross section library. This result suggests that the proposed two-step lattice calculation approach is a promising option to enhance the applicability of the AMPX/SCALE system to fast system analysis.
[en] Highlights: • An acceleration scheme derived from DSA is proposed. • The scheme is defined piecewise, so that it can be straightforwardly parallelized. • The scheme is designed to be no harder to implement than regular DSA. • The scheme converges as well as a standard DSA in optically thick enough systems. - Abstract: The method of discrete ordinates (SN) is a popular choice for the solution of the neutron transport equation. It is however well known that it suffers from slow convergence of the scattering source in optically thick and diffusive media, such as pressurized water nuclear reactors (PWR). In reactor physics applications, the SN method is thus often accompanied by an acceleration algorithm, such as Diffusion Synthetic Acceleration (DSA). With the recent increase in computational power, whole core transport calculations have become a reasonable objective. It however requires using large computers and parallelizing the transport solver. Due to the elliptic nature of the DSA operator, its parallelization is not straightforward. In this paper, we present an acceleration operator derived from DSA, but defined in a piecewise way such that its parallel implementation is straightforward. We mathematically show that, for optically thick enough media, this Piecewise Diffusion Synthetic Acceleration (PDSA) scheme preserves the good properties of DSA. This conclusion is supported by numerical experiments.
[en] PROTEUS is the neutron transport solver package developed at Argonne National Laboratory under the DOE Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. For the purposes of this report, we consider the PROTEUS package to include the three solvers PROTEUS-NODAL, PROTEUS-MOC, and PROTEUS-SN, as well as the PROTEUS mesh tools and utilities.
[en] Highlights: • Wielandt shift algorithm is employed to deal with the high dominance ratio issue. • Amulti-group GMRES algorithm is investigated to handle the extra up-scattering. • The multi-group GMRES and CMR algorithms can jointly provide a speedup of 14. - Abstract: For PWR whole-core pin-by-pin calculation, a parallel multi-group neutron transport calculation code named EFEN was developed based on the Exponential Function Expansion Nodal SP3 method. Considering the large number of unknowns, it was accelerated by using Coarse Mesh Rebalance (CMR) method. However, its efficiency still requires further improvement. In this paper, the acceleration of EFEN with Wielandt shift algorithm and multi-group Generalized Minimal Residual (GMRES) algorithm are studied. To deal with the high dominance ratio for PWR pin-by-pin problems, Wielandt shift algorithm is employed by transferring part of the fission source to pseudo scattering source. However, the pseudo scattering treatment would lead to an extra up-scattering issue which would increase the burden of the classical multi-group iteration for scattering source. Consequently, instead of using the multi-group Gauss-Seidel (GS) algorithm, a multi-group GMRES algorithm that solves all the energy groups simultaneously is adopted to deal with the extra up-scattering problem. Verifications and analysis of these algorithms are performed on a 10 × 1 multi-assembly pin-by-pin problem and a more realistic multi-group PWR whole-core pin-by-pin problem. Encouraging conclusions are demonstrated by the numerical results. (1) The number of power iteration can be reduced by a factor of about 6–10 by utilizing the Wielandt shift algorithm with a shifting factor of 0.01. (2) Multi-group GMRES algorithm accelerates the multi-group iteration significantly. The combination of these two can provide a speedup of 3.6 for a typical 8-group pin-by-pin calculation with 289 × 289 × 56 meshes. In addition, higher speedup of 14.0 can be obtained by combining the multi-group GMRES algorithm with the existing CMR method.
[en] Bayesian methods are known for treating the so-called data re-assimilation. The Bayesian inference applied to core physics allows us to get a new adjustment of nuclear data using the results of integral experiments. This theory leading to reassimilation encompasses a broader approach. In previous papers, new methods have been developed to calculate the impact of nuclear and manufacturing data uncertainties on neutronics parameters. Usually, adjustment is performed step by step with one parameter and one experiment by batch. In this document, we rewrite Orlov theory to extend to multiple experimental values and parameters adjustment. We found that the multidimensional system expression looks like can be written as the mono-dimensional system in a matrix form. In this extension, correlation terms appears between experimental processes (manufacturing and measurements) and we discuss how to fix them. Then formula are applied to the extension to the Boltzmann/Bateman coupled problem, where each term could be evaluated by computing depletion uncertainties, studied in previous papers. (authors)