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[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] Highlights: • Thorough analysis on all the cases in C5G7-TD benchmark. • Parametric study on the time step size. • Comprehensive comparison with other codes’ results. - Abstract: Verification and Validation (V&V) serves an important role in assessing the numerical methods implemented in a neutron transport code. However, very few benchmarks are available for verifying and validating the transient capability of neutron transport codes. In this paper, the transient methodology of the Transient Multilevel (TML) Method used in the MPACT code was verified using Phase I of the recently developed OECD/NEA C5G7-TD benchmark, which was specifically designed for validating the transport space-time simulations. The results in MPACT agree well with results of other codes. While this is not code validation, the results contributes to the MPACT verification base and provide an additional solution for the C5G7-TD benchmark which can increase the importance of the OECD benchmark to assess the performance of other transient neutron transport codes.
[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] 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] In this paper, spacial domain-decomposed parallel Matrix MOC and relevant multi-domain coupled PGMRES accelerating algorithm were studied. In this algorithm, PGMRES from PETSc library was adopted to solve the angular flux of inner boundaries directly, thus improving the convergence rate. Numerical results demonstrated that the multi-domain coupled PGMRES algorithm keeps good accuracy and obtains great speed ratio. (authors)
[en] A linear-algebraic form of the equations of the method of characteristics, which is used to approximate the neutron transport equation, is obtained. It is shown on the basis of the obtained linear-algebraic form that the discrete form of the conjugate equation differs from the algebraically discrete problem constructed by linear-algebraic transformations of the discrete form of the normal problem. The reason for the discrepancy lies in the approximation of the volumes of the spatial cells in covering the working region by a network of characteristics. It is shown by means of test calculations that when the network of characteristics is refined the solution of the conjugate transport equation converges to the solution of the algebraically conjugate problem.
[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)
[en] Solution of the k-eigenvalue transport problem has been limited in lattice codes to the fundamental mode corresponding to the largest eigenvalue. Despite the fact that the higher order modes have no physical meaning, they can have significant uses in different applications. While the fundamental mode represents the asymptotic behaviour of the neutron flux, higher modes describe the small perturbations about it; hence, they can be employed in perturbation studies. Another important application of the higher modes is flux synthesis or mapping. Starting with a reference solution of the neutron flux at a coarse level and a number of modes at a finer level, detailed flux distribution can be reconstructed from a coarse solution. In this work, an implementation of a neutron flux modes solver in DRAGON is described. The solver is based on the QZ decomposition algorithm. The approach is described and results are presented. (author)
[en] Highlights: • A coupling between neutron transport and thermomechanics is performed. • A multiphysics approach, based on the Improved Quasi-static Method, is proposed. • Coupling techniques and time-step control strategies are tested in this frame. - Abstract: The quasi-static method is widely used for space- and time-dependent neutron transport problems. It is based on the factorization of the flux into the product of two functions, an “amplitude” depending only on time and a “shape” which depends on all variables. Thanks to this factorization, long time-steps can be used for the computation of the shape, leading to a substantial reduction of the calculation time. Two algorithms, based on the quasi-static factorization, can be found in the literature: the “Improved Quasi-static Method” (IQM), and the “Predictor-Corrector Quasi-static Method” (PCQM). In this paper we show, on the example of the Godiva experiment, that the IQM algorithm can be easily adapted to multi-physics simulations. Moreover, most of the common coupling or time-step control strategies are compatible with this algorithm and we test some of them here. In particular, a technique taken from existing codes with point-kinetic modules and based on feedback coefficients is found, in our case, to be especially efficient and gives precise and fast results. This shows that the multi-physics IQM presented in this paper is compatible with these existing codes, and may be a way to couple them with neutron transport solvers.