On the stability of the Discrete Generalized Multigroup method

This paper investigates the stability of the recondensation procedure of the Discrete Generalized Multigroup method and proposes alternatives to improve stability of the original formulation. Instabilities are shown to happen when employing a simple Picard fixed point iteration and an ill-informed group mapping scheme. This work presents a mapping procedure that improves stability of the original method for fine group calculations. Additionally, a relaxation scheme, Krasnoselskij iteration, is introduced to the fixed point iteration to further improve the stability characteristics and remove the need for fine group flux updates. Both improvements are applied on heterogeneous problems using the SHEM361 and the NG2042 group structures. The results indicate improved stability from a well-informed group mapping and demonstrate the possibility of eliminating the need for fine group flux updates.United States. Dept. of Energy. Naval Reactors Divisio

Solving eigenvalue response matrix equations with nonlinear techniques

This paper presents new algorithms for use in the eigenvalue response matrix method (ERMM) for reactor eigenvalue problems. ERMM spatially decomposes a domain into independent nodes linked via boundary conditions approximated as truncated orthogonal expansions, the coefficients of which are response functions. In its simplest form, ERMM consists of a two-level eigenproblem: an outer Picard iteration updates the k-eigenvalue via balance, while the inner λ -eigenproblem imposes neutron balance between nodes. Efficient methods are developed for solving the inner λ-eigenvalue problem within the outer Picard iteration. Based on results from several diffusion and transport benchmark models, it was found that the Krylov-Schur method applied to the λ -eigenvalue problem reduces Picard solver times (excluding response generation) by a factor of 2–5. Furthermore, alternative methods, including Picard acceleration schemes, Steffensen’s method, and Newton’s method, are developed in this paper. These approaches often yield faster k-convergence and a need for fewer k-dependent response function evaluations, which is important because response generation is often the primary cost for problems using responses computed online (i.e., not from a precomputed database). Accelerated Picard iteration was found to reduce total computational times by 2–3 compared to the unaccelerated case for problems dominated by response generation. In addition, Newton’s method was found to provide nearly the same performance with improved robustness

Parallel Fission Bank Algorithms in Monte Carlo Criticality Calculations

In this work we describe a new method for parallelizing the source iterations in a Monte Carlo criticality calculation. Instead of having one global fission bank that needs to be synchronized, as is traditionally done, our method has each processor keep track of a local fission bank while still preserving reproducibility. In doing so, it is required to send only a limited set of fission bank sites between processors, thereby drastically reducing the total amount of data sent through the network. The algorithm was implemented in a simple Monte Carlo code and shown to scale up to hundreds of processors and furthermore outperforms traditional algorithms by at least two orders of magnitude in wall-clock time

Multigroup diffusion preconditioners for multiplying fixed-source transport problems

Several preconditioners based on multigroup di usion are developed for application to multiplying fi xed-source transport problems using the discrete ordinates method. By starting from standard, one-group, diff usion synthetic acceleration (DSA), a multigroup diff usion preconditioner is constructed that shares the same fi ne mesh as the transport problem. As a cheaper but effective alternative, a two-grid, coarse-mesh, multigroup diff usion preconditioner is examined, for which a variety of homogenization schemes are studied to generate the coarse mesh operator. Finally, a transport-corrected diff usion preconditioner based on application of the Newton-Shulz algorithm is developed. The results of several numerical studies indicate the coarse-mesh, diff usion preconditioners work very well. In particular, a coarse-mesh, transport-corrected, diff usion preconditioner reduced the computational time of multigroup GMRES by up to a factor of 17 and outperformed best-case Gauss-Seidel results by over an order of magnitude for all problems studied

An energy recondensation method using the discrete generalized multigroup energy expansion theory

In this paper, the discrete generalized multigroup (DGM) method was used to recondense the coarse group cross-sections using the core level solution, thus providing a correction for neighboring effect found at the core level. This approach was tested using a discrete ordinates implementation in both 1-D and 2-D. Results indicate that 2 or 3 iterations can substantially improve the flux and fission density errors associated with strong interfacial spectral changes as found in the presence of strong absorbers, reflector of mixed-oxide fuel. The methodology is also proven to be fully consistent with the multigroup methodology as long as a flat-flux approximation is used spatially

Détermination de la composition chimique descendres provenant de centrales thermiques au pétrole par activation neutronique

Principe de fonctionnement des centrales thermiques au pétrole -- Quantité de cendres produites -- Disposition des déchets -- Risques potentiels -- Principe de l'analyse par activation -- Rappel de notions fondamentales -- méthode d'activation utilisée et relations mathématiques correspondantes -- Interaction des rayons gamma avec la matière -- Analyse du spectre -- Limite de détection et de décision -- Expérimentation en laboratoire -- Préparation des échantillons -- Appareils utilisés -- Les mesures effectuées -- Analyse de capsule vide -- Analyse quantitative du standard SRM 1633a -- Analyse quantitative des échantillons -- La centrale de Tracy, Québec -- Central de Lennox, Ontario -- Centrale de Tufts-Cove, Nouvelle Écosse -- Centrale de Coleson Cove, Nouveau-Brunswick -- Validité des résultats et limitation de l'analyse par activation -- Analyse de la granulométrie -- Comparaison des cendres volantes et cendres de fond de centrales thermiques au pétrole -- Comparaison des concentrations des cendres volantes de centrales thermiques au charbon et au pétrole -- Sources d'erreurs -- Valorisation des cendres -- Utilisation du vanadium

The OpenMC Monte Carlo particle transport code

A new Monte Carlo code called OpenMC is currently under development at the Massachusetts Institute of Technology as a tool for simulation on high-performance computing platforms. Given that many legacy codes do not scale well on existing and future parallel computer architectures, OpenMC has been developed from scratch with a focus on high performance scalable algorithms as well as modern software design practices. The present work describes the methods used in the OpenMC code and demonstrates the performance and accuracy of the code on a variety of problems.United States. Department of Energy (DE-AC05-00OR22725

A Cumulative migration method for computing rigorous transport cross sections and diffusion coefficients for LWR lattices with Monte Carlo

A new method for computing homogenized assembly neutron transport cross sections and diffusion coefficients that is both rigorous and computationally efficient is proposed in this paper. In the limit of a homogeneous hydrogen slab, the new method is equivalent to the long-used, and only-recently-published CASMO transport method. The rigorous method is used to demonstrate the sources of inaccuracy in the commonly applied “out-scatter” transport correction. It is also demonstrated that the newly developed method is directly applicable to lattice calculations performed by Monte Carlo and is capable of computing rigorous homogenized transport cross sections for arbitrarily heterogeneous lattices. Comparisons of several common transport cross section approximations are presented for a simple problem of infinite medium hydrogen. The new method has also been applied in computing 2-group diffusion data for an actual PWR lattice from BEAVRS benchmark.Idaho National Laboratory (Contract DE-AC07-05ID14517

Development of a Graphical User Interface for In-Core Fuel Management Using MCODE

In the present work, a graphical user interface is developed to automate in-core fuel management using MCODE, an MCNP-ORIGEN linkage code. Data abstraction is achieved by means of five object classes that define the run, fuel assembly locations, fuel assemblies, fuel paths, and materials. The GUI and an associated fuel management wrapper were developed in Python, with the PyQt extension being used for GUI-specific features. To validate the fuel management wrapper, a model of the MIT Reactor core was used to run an equilibrium core. The results show that the wrapper performs reliably. Together, these tools will help the staff at the MITR perform in-core fuel management calculations quickly and with a higher level of detail than that previously possible

Predicting Correlation Coefficients for Monte Carlo Eigenvalue Simulations

Monte Carlo methods are most often considered as a reference for neutron transport simulations since very limited approximations are made abount nuclear data and system geometry. To report uncertainty of any tally evaluated as generation averages, the sample variance is divided by the number of active generations, which is based on the assumption that the neutron generations are independent. Correlation effects between neutrons in multiplying systems, particularly when performing power iteration to evaluate eigenvalues have been observed in previous work. Neglecting the correlation effect results in an underestimate of uncertainty reported by Monte Carlo calculations. Previous work has also proposed methods to predict the underestimation ratio. Yamamoto et al expanded the fission source distribution with diffusion equation modes, performed numerical simulation of the AR(autoregressive) process of the expansion coefficients and used the correlation of the AR process to predict that of the Monte Carlo eigenvalue simulation. Sutton applied the discretized phase space (DPS) approach to predict the underestimation ratio but the method cannot predict the ratio when one neutron generates offspring in different phase space regions or generates a random number of offspring. This paper presents a method to predict the correlation effect with the model of multitype branching processes (MBP). The method requires simulations for one generation of neutrons without knowing the source distribution and can predict the underestimation ratio for the cases where the traditional DPS approach does not work. The generation-to-generation correlation determines the convergence rate of active generations, the bias of variance estimator for each generation and the underestimation ratio of variance estimator for tallies averaged over active generations. The generation-to-generation correlation is characterized by the Auto-Correlation Coefficients (ACC) between tallies from different generations.United States. Dept. of Energy (Consortium for Advanced Simulation of Light Water Reactors. Contract DE-AC05-00OR22725