Search NASA⌕ Search

SEARCH · Search NASA

Results for “Multigroup”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Converged accelerated finite difference scheme for the multigroup neutron diffusion equation

Computer codes involving neutron transport theory for nuclear engineering applications always require verification to assess improvement. Generally, analytical and semi-analytical benchmarks are desirable, since they are capable of high precision solutions to provide accurate standards of comparison. However, these benchmarks often involve relatively simple problems, usually assuming a certain degree of abstract modeling. In the present work, we show how semi-analytical equivalent benchmarks can be numerically generated using convergence acceleration. Specifically, we investigate the error behavior of a 1D spatial finite difference scheme for the multigroup (MG) steady-state neutron diffusion equation in plane geometry. Since solutions depending on subsequent discretization can be envisioned as terms of an infinite sequence converging to the true solution, extrapolation methods can accelerate an iterative process to obtain the limit before numerical instability sets in. The obtained results have been compared to the analytical solution to the 1D multigroup diffusion equation when available, using FORTRAN as the computational language. Finally, a slowing down problem has been solved using a cascading source update, showing how a finite difference scheme performs for ultra-fine groups (104 groups) in a reasonable computational time using convergence acceleration. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Nonlinear diffusion acceleration for the multigroup transport equation discretized with S{sub N} and continuous FEM with rattlesnake

Nonlinear diffusion acceleration (NDA) can improve the performance of a neutron transport solver significantly especially for the multigroup eigenvalue problems. The high-order transport equation and the transport-corrected low-order diffusion equation form a nonlinear system in NDA, which can be solved via a Picard iteration. The consistency of the correction of the low-order equation is important to ensure the stabilization and effectiveness of the iteration. It also makes the low-order equation preserve the scalar flux of the high-order equation. In this paper, the consistent correction for a particular discretization scheme, self-adjoint angular flux (SAAF) formulation with discrete ordinates method (S{sub N}) and continuous finite element method (CFEM) is proposed for the multigroup neutron transport equation. Equations with the anisotropic scatterings and a void treatment are included. The Picard iteration with this scheme has been implemented and tested with RattleS{sub N}ake, a MOOSE-based application at INL. Convergence results are presented. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Space-Dependent Wielandt Shift Methods for Multigroup Diffusion Eigenvalue Problems

In the calculation of neutronic eigenfunctions and eigenvalues, it is often desirable to approximate the neutron transport equation by a diffusion equation that requires significantly less computational resources to solve. Even when a full transport solution is needed, the solution of the diffusion system can be used to accelerate iterative methods for calculating the transport eigenfunction and eigenvalue. The convergence rate of the basic power iteration method for eigenvalue problems is governed by the dominance ratio; realistic reactor core problems often have high dominance ratios and the power iteration method can converge slowly as a result. A common technique for accelerating the convergence of power iteration is the Wielandt shift (WS) method, which reduces the dominance ratio by 'shifting' the eigenvalue spectrum using an estimate of the desired eigenvalue. WS provides a significant speedup over power iteration if the eigenvalue estimate is close to the true eigenvalue, but it can be difficult to obtain such an estimate. In practice, the shift in the WS method can be dynamically updated in the iteration scheme, in a way that depends on the eigenvalue estimates from the most recent iterations. We present a physically-motivated Space-Dependent Wielandt Shift (SDWS) for solving multigroup diffusion eigenvalue problems. The space-dependence of the eigenvalue shift in SDWS enables a more effective acceleration of the power iteration scheme than WS at the beginning of the iteration scheme, when the current estimate of the eigenvalue is not close to the actual eigenvalue. Several variants of SDWS are discussed here, including an SDWS method that combines the strengths of SDWS (in the early iterations) with those of standard WS (in the later iterations). Numerical results from a 1-D multigroup diffusion problem demonstrate an order of magnitude speedup over power iteration and a 41% speedup over a standard WS technique. This speedup is problem-dependent and appears to be greater for 'more difficult' problems. In this summary, the term 'speedup' refers to a reduction in the number of iterations required to converge to the correct eigenvalue and eigenfunction. Because the scattering is treated fully implicitly (i.e., it is part of the left-hand side of the diffusion system and directly inverted), the computational cost of a single iteration does not vary significantly among the methods discussed in this summary. The number of iterations is therefore representative of the total computational cost for a method. We acknowledge that certain iterative solvers for linear systems (e.g., GMRES) require more computational time to converge when the system is nearly singular (i.e., when a very aggressive Wielandt shift is applied). Nonetheless, when using SDWS in the manner described in this summary, we have seen that the reduction in computational time from reducing the number of power iterations generally outweighs the extra computational time required by iterative solvers such as GMRES. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Multigroup cross section generation capability in GRIFFIN

GRIFFIN is an advanced reactor multiphysics application built on the object-oriented simulation environment (MOOSE) and is jointly developed by Idaho National Laboratory and Argonne National Laboratory. The cross section application programming interface, originally developed for the PROTEUS code, has been integrated into GRIFFIN to prepare cross sections for thermal reactor applications with heterogeneous geometries. Additional improvements have been made by implementing an on-the-fly slowing down method, a double heterogeneity treatment capability, and updating the procedure to generate the fine multigroup library. The cross section preparation capability in GRIFFIN was verified for graphite-moderated TRISO fuel-based reactor benchmark problems: unit-cell problems of VHTR and EMPIRE micro reactor and HTTR assembly problems. Eigenvalues and multigroup cross sections of GRIFFIN agreed very well with those of the continuous-energy Monte Carlo code Serpent2 within 200 pcm in eigenvalue and 2% in cross sections. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

Reduced-Order Modeling of Multigroup Neutron Cross Sections for High-Temperature Gas-cooled Reactors

Abstract – Deterministic neutronics calculations rely on multigroup neutron cross section libraries, which consist of databases of tabulated values, used to calculate the neutron cross sections through multivariate linear interpolation. However, interpolation of the multidimensional cross section data becomes memory inefficient and time consuming as the number of tabulations increases, significantly slowing down the neutronics calculation, especially in the case of microscopic cross section libraries where every isotope (on the order of hundreds) has its own set of specific reactions and cross sections. In order to address this challenge, this work constructs efficient and robust reduced-order models (ROMs) of the multi-group cross sections to support the Griffin simulation of high-temperature gas-cooled reactors (HTGRs). The first part of the study investigates the linearity of the multigroup cross section data across isotopes, reaction types, and energy groups on pre-generated datasets for the purpose of dimensionality reduction. Secondly, a down-selection of ROM techniques is presented on representative classical machine learning (ML) techniques, including variants of linear regression, kernel-based methods, tree-based algorithms, and artificial neural networks. The selection criteria jointly consider the memory efficiency, predictive accuracy, prediction speed, and scalability in comparison to the multidimensional interpolation. Among all the ML techniques, deep neural networks (DNNs) have proven to be the best selection with sufficient accuracy, high robustness, good memory efficiency, great scalability, and superior flexibility. DNNs have been trained for all isotopes in this work and systematic Griffin testing is ongoing to ensure the feasibility of this ROM technique for predicting cross section and reducing memory requirements without a significant sacrifice in computational performance.

42 - ENGINEERING↗
DOE OSTI2019

Development of the multigroup cross section library for the CASL neutronics simulator MPACT: Method and procedure

The MPACT neutronics module of the Consortium for Advanced Simulation of Light Water Reactors (CASL) core simulator is a 3D whole core transport code being developed for the CASL toolset known as the Virtual Environment for Reactor Analysis (VERA). Key characteristics of the MPACT code include a subgroup method for resonance self-shielding and a whole-core transport solver with a 2D/1D synthesis method. The AMPX and SCALE code packages have been significantly improved to include intermediate resonance parameters, as well as new modules to enhance the accuracy of resonance data and scattering matrices for the Bondarenko approach and transport cross sections of hydrogen. In addition, CASL XSTools have been developed to generate the MPACT multigroup cross section library. A simple super-homogenization method for 238U has been developed to resolve reaction rate discrepancy issues caused by angle-dependent total cross sections, poor scattering matrices, and a poor resonance interference model at coarse group structure. Here, due to the limitation of computing capacity that can occur even in high performance computing, a new 51-group structure has been developed for efficient simulation that is applicable for both pressurized water reactor (PWR) and boiling water reactor (BWR) simulations. A new ENDF/B-VII.1 MPACT 51-group library has been developed using the AMPX/SCALE and XSTools code packages, and it has been verified and validated by performing various benchmark calculations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2019

SCALE/AMPX multigroup libraries for sodium-cooled fast reactor systems

New multigroup cross section libraries and associated covariance files that are optimized for the analysis of sodium-cooled fast reactors were generated with the AMPX tools distributed with the SCALE code system. These new libraries account for the fast neutron flux spectrum with sufficient resolution of resonances in the higher energy range to reproduce continuous-energy reference results and to provide the basis for sensitivity and uncertainty analyses of fast spectrum systems with the SCALE code system. The performance of the new libraries was investigated in terms of the eigenvalue, the neutron flux and reaction rates in criticality calculations, and the generation of group constants. A library using 302 energy groups and a fast neutron flux spectrum as the weighting function led to very good agreement with reference continuous-energy results. As a result, the performance of the new library was demonstrated in calculations of experiments from the International Criticality Safety Benchmark Evaluation Project handbook.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Space-energy separated representations for multigroup neutron diffusion using proper generalized decompositions

Proper generalized decomposition (PGD) can be described as a numerical extension of separation of variables and thus be employed as a solution technique for multi-dimensional problems, where dimensions should be understood in the phase-space context of the governing law at hand. This paper presents a PGD approach on efficiently solving problems involving multigroup neutron diffusion. Two PGD approaches are described: space-only and space-energy decompositions. Numerical results include 2-D and 3-D examples with two-, seven-, and 145-group structures. The PGD solutions are compared against traditional multi-dimensional finite element discretization. For few-group problems, both PGD approaches prove effective for mildly heterogeneous geometries, but showed reduced performance with increasing heterogeneity. The space-energy representation was found to be slower than the space-only approach for two-group problems, but proved more effective for seven-group problems. For even larger numbers of groups, the space-energy PGD decomposition was very effective at reducing the computational time.

42 ENGINEERING↗
DOE OSTI2024

Efficient continuous Energy-Multigroup hybrid depletion scheme using the Shift Monte Carlo code. Part I: Energy condensation sensitivity analysis

Monte Carlo (MC) codes coupled to depletion solvers are increasingly used to provide high fidelity fuel cycle modeling capabilities. Here, these coupled depletion-MC tools produce accurate results in general but can experience nonphysical spatial oscillations when time steps are large or when a system’s dominance ratio approaches unity. Two substepping techniques have been developed previously to remedy and dampen these spatial oscillations without needing to reduce step sizes. The first approach relied on higher-order techniques to account for spectral changes within steps (extrapolation and interpolation techniques). The second approach used the first order perturbation (FOP) theory to account for the change in the one-group spatial flux distribution within steps. This paper develops a hybrid depletion methodology which, in a way, combines how the flux is handled in both substepping techniques. Specifically, the multigroup (MG) MC Shift code is used to update the flux distribution within steps rather than a one-group FOP solver. A fully reflected pincell is investigated, which is not spatially dependent in the MG representation. Thus, the analysis in this paper is an initial demonstration of hybrid depletion. An upcoming companion paper will focus on how the hybrid depletion dampens spatial oscillations. The hybrid depletion approach is verified to be consistent with previous constant extrapolation depletion (CED) methods. This paper finds that the hybrid CED exhibits some error in the eigenvalue and one group constants within macro steps. To address this discrepancy, a simple interpolation scheme (CELI) is investigated. This work found that CELI sufficiently addresses the discrepancy in spectrum for macro steps up to 100 days. Overall, this work demonstrates that the hybrid depletion method can significantly reduce the number of high fidelity MC executions in a MC-coupled depletion with an acceptable eigenvalue error.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2015

Gray and multigroup radiation transport models for two-dimensional binary stochastic media using effective opacities

One-dimensional models for the transport of radiation through binary stochastic media do not work in multi-dimensions. In addition, authors have attempted to modify or extend the 1D models to work in multidimensions without success. Analytic one-dimensional models are successful in 1D only when assuming greatly simplified physics. State of the art theories for stochastic media radiation transport do not address multi-dimensions and temperature-dependent physics coefficients. Here, the concept of effective opacities and effective heat capacities is found to well represent the ensemble averaged transport solutions in cases with gray or multigroup temperature-dependent opacities and constant or temperature-dependent heat capacities. In every case analyzed here, effective physics coefficients fit the transport solutions over a useful range of parameter space. The transport equation is solved with the spherical harmonics method with angle orders of n=1 and 5. Although the details depend on what order of solution is used, the general results are similar, independent of angular order.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Multigroup Examination of Nickel-Reflected HEU System

Critical configurations of HEU-MET-FAST-003 (HMF-003) from the International Criticality Safety Benchmark Evaluation Project Handbook were modeled for addition into the Verified, Archived Library of Inputs and Data maintained at Oak Ridge National Laboratory. HMF-003 contains models of a highly enriched uranium sphere with a spherical metal reflector of natural uranium, tungsten carbide, or nickel. For these simple models, good agreement is expected between the k eff calculated with continuous-energy (CE) and multigroup (MG) transport. However, using the CSAS5 sequence of the SCALE 6.2.4 package, the 8 in. thick nickel reflector model resulted in a difference of around 1.2 % Δ k . Results presented a clear indication of poor performance for the SCALE 252-group based on ENDF/B-VII.1 cross section library for this model. The bias was investigated over a range of nickel thickness and then compared with other MG libraries available in SCALE 6.2.4. As the nickel thickness increases, the MG k eff deviates from the CE result, confirming a performance issue with the MG calculation. Additionally, the reactions were compared between the two libraries to help determine the cause of k eff bias. Finally, additional MG libraries within SCALE 6.3 and based on ENDF/B-VII.1 and ENDF/B-VIII were reviewed. The 302-group and 1597-group result in significant improvements compared with the 252-group library. Nickel cross sections were modified from ENDF/B-VII.1 to ENDF/B-VIII. For the ENDF/B-VIII library, the deviation between the CE libraries and MG libraries is less pronounced than for ENDF/VII.1, except for the 1597-group. This examination clearly indicates the importance of validating calculations with applicable benchmark experiments and caution when using MG libraries.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

Multigroup Free-atom Doppler-broadening Approximation. Experiment

The multigroup energy Doppler-broadening approximation agrees with continuous energy Dopplerbroadening generally to within ten percent for the total cross sections of 1 H, 56 Fe, and 235 U at 250 lanl. Although this is probably not good enough for broadening from room temperature through the entire temperature range in production use, it is better than any interpolation scheme between temperatures proposed to date, and may be good enough for extrapolation from high temperatures. The method deserves further study since additional improvements are possible.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2013

Release of the mtmg01ex NDI Neutron Multigroup Data Library

We have released the multi-temperature neutron multigroup transport library mtmg01ex, consisting of 181 isotope tables from mtmg01 and 18 element tables calculated from the isotope tables, all at 15 temperatures. These data, based primarily on the evaluations that produced the lanl2006 library, include gamma production and americium branching data. They were subjected to our standard production library testing. Because there are still known problems with and unanswered questions about multi-temperature data, including data size and load time issues, we do not recommend this data for general use; however, its quality is good enough for production release, and we request user help in addressing the remaining problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

TRT Compton Scattering Data: Comparisons between LLNL and LANL: Multigroup

This memo is one of a pair of reports comparing Compton scattering data in the context of thermal radiation transport (TRT). This document focuses on Multigroup (MG) data while the other report focuses on Pointwise (PW) data. These complementary analyses, via PW comparisons, show if the same physics are used and if fundamental bugs are present, and, via MG comparisons, quantify macroscopic Compton effects such as mean amplification factors. No averaging of Compton data over photon energy is done for the PW comparisons, while lab-dependent numerical resolution choices become relevant for the MG comparisons. For this MG-comparison report, we make and document the numerical assumptions we use to convert LLNL PW data into MG data. This document plots and quantifies differences in Compton scattering data between MG LANL and LLNL for four disparate temperatures on a logarithmically-spaced photon-energy grid. In addition to LANL and LLNL data, we add a third and fourth independent vote from data generated by Brooks Kinch (LANL postdoc). For the purposes of these comparisons, we neglect induced scattering.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Multigroup Scattering in Monte Carlo Radiation Transport Codes [Slides]

Legendre truncations to multigroup scattering distributions are not amenable to Monte Carlo sampling due to negative values. We have implemented two moment-preserving methods in MGMC that capture the shape of the truncation, are non-negative over [-1, 1], and can be efficiently sampled on CPUs and GPUs. MGMC can now simulate neutrons with anisotropic scattering mechanics and MGMC shows good agreement with LANL production codes PARTISN.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

The Influence of Demographic Variables on the Pooled Rideshare Acceptance Model Multigroup Analyses (PRAMMA)

Building on our prior research with a national survey sample of 5385 US participants, the Pooled Rideshare Acceptance Model (PRAM) was built upon two factor analyses. This exploratory study extends the PRAM framework using the Pooled Rideshare Acceptance Model Multigroup Analyses (PRAMMA) to examine how 16 demographic variables influence and interact with the acceptance of Pooled Rideshare (PR), filling a gap in understanding user segmentation and personalization. Using a national sample of 5385 US participants, this methodological approach allowed for the evaluation of how PRAM variables such as safety, privacy, service experience, and environmental impact vary across diverse groups, including gender, generation, driver’s license, rideshare experience, education level, employment status, household size, number of children, income, vehicle ownership, and typical commuting practices. Factors such as convenience, comfort, and passenger safety did not show significant differences across the moderators, suggesting their universal importance across all demographics. Furthermore, geographical differences did not significantly impact the relationships within the model, suggesting consistent relationships across different regions. The findings highlight the need to move beyond a “one size fits all” approach, demonstrating that tailored strategies may be crucial for enhancing the adoption and satisfaction of PR services among various demographic groups. The analyses provide valuable insight for policymakers and rideshare companies looking to optimize their services and increase user engagement in PR.

moderator↗
DOE OSTI2017

Multigroup Monte Carlo on GPUs: Comparison of history- and event-based algorithms

This article presents an investigation of the performance of different multigroup Monte Carlo transport algorithms on GPUs with a discussion of both history-based and event-based approaches. Several algorithmic improvements are introduced for both approaches. By modifying the history-based algorithm that is traditionally favored in CPU-based MC codes to occasionally filter out dead particles to reduce thread divergence, performance exceeds that of either the pure history-based or event-based approaches. The impacts of several algorithmic choices are discussed, including performance studies on Kepler and Pascal generation NVIDIA GPUs for fixed source and eigenvalue calculations. Single-device performance equivalent to 20–40 CPU cores on the K40 GPU and 60–80 CPU cores on the P100 GPU is achieved. Last, in addition, nearly perfect multi-device parallel weak scaling is demonstrated on more than 16,000 nodes of the Titan supercomputer.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Development of the multigroup cross section library for the CASL neutronics simulator MPACT: Verification

The MPACT neutronics module of the Consortium for Advanced Simulation of Light Water Reactors (CASL) core simulator is a 3D whole core transport code being developed for the CASL toolset, known as the Virtual Environment for Reactor Analysis (VERA). Key characteristics of the MPACT code include a subgroup method for resonance self-shielding and a whole-core transport solver with a 2D/1D synthesis method. Depletion capability is supported by coupling SCALE-ORIGEN with MPACT. A new ENDF/B-VII.1 MPACT 51-group library has been developed by using the AMPX/SCALE and CASL-XSTools code packages based on the procedure introduced in the companion paper, “Development of the Multigroup Cross Section Library for the CASL Neutronics Simulator MPACT: Method and Procedure.” The cross section library generation procedure, cross section library, and MPACT transport capability have been verified by performing various benchmark calculations and comparing the benchmark results to the continuous-energy (CE) Monte Carlo results. Furthermore, the code-to-code comparison for the benchmarks shows that the CASL neutronics simulator MPACT and its 51-group library are working reasonably.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗