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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

A flexible linear diffusion acceleration to k-eigenvalue neutron transport with SN discontinuous finite element method

In this paper, we derive a flexible linear diffusion acceleration (LDA) for k-eigenvalue neutron transport discretized with discontinuous finite element method (DFEM) and discrete ordinates(SN). This LDA is based on our two pieces of previous works: the flexible non linear diffusion acceleration (NDA) for DFEM-SN and LDA for k-eigenvalue neutron transport using pre-conditioned Jacobian-free Newton-Krylov with self-adjoint angular flux (SAAF), continuous finite element method(CFEM), and SN. We point out the differences between LDA and NDA for DFEM-SN and the difference between DFEM-SN and SAAF-CFEM-SN for LDA. Numerical tests are presented to compare the convergence behaviour of NDA and LDA. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Divergence Reduction in Monte Carlo Neutron Transport with On-GPU Asynchronous Scheduling

While Monte Carlo Neutron Transport (MCNT) is near-embarrasingly parallel, the effectively unpredictable lifetime of neutrons can lead to divergence when MCNT is evaluated on GPUs. Divergence is the phenomenon of adjacent threads in a warp executing different control flow paths; on GPUS, it reduces performance because each work group may only execute one path at a time. The process of Thread Data Remapping (TDR) resolves these discrepancies by moving data across hardware such that data in the same warp will be processed through similar paths. A common issue among prior implementations of TDR is the synchronous nature of its remapping and processing cycles, which exhaustively sort data produced by prior processing passes and exhaustively evaluate the sorted data. In another work, we defined a method of remapping data through an asynchronous scheduler which allows for work to be stored in shared memory and deferred arbitrarily until that work is a viable option for low-divergence evaluation. This article surveys a wider set of cases, with the goal of characterizing performance trends across a more comprehensive set of parameters. These parameters include cross sections of scattering/capturing/fission, use of implicit capture, source neutron counts, simulation time spans, and tuned memory allocations. Across these cases, we have recorded minimum and average execution times, as well as a heuristically tuned near-optimal memory allocation size for both synchronous and asynchronous scheduling. Across the collected data, it is shown that the asynchronous method is faster and more memory efficient in the majority of cases, and that it requires less tuning to achieve competitive performance.

Computer Science↗
DOE OSTI2025

Single Grid Error Estimation for Neutron Transport Solvers

The method of nearby problems (MNP) is a solution verification technique that does not require the use of multiple spatial grids. To estimate spatial discretization error without requiring a high-fidelity spatial grid, an analytical curve fit is interpolated from the numerical solution. The residual between the curve fit solution and numerical solution is calculated and added as an additional source term to the governing equation. The nearby solution is estimated using the updated source term and boundary conditions to remain consistent with the curve fit interpolation. The nearby solution can be compared to the curve fit solution as a discretization error estimation while using a single spatial grid. Without the use of higher fidelity spatial grids, the MNP is able to approximate the spatial discretization error, a facet of solution verification. The application of the method of nearby problems is presented for one- and two-dimensional neutron transport problems for both fixed source and criticality problems on the spatial variable. The fixed source results demonstrate the effectiveness of nearby problems for spatial error identification using the discrete ordinates method. Criticality results are shown to identify area of high spatial error for the C5G7 problem as well as for the discrete ordinates solver. A novel approach of combining the capabilities of Monte Carlo with the discrete ordinates nearby problems is presented for one- and two-dimensional fixed source problems. In conclusion, the MNP demonstrates its effectiveness at identifying spatial error on a single structured grid with a wide variety of neutron transport problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Formulation of the density eigenvalue problem in neutron transport for relevant engineering applications

A new formulation of the density eigenvalue problem for the neutron transport equation is presented. This new eigenvalue, named ζ eigenvalue can be introduced freely in the transport model, acting on a selected portion of the phase space. Despite its broader applications and its connection with the nature of the transport operator, the ζ eigenvalue has been presented here mainly as a design-oriented technique for the efficient evaluation of the critical concentration for a specific nuclide (or mixture of nuclides). This new eigenvalue is particularly adequate to study the definition of the material composition in the criticality design process of a multiplying system. The method is then applied for the study of classical problems such as the critical moderation ratio and the poison concentration to control the reactor. Some results are presented in one dimensional configuration using the multi- group spherical harmonics approach. This eigenvalue formulation proves to be a convenient and useful way to attain criticality, also for complex, realistic systems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2019

An a posteriori residual-based spatial discretization error estimator for S N neutron transport

The “residual source estimator”, an implicit residual-based spatial discretization error estimator for S N neutron transport methods, is introduced. The estimator uses an approximation of the residual as a fixed source for an analogous transport problem whose solution is the error estimate, using the same transport operator as the original numerical solution. The complete derivation of the residual source estimator, the approximation of the residual, and higher-order derivatives is included. The performance of the residual source estimator for 0-order DGFEM is tested against reference solutions. For problems with true solutions discontinuous in the first derivative across the singular characteristics, the residual source estimator is generally accurate, precise, and computationally affordable compared to similar estimators. It suffers in problems where solutions are discontinuous, particularly when the discontinuity inflicts significant inaccuracies on the discrete solution; however, compared to other estimators, which suffer similarly, it remains a competitive option.

42 ENGINEERING↗
DOE OSTI2020

Multigroup Constant Calculation with Static α-Eigenvalue Monte Carlo for Time-Dependent Neutron Transport Simulations

Herein, multigroup constants for deterministic methods that preserve the time-dependent physics of the neutron transport equations are derived. Alternative multigroup constant weighting spectra are discussed: (1) the fundamental k-eigenfunction, (2) the fundamental α-eigenfunction, and (3) a composite of several α-modes. To generate the fundamental α-eigenfunction for calculating the multigroup constants, a static fundamental α-eigenvalue method is implemented into the open source Monte Carlo code OpenMC. Several static and kinetic problems are devised to verify the implementations and to investigate the relative performance of the alternative multigroup constant weighting spectra. Results emphasize that as a multigroup constant weighting spectrum, the fundamental α-eigenfunction offers physical characteristics that make it advantageous (in producing accurate solutions) over the typically used fundamental k-eigenfunction.

42 ENGINEERING↗
DOE OSTI2024

Neutron transport methods for multiphysics heterogeneous reactor core simulation in Griffin

Griffin is a reactor physics application based on the Multiphysics Object-Oriented Simulation Environment (MOOSE). This work discloses the methods, algorithms, and implementation for simulating heterogeneous reactor dynamics models. Griffin utilizes a discontinuous finite-element method with discrete ordinates (DFEM-S ) to discretize the field variable of the multigroup neutron transport equation. Multiphysics feedback is handled using two-step tabulated cross-section methodology. Feedback quantities are evaluated using the MOOSE-MultiApp system to couple various engineering phenomena, such as heat conduction and thermal fluids. The multiphysics DFEM-S system is solved using fixed-point iteration with a fully asynchronous parallel sweeper, unstructured coarse-mesh finite difference acceleration, and a multi-timescale improved quasi-static method scheme. The implementation is applied to a multiphysics microreactor model, with two transients: one initiated by a single heat-pipe failure and another by control drum rotation. Importantly, these examples demonstrate the ability of Griffin to tractably solve the neutron transport equation considering seven independent variables and feedback.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1996

A Systematic Solution Approach for Neutron Transport Problems in Diffuse Regimes

A systematic solution approach for the neutron transport equation, based on a least-squares finite-element discretization, is presented. This approach includes the theory for the existence and uniqueness of the analytical as well as of the discrete solution, bounds for the discretization error, and guidance for the development of an efficient multigrid solver for the resulting discrete problem. To guarantee the accuracy of the discrete solution for diffusive regimes, a scaling transformation is applied to the transport operator prior to the discretization. The key result is the proof of the V-ellipticity and continuity of the scaled least-squares bilinear form with constants that are independent of the total cross section and the absorption cross section. For a variety of least-squares finite-element discretizations this leads to error bounds that remain valid in diffusive regimes. Moreover, for problems in slab geometry a full multigrid solver is presented with V(1, 1)-cycle convergence rates approximately equal to 0.1, independent of the size of the total cross section and the absorption cross section.

Manteuffel, T. A.↗
DOE OSTI2023

Multigroup Neutron Transport Using a Collision-Based Hybrid Method

A collision-based hybrid algorithm for the discrete ordinates approximation of the neutron transport equation is extended to the isotropic multigroup setting. The algorithm uses discrete energy and angle grids at two different resolutions and approximates the fission and scattering sources on the coarser grids. The coupling of a collided transport equation, discretized on the coarse grid, with an uncollided transport equation, discretized on the fine grid, yields an algorithm that, in most cases, is more efficient than the traditional multigroup approach. In conclusion, the improvement over existing techniques is demonstrated for time-dependent problems with different materials, geometries, and energy groups.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Eigenmode Analysis of Pulsed Neutron Transport Simulations

We discuss the time dependent behavior of some simple pulsed neutron simulations of subcritical problems in slab geometry. Our intent is to investigate the eigenvalue structure of the discretized neutron transport equation and to show under some reasonable assumptions that a dominant time eigenvalue exists that has a nonnegative eigenvector that determines the long time dependent behavior of the solution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

On the convergence of the fixed point method for solving neutron transport alpha eigenvalue problems

It was shown that the Fixed Point Method (also known as the Rayleigh Quotient Method) is several times faster than the Critical Search Method for solving neutron transport alpha eigenvalue problems. It was also shown that the Fixed Point Method is able to determine the alpha eigenvalues of sub-critical systems that are beyond the reach of the Critical Search Method. Despite these significant advances, the Fixed Point Method remains an unproven algorithm. Here, this report provides a proof.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Analytical benchmark solution for 1-D neutron transport coupled with thermal conduction and material expansion

In this work we present fully analytical solutions for a class of finite, homogeneous, 1-D slab benchmark problems with nonlinear temperature feedback effects. The proposed class of benchmarks include multiplicative 1-D neutron transport (limited to quasistatic S{sub 2} with μ = ±1) coupled with thermal conduction, convection, Doppler broadening, and expansion effects along the length of the slab. This class of benchmark models, along with the corresponding analytical solutions, are valuable for validating multiphysics analysis frameworks that support coupled neutronics/thermal/structural calculations. Analytical solutions for the benchmarks are obtained by introducing an ansatz that the equilibrium flux and temperature distributions in the slab have the same shape. Specific values for the total microscopic cross section, σ{sub t,0}, and conductive heat transfer coefficient, h, that satisfy the assumed ansatz are then determined. A discussion of the procedure for generating benchmark models and analytical solutions is provided, along with numerical results for an example set of model parameters and thoughts on practical applications of the benchmarks for multiphysics code validation. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Experimental validation of a high fidelity Monte Carlo neutron transport model of the MIT graphite exponential pile

High-fidelity modeling and simulation were performed for the MIT graphite exponential pile (MGEP) using Monte Carlo neutron transport codes OpenMC and MCNP, and the results were validated by experimental data. The MGEP is being used as the test bed for the design of an autonomous control system for the pile's neutron flux distribution. The main contribution of this work is to generate the training data sets of neutron flux distributions with different locations of control rods that perturb the neutron flux profiles. First, code -to-code cross verification between OpenMC and MCNP was performed to ensure consistency of the numerical modeling within statistical uncertainties. To validate the accuracy of this high-fidelity model, a series of neutron flux measurements were conducted using a Helium-3 (He-3) neutron detector on a mobile platform that is placed inside the pile. Second, the neutron flux profiles were measured in four vertical layers of interest, and compared to the corresponding simulation results. The comparison results shows that the root mean square error is less than 2.5% in the two upper layers, and less than 4.5% in all four measured layers. Here the results validated the accuracy of the modeling and simulation. Finally, the relative change of the neutron flux profiles from moving control rods was analyzed, which identified the layer that has the best sensitivity regarding the control rods movements. Thus, this work identified and provided training data sets of both simulated and experimental neutron flux profiles in the most sensitive layer, paving the path forward to the real-time experimental demonstration of the autonomous control system.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Reduced-order modeling of neutron transport separated in energy by Minimax Proper Generalized Decomposition

In this article, we demonstrate a Petrov-Galerkin Proper Generalized Decomposition (PGD) known as Minimax PGD for modeling neutron transport separated in energy. To compare the Minimax with the classical Galerkin PGD, we assess both on a model problem of UO{sub 2} or Mixed Oxide (MOX) fuel pins in an infinite lattice with 3 industry-standard energy meshes. We find the Minimax PGD achieves a superior decomposition to Galerkin PGD, both with and without update of the energy modes. This suggests Minimax PGD may be more computationally efficient, provided this reduction in modes (to achieve a given accuracy) outweighs the cost of solving the necessary adjoint problems. In either case, we note that PGD offers an a priori Reduced-Order Model (ROM) which may be dramatically cheaper to solve than the full-order model, especially in problems with fine to ultrafine energy meshes. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

The Effect of the Flux Separability Approximation on Multigroup Neutron Transport

The angular dependence of flux-weighted multigroup cross sections is commonly neglected when generating multigroup libraries. The error of this flux separability approximation is typically not isolated from other error sources due to a lack of availability of library generation and corresponding solvers that cannot relax this approximation. These errors can now be isolated and quantified with the availability of a multigroup Monte Carlo transport and multigroup library-generation capability in the OpenMC Monte Carlo transport code. This work will discuss relevant details of the OpenMC implementation, provide an example case useful for detailing the type of errors one can expect from making the flux separability approximation, and end with more realistic problems which show the impact of the approximation and highlight how it can strongly arise from an energy-dependent resonance absorption effect. Since the angle-dependence is intrinsically linked to the energy group structure, these examples also show that relaxing the flux separability approximation with angle-dependent cross sections could be used to reduce either the fine-tuning required to set a multigroup energy structure for a specific reactor type or the number of energy groups required to obtain a desired level of accuracy for a given problem. This trade-off could increase the costs of generating multigroup cross sections, and has the potential to require more memory for storing the multigroup library during the transport calculations, but it can significantly reduce the computational time required since the runtime of a discrete ordinates or method of characteristics neutron transport solver scales roughly linearly with the number of groups.

42 ENGINEERING↗
DOE OSTI2022

Predicting deviations in ex-core detector response in Krsko NPP during an earthquake with Monte-Carlo neutron transport methods

To study the response of ex-core detectors during an earthquake, an approach using Monte Carlo code MCNP was developed. As a first step to predict the response of the ex-core detectors a detailed MCNP model of the Krsko reactor core was created. A detailed MCNP core model was used to calculate 3D power distributions inside the core. Calculated power distributions were verified by comparison to the CORD-2 calculations, which is currently used for core design calculation verification of the Krsko nuclear power plant. Due to the outside the core position of the neutron detectors, the hybrid code ADVANTG is used to generate weight windows to speed up neutron transport outside the reactor core. To be able to use ADVANTG, fixed neutron source had to be reconstructed from the criticality core calculation. It was found that the power range ex-core detector movement has a negligible effect on the value of the thermal neutron flux at the active part of the detector. However, the 5 cm radial movement of the intermediate-range detector leads to 7 % - 8 % change in thermal neutron flux within the active intermediate-range detector region. The analysis continued with the evaluation of the effect of core barrel movement on the ex-core detector response. It was determined that the 2 mm core barrel radial oscillation can lead to ∼ 4% change in thermal neutron flux within the active detector region. It was evaluated that reactor core movement inside the baffle can lead up to ∼ 1.9% and ∼ 1.3% deviation in power-range and intermediate-range detector signal respectively. Analysis showed that the mechanical movement of ex-core neutron detectors could not explain the fluctuations in the ex-core detector signal. However, combined core barrel and reactor core inside baffle oscillations could be a probable reason for the observed fluctuations in the ex-core detector signal during an earthquake. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗