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All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Derivation of Effective Properties Based on Porous Scale Simulations Using Filtering Techniques

This study presents a method for derivation of effective properties at the interface and in-depth of porous materials. The method defines a Representative Elementary Volume (REV) and applies filtering techniques to computer effective properties such as porosity and flow quantities, such as velocity and pressure. The script, developed to process the data was tested on the VTK type files that contain the mesh information and the flow solution. The method allows to choose between two types of filters, such as cellular and top-hat and define the size of the REV and number of samples along the domain. Extraction of the REV from the domain is performed to exact boundaries requested for the user. This is done using a triangulation technique and cutting through the cells to comply to the requested boundaries of the volume. The method can be applied to both structured and unstructured meshes. Filtering the material porosity and flow quantities involves integration of the numerical data. The algorithm provides three integration methods, such as Riemann sum, Monte Carlo and Quadrature rule to perform the integration. The Monte-Carlo technique permits the use of either uniform or linearly spaced distribution of points. The Quadrature rule is currently applicable to tetrahedral element types. The Monte Carlo and Quadrature rule methods require interpolation of the flow quantities at the sample points. For interpolation, two methods were tested and are readily available, Gaussian interpolation and re-sampling. It has been shown that re-sampling method has better consistency and acceptable accuracy in interpolation of the data. The algorithm was written in Python language and uses a number of modules. The major module besides numpy is PyVista. It is used to process the computational domain, clip the REV and interpolate the data. Quadrature rule integration was performed using a quadpy module. ParaView software was used externally to convert the flow solution to the VTK (or more specifically VTU) format. Integration of ParaView in the same environment with PyVista encountered problems and could not be implemented in this work. The developed algorithm is expected to be applicable to unstructured meshes and more complex porous structures as soon as the data can be passed in VTK type format. With the report is provided Python script for filtering the solution and a Matlab script for simple generation and processing of 2-D and 3-D porous channel geometries. The two scripts don't communicate.

Alexsander Zibitsker↗
NASA NTRSDate not supplied

Magnetic Mapping in the Inner Magnetosphere using Kamodo

Many models require specialized access and interpolation schemes to effectively extract and interpolate their outputs. In particular, the Block-Adaptive Tree Solarwind Roe Upwind Scheme (BATSRUS) component of the Space Weather Modeling Framework (SWMF) requires Kamodo to take advantage of its block-based adaptive grid structure, and the Lyon-Fedder Mobarry magnetosphere model (or its successor GAMERA) needs a scheme that appreciates the distorted spherical arrangement of grid vertices on a non-orthogonal grid. With the flythrough layer developed by Ringuette et al. (SH42E-2337), the underlying model readers have been adapted to use multiple time steps in a single Python session to perform 4- dimensional interpolations in time and space. Kamodo now utilizes lazy interpolation that loads data only when needed. We present the successful integration of SWMF/BATSRUS magnetosphere access and interpolation into the new 4D Kamodo framework utilizing an external library of C code. Through function composition, Kamodo facilitates the calculation of derived quantities and the transformation of positions and vectors into different coordinate systems. This work is a significant step towards performing field line tracing in Kamodo with SWMF magnetosphere outputs.

Lutz Rastaetter↗
DOE OSTI2016

Dimensionality Reduction Algorithms for Big Nuclear Data Streams with Application to SCALE Cross Sections

A central problem in performing accurate nuclear reactor simulations is the ability to capture the changes in the few group microscopic cross sections as functions of system state, e.g. moderator density, fuel temperature, or neutron spectrum, and time and/or burnup of the fuel. For most reactor simulation scenarios, this results in huge data stream, which must be interpolated as needed by downstream calculations (e.g., core-wide simulation). This is typically accomplished by using sophisticated interpolating functions to capture the few-group variations over the wide range of conditions expected during operation. To address handling this big data, this paper explores the use of dimensionality reduction (DR) techniques to identify the true dimensionality of the data prior to its use in the calculations. This could significantly reduce the computational cost required for data processing/manipulation, thus reducing a significant portion of the total calculations time. By way of an example, in the current version of the ORIGEN-ARP module, the assembly-averaged microscopic cross sections at different conditions, e.g., fuel enrichments, irradiation history and water density, which are calculated using the TRITON sequence and interpolated on-demand by the ARP module to model assembly depletion for a wide range of assembly types (e.g. Westinghouse 17x17 and GE 9x9) over a wide range of conditions. This approach typically results in ∼1 GB per assembly type, which although not insurmountable, can be impractical for distribution. and it is the premise of this paper that most of this data is heavily correlated and hence can take great benefit of condensation via DR. To demonstrate DR, the proposed algorithm is applied to the nuclear data streams generated by SCALE 6.1. Using the depletion sequence (TRITON), microscopic cross sections are calculated for a mixed oxide (MOX) fuel assembly design at a representative range of fuel enrichments and fuel burnup. In conventional core simulators, multi dimensional interpolation of these cross sections is used to provides neutronics feedback due to local conditions without returning to expensive TRITON calculations for every change. This paper shows that dimensionality reduction can help compress the size of the cross section data without sacrificing the accuracy of their reconstruction at all conditions of interest. This work explores the application of dimensionality reduction algorithms to nuclear data streams typically employed in support of conventional full-core reactor calculations which rely on interpolation of pre-calculated microscopic cross sections. In particular, analysis of the few group MOX cross sections revealed that a large degree of dependencies exist between the few-group cross sections, which can be revealed via range-finding algorithms. Specifically, correlations between different reaction types for the same isotope have been identified, and correlations between different enrichments and correlations across different isotopes have been identified. This paper demonstrates that the reduction errors can be quantified, and they are uncorrelated with the range of variations for the various cross sections. In future work, we will focus on identifying the smallest rank that takes into account all types of correlations across the range of conditions used to model cross section variations. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Feasibility of DEIM for retrieving the initial field via dimensionality reduction

When parameter estimation is solved in a high-dimensional space, the dimensionality reduction strategy becomes the primary consideration for alleviating the tremendous computational cost. Here, the discrete empirical interpolation method (DEIM) is explored to retrieve the initial condition (IC) by combining the polynomial chaos (PC) based ensemble Kalman filter (i.e. PC-EnKF), where a non-intrusive PC expansion is considered as a surrogate model in place of the forward model in the prediction step of the ensemble Kalman filter, resulting in fewer forward model integrations but with a comparable accuracy as Monte Carlo-based approaches. The DEIM acts as a hyper-reduction tool to provide the low-dimensional input for the high-dimensional initial field, which can be reconstructed using the information on the sparse interpolation grid points that is adaptively obtained through PC-EnKF data assimilation method. Thus an innovative framework to reconstruct the IC is developed. The detailed procedure at each assimilation iteration includes: the determination of the spatial interpolation points, the estimation of the initial values on the interpolation locations using the optimal observations, and the reconstruction of IC in the full space. The current study uses the reconstruction field of initial conditions of the Navier-Stokes equations as an example to illustrate the efficacy of our method. The experimental results demonstrate the proposed algorithm achieves a satisfactory reconstruction for the initial field. The proposed method helps to extend the applicable area of DEIM in solving inverse problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

SU-F-I-08: CT Image Ring Artifact Reduction Based On Prior Image

Purpose: In computed tomography (CT) system, CT images with ring artifacts will be reconstructed when some adjacent bins of detector don’t work. The ring artifacts severely degrade CT image quality. We present a useful CT ring artifacts reduction based on projection data correction, aiming at estimating the missing data of projection data accurately, thus removing the ring artifacts of CT images. Methods: The method consists of ten steps: 1) Identification of abnormal pixel line in projection sinogram; 2) Linear interpolation within the pixel line of projection sinogram; 3) FBP reconstruction using interpolated projection data; 4) Filtering FBP image using mean filter; 5) Forwarding projection of filtered FBP image; 6) Subtraction forwarded projection from original projection; 7) Linear interpolation of abnormal pixel line area in the subtraction projection; 8) Adding the interpolated subtraction projection on the forwarded projection; 9) FBP reconstruction using corrected projection data; 10) Return to step 4 until the pre-set iteration number is reached. The method is validated on simulated and real data to restore missing projection data and reconstruct ring artifact-free CT images. Results: We have studied impact of amount of dead bins of CT detector on the accuracy of missing data estimation in projection sinogram. For the simulated case with a resolution of 256 by 256 Shepp-Logan phantom, three iterations are sufficient to restore projection data and reconstruct ring artifact-free images when the dead bins rating is under 30%. The dead-bin-induced artifacts are substantially reduced. More iteration number is needed to reconstruct satisfactory images while the rating of dead bins increases. Similar results were found for a real head phantom case. Conclusion: A practical CT image ring artifact correction scheme based on projection data is developed. This method can produce ring artifact-free CT images feasibly and effectively.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Spiner vs EOSPAC6: capabilities, performance, and accuracy considerations

The Cross-Cutting Capabilities Project (XCAP) has significant interest in collecting and implementing a common set of libraries to be used across the various production hydro-codes at LANL. A common set of libraries will help facilitate comparisons between codes. In addition to minimizing variables for comparisons and physics validation, efforts toward optimization and porting of packages for future architectures will be more efficient. As part of this push Singularity is being considered as an inclusive materials interface library. One crucial part of this library is the importing, inverting, and interpolation of equation of state (EOS) data. Currently the Lagrangian Applications Project (LAP) and Safety Applications Project (SAP) are using EOSPAC6 for delivery EOS data. The Eulerian Applications Project (EAP) has historically used TEOS and more recently an implementation of Singularly via a package called Spiner for EOS interpolation. Singularity currently has the option of using several analytical EOS models, directly employing SESAME via Spiner, or directly using SESAME via EOSPAC6 (not optimized yet). Assuming Singularity moves forward as a common platform for the implementation of materials models, a decision will need to be made on which EOS interpolation package XCAP should move forward with, given resources and people are finite. We will attempt to address pros and cons of Spiner and EOSPAC6 and the trade-offs that should be considered during the decision making process. This report is intended as an ASC-PEM-EOS perspective on what is needed in an EOS interpolation package. Performance and Accuracy sections will mostly address data from comparison studies in LA-UR-22-22699.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
NASA NTRS2015

Arc Jet Facility Test Condition Predictions Using the ADSI Code

The Aerothermal Design Space Interpolation (ADSI) tool is used to interpolate databases of previously computed computational fluid dynamic solutions for test articles in a NASA Ames arc jet facility. The arc jet databases are generated using an Navier-Stokes flow solver using previously determined best practices. The arc jet mass flow rates and arc currents used to discretize the database are chosen to span the operating conditions possible in the arc jet, and are based on previous arc jet experimental conditions where possible. The ADSI code is a database interpolation, manipulation, and examination tool that can be used to estimate the stagnation point pressure and heating rate for user-specified values of arc jet mass flow rate and arc current. The interpolation is performed in the other direction (predicting mass flow and current to achieve a desired stagnation point pressure and heating rate). ADSI is also used to generate 2-D response surfaces of stagnation point pressure and heating rate as a function of mass flow rate and arc current (or vice versa). Arc jet test data is used to assess the predictive capability of the ADSI code.

fluid dynamics↗
DOE OSTI2016

Optimal Temperature Grid For Accurate Doppler Kernel Reconstruction

For computational efficiency, both Monte Carlo and deterministic neutron transport codes often rely on pre-tabulated cross section sets and simple interpolation schemes to represent the Doppler broadening of the cross sections at a needed temperature. Accurate accounting of Doppler effects is of paramount importance for reactor analysis since it impacts the power distribution and the reactor response during transients. Temperature interpolation methods for Doppler broadening have traditionally been physically motivated engineering curve-fits, selected upon best-performance criteria on important nuclides. Kernel reconstruction methods have recently been introduced to perform fast and efficient Doppler broadening interpolation as the result of an optimization problem,, . Out of all the possible kernels analyzed, the temperature-optimized free Doppler kernel reconstruction method was shown to significantly outperform traditional Doppler broadening interpolation methods. Detailed derivations will be part of an upcoming journal paper. In this article, key formulae and results for performing free Doppler kernel reconstruction are summarized, and a study of the optimal temperature grid (T{sub j}) selection is presented. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

Energy deposition validation results for the evaluated electron data library in FRENSIE - 25357

The Framework for Research in Nuclear Science and Engineering (FRENSIE) is a collection of packages written in C++ that are designed primarily to aid in methods development. A recent development in FRENSIE is the modeling of single scattering electron interactions using the data in the Evaluated Electron Data Library (EEDL) from Lawrence Livermore National Laboratory (LLNL). Preliminary verification and validation (V and V) results using the well-known Lockwood energy deposition experiment and a comparison with MCNP6.2 were performed using several bivariate grid policies (Unit-base, Correlated, Unit-base Correlated), interpolation schemes (lin-lin, log-log, lin-log), and physics options (Coupled and Decoupled Elastic Scattering). The results show an agreement to within 0.5% between MCNP6.2 and FRENSIE when using the same bivariate grid policy (Correlated) and interpolation scheme (log-log). When compared to the experimental results of the Lockwood experiment, it was found that a Unit-base bivariate grid policy, lin-lin interpolation scheme, and lin-log interpolation scheme did not produce accurate results for the energy deposition in test problems. The log-log Correlated and Unit-base Correlated results showed the greatest agreement with the Lockwood experiment. The total energy deposition matched the experimental data to within 3%. Both the Correlated and Unit-base Correlated results had a tendency to estimate a higher energy deposition near the peaks and a lower energy deposition near the tails. The differences between coupled elastic scattering and decoupled scattering models were shown to be more prominent at higher energies with the results of the coupled elastic scattering being more accurate for the peak and less accurate for the tail of the energy deposition profiles. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2018

Predicting photovoltaic soiling losses using environmental parameters: An update

This study presents an investigation on the correlations between soiling losses and environmental parameters at 41 locations in the United States, with the aim of analyzing the possibility of predicting soiling losses at a site even when soiling data are not available. The results of this work, which considers the largest pool of soiling data points systematically investigated so far, confirm that a single-variable regression based on particulate matter concentration returns the best correlations with soiling, with adjusted coefficients of determination up to 70%, corresponding to RMSE as low as 0.9%. Among the various particulate matter datasets investigated, a gridded Environment Protection Agency dataset is for the first time found to return correlations similar to those obtained by interpolating particulate matter monitoring station data. We discuss in detail the different interpolation techniques used to process the particulate matter concentrations because they can greatly impact the correlations. Specifically, the correlation coefficients between soiling and particulate matter range between 70% and less than 20%, depending on the interpolation methods and monitoring distance. Spatial interpolation methods based on inverse distance weighting are found to return better correlations than a nearest neighbor or a simple average approach, especially when large distances are considered. Similarly, the effects of different rain thresholds used to calculate the length of the dry periods are examined. An enhanced two-variable regression is found to achieve higher-quality correlations, with adjusted R2 of 90% (RMSE = 0.55%), also suggesting that high and low soiling locations might be differentiated depending on fixed particulate matter or rainfall thresholds.

14 SOLAR ENERGY↗
DOE OSTI2018

Dynamic graphs, community detection, and Riemannian geometry

A community is a subset of a wider network where the members of that subset are more strongly connected to each other than they are to the rest of the network. In this paper, we consider the problem of identifying and tracking communities in graphs that change over time {dynamic community detection} and present a framework based on Riemannian geometry to aid in this task. Our framework currently supports several important operations such as interpolating between and averaging over graph snapshots. We compare these Riemannian methods with entry-wise linear interpolation and that the Riemannian methods are generally better suited to dynamic community detection. Next steps with the Riemannian framework include developing higher-order interpolation methods (e.g. the analogues of polynomial and spline interpolation) and a Riemannian least-squares regression method for working with noisy data.

dynamic community detection↗
DOE OSTI2024

An Envelope Time Synchronous Averaging for Wind Turbine Gearbox Fault Diagnosis

Vibration-based condition monitoring techniques are widely used for diagnosing faults in rotating machines. These techniques are implemented in the time domain, the frequency domain, or both. However, the composite and noisy nature of the raw data collected requires a preprocessing stage such as filtering and decomposition using in-depth processing techniques. Moreover, these methods require good frequency resolution and involve examining a broad frequency range to discern both healthy and faulty cases. In this work, we introduce a simple and fast diagnostic scheme for wind turbine gear teeth wear based on time domain analysis. The proposed method is based on the local minima interpolation of a filtered version of the vibration signal following time synchronous averaging (TSA) technique. Given tachometer signal, the TSA of the vibration data is performed using MTALAB software. Then, local minima of the filtered signal are interpolated using the Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) function. The variance of the interpolated curve built a gear fault index. The derived fault index resulting of the proposed technique allows a substantial distinction between the healthy and faulty cases. Its efficiency is validated using 10 real-world datasets of vibration stemmed from a wind turbine planetary gearbox. The proposed method boasts a low computation time and ease of interpretation, specifically beneficial for gearbox fault diagnosis purposes.

fault diagnosis↗
DOE OSTI2016

Adaptive model order reduction for the Jacobian calculation in inverse multi-frequency problem for Maxwell's equations

Here this work develops a model order reduction method for a numerical solution of an inverse multi-frequency eddy current problem using a rational interpolation of the transfer function in the complex plane. We use the Pade interpolation in the complex frequency plane; this allows us to speed up the calculation of the frequency-dependent Jacobian in the inversion procedure without loosing accuracy. Interpolating frequencies are chosen adaptively to reduce the maximal approximation error. We use the error indicator that is equivalent to a seminorm of the residual. The efficiency of the developed approach is demonstrated by applying it to the inverse magnetotelluric problem, which is a geophysical electromagnetic remote sensing method used in mineral, geothermal, and groundwater exploration. In this application, the transfer function values are needed for shifts in a purely imaginary interval. Thus we consider the interpolating shifts in the same interval as well as in a purely real interval, containing the spectrum of the operator. Numerical tests show an excellent performance of the proposed methods characterized by a significant reduction of computational time without loss of accuracy of the calculated Jacobian.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

On the applicability of the Redlich-Kister framework for viscosity estimation of molten halide salt mixtures

For molten halide salt mixtures already being utilized or under consideration for carbon-free energy production systems, it is crucial that their viscosity is well understood so that system thermal hydraulics can be reliably assessed. Because of the difficulty in accurately measuring molten halide viscosity and the sheer size of the matrix of possible higher order salt mixtures that may be of interest to the energy industry, there are several gaps in the quantified understanding of molten halide viscosity across this matrix. As such, both first-principles and semi-empirical modeling techniques may be crucial for rapidly assessing this broad, complex compositional domain. Herein, the Redlich-Kister framework is applied to assess the feasibility of broadly interpolating and estimating the viscosity of several pseudobinary and pseudoternary molten halide salt systems that may be of key interest to the energy industry. The framework is based on the assumption that an ideal component and a nonideal component collectively describe the viscosity as a function of composition and temperature for a given molten halide system. Three different ideal models were considered for the ideal component, including Grunburg-Nissan, Katti-Chaudhri, and Gambill methods. Regarding the pseudobinary interpolations, the Redlich-Kister models with either the Grunburg-Nissan or Katti-Chaudhri models as the ideal component resulted in either highly (average error less than 5%) or reasonably (average error less than 15%) accurate interpolations of pseudobinary halide viscosity; BeF 2 - or UF 4 -bearing salts tended to result in reasonably accurate interpolations, whereas other pseudobinary mixtures tended to show high accuracy. Regarding the pseudoternary extrapolations, the Redlich-Kister framework shows reasonable success at estimating the extent to which a pseudoternary system may indicate deviations from ideal Grunburg-Nissan mixing, where discrepancies with comparative experimental data generally stay within 30%. Finally, the primary reasons identified for such discrepancies are (1) inaccuracy in the underlying experimental data, (2) different complexation behavior in the higher order systems compared to the pseudobinary subsystems, and (3) extrapolation into temperatures too far out of the domain, which is valid for the underlying experimental data feeding the Redlich-Kister model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Observer Evaluation of a Metal Artifact Reduction Algorithm Applied to Head and Neck Cone Beam Computed Tomographic Images

Purpose and Objectives: To quantify, through an observer study, the reduction in metal artifacts on cone beam computed tomographic (CBCT) images using a projection-interpolation algorithm, on images containing metal artifacts from dental fillings and implants in patients treated for head and neck (H&N) cancer. Methods and Materials: An interpolation-substitution algorithm was applied to H&N CBCT images containing metal artifacts from dental fillings and implants. Image quality with respect to metal artifacts was evaluated subjectively and objectively. First, 6 independent radiation oncologists were asked to rank randomly sorted blinded images (before and after metal artifact reduction) using a 5-point rating scale (1 = severe artifacts; 5 = no artifacts). Second, the standard deviation of different regions of interest (ROI) within each image was calculated and compared with the mean rating scores. Results: The interpolation-substitution technique successfully reduced metal artifacts in 70% of the cases. From a total of 60 images from 15 H&N cancer patients undergoing image guided radiation therapy, the mean rating score on the uncorrected images was 2.3 ± 1.1, versus 3.3 ± 1.0 for the corrected images. The mean difference in ranking score between uncorrected and corrected images was 1.0 (95% confidence interval: 0.9-1.2, P<.05). The standard deviation of each ROI significantly decreased after artifact reduction (P<.01). Moreover, a negative correlation between the mean rating score for each image and the standard deviation of the oral cavity and bilateral cheeks was observed. Conclusion: The interpolation-substitution algorithm is efficient and effective for reducing metal artifacts caused by dental fillings and implants on CBCT images, as demonstrated by the statistically significant increase in observer image quality ranking and by the decrease in ROI standard deviation between uncorrected and corrected images.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2019

A variable high-order shock-capturing finite difference method with GP-WENO

Here, we present a new finite difference shock-capturing scheme for hyperbolic equations on static uniform grids. The method provides selectable high-order accuracy by employing a kernel-based Gaussian Process (GP) data prediction method which is an extension of the GP high-order method originally introduced in a finite volume framework by the same authors. The method interpolates Riemann states to high order, replacing the conventional polynomial interpolations with polynomial-free GP-based interpolations. For shocks and discontinuities, this GP interpolation scheme uses a nonlinear shock handling strategy similar to Weighted Essentially Non-Oscillatory (WENO), with a novelty consisting in the fact that nonlinear smoothness indicators are formulated in terms of the Gaussian likelihood of the local stencil data, replacing the conventional L 2 -type smoothness indicators of the original WENO method. We demonstrate that these GP-based smoothness indicators play a key role in the new algorithm, providing significant improvements in delivering high – and selectable – order accuracy in smooth flows, while successfully delivering non-oscillatory solution behavior in discontinuous flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Collocation methods for nonlinear differential equations on low-rank manifolds

We introduce new methods for integrating nonlinear differential equations on low-rank manifolds. These methods rely on interpolatory projections onto the tangent space, enabling low-rank time integration of vector fields that can be evaluated entry-wise. A key advantage of our approach is that it does not require the vector field to exhibit low-rank structure, thereby overcoming significant limitations of traditional dynamical low-rank methods based on orthogonal projection. To construct the interpolatory projectors, we develop a sparse tensor sampling algorithm based on the discrete empirical interpolation method (DEIM) that parameterizes tensor train manifolds and their tangent spaces with cross interpolation. Using these projectors, we propose two time integration schemes on low-rank tensor train manifolds. The first scheme integrates the solution at selected interpolation indices and constructs the solution with cross interpolation. The second scheme generalizes the well-known orthogonal projector-splitting integrator to interpolatory projectors. We demonstrate the proposed methods with applications to several tensor differential equations arising from the discretization of partial differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

On-the-fly Doppler broadening of unresolved resonance region cross sections

In this paper, two methods for computing temperature-dependent unresolved resonance region cross sections on-the-fly within continuous-energy Monte Carlo neutron transport simulations are presented. The first method calculates Doppler broadened cross sections directly from zero-temperature average resonance parameters. In a simulation, at each event that requires cross section values, a realization of unresolved resonance parameters is generated about the desired energy and temperature-dependent single-level Breit-Wigner resonance cross sections are computed directly via the analytical Ψ-x Doppler integrals. The second method relies on the generation of equiprobable cross section magnitude bands on an energy-temperature mesh. Within a simulation, the bands are sampled and interpolated in energy and temperature to obtain cross section values on-the-fly. Both of the methods, as well as their underlying calculation procedures, are verified numerically in extensive code-to-code comparisons. Energy-dependent pointwise cross sections calculated with the newly-implemented procedures are shown to be in excellent agreement with those calculated by a widely-used nuclear data processing code. Relative differences at or below 0.1% are observed. Integral criticality benchmark results computed with the proposed methods are shown to reproduce those computed with a state-of-the-art processed nuclear data library very well. In simulations of fast spectrum systems which are highly-sensitive to the representation of cross section data in the unresolved region, k-eigenvalue and neutron flux spectra differences of <10 pcm and <1.0% are observed, respectively. The direct method is demonstrated to be well-suited to the calculation of reference solutions — against which results obtained with a discretized representation may be assessed — as a result of its treatment of the energy, temperature, and cross section magnitude variables as continuous. Also, because there is no pre-processed data to store (only temperature-independent average resonance parameters) the direct method is very memory-efficient. Typically, only a few kB of memory are needed to store all required unresolved region data for a single nuclide. However, depending on the details of a particular simulation, performing URR cross section calculations on-the-fly can significantly increase simulation times. Alternatively, the method of interpolating equiprobable probability bands is demonstrated to produce results that are as accurate as the direct reference solutions, to within arbitrary precision, with high computational efficiency in terms of memory requirements and simulation time. Analyses of a fast spectrum system show that interpolation on a coarse energy-temperature mesh can be used to reproduce reference k-eigenvalue results obtained with cross sections calculated continuously in energy and directly at an exact temperature to within <10 pcm. Probability band data on a mesh encompassing the range of temperatures relevant to reactor analysis usually require around 100 kB of memory per nuclide. Finally, relative to the case in which probability table data generated at a single, desired temperature are used, minor increases in simulation times are observed when probability band interpolation is employed.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗