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At least 469 records · Page 26

(U) Radiation Transport Sensitivity Capabilities Applicable to INRAD

Intrinsic radiation (INRAD) calculations involve calculating the neutron and gamma-ray source rate densities from given compositions and densities of materials and the subsequent transport of the neutrons and gamma rays to detectors that may be stood off or internal. Related problems deal with measures of subcritical multiplication, such as the k eff eigenvalue. Realistic estimates of the uncertainties in calculated INRAD results are desired. One approach to uncertainty quantification begins with sensitivity analysis. This report describes the present capabilities that XCP-7 can apply to compute sensitivities in INRAD problems and areas where work is needed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Algebraic Multigrid with Optimal Interpolation and Adaptive Smoothers (Final Report)

The project team continued with work on developing new bootstrap AMG techniques for solving symmetric and non-symmetric PDE systems. The focus of this work is to derive more reliable measures of the quality of the coarse space set than the convergence rate of the standard F-relaxation form of CR and a more robust form of interpolation than the so-called ideal form. We have successfully derived a sharp variant of CR that gives the precise convergence rate of the two-grid method using this optimal interpolation and, in addition, we derived a new Generalized Bootstrap AMG setup algorithm that uses as its main tool a multilevel eigensolver for the generalized eigenvalue problem involving the system matrix and the symmetrized smoother. In addition, the approach allows for general block smoothers with overlap. We have applied the method to scalar diffusion problems, linear elasticity, and Maxwell’s and the method shows marked improvements over existing AMG methods for these problems. In addition, the team worked with CASC members on new forms of ideal AMG interpolation.

97 MATHEMATICS AND COMPUTING↗

CSPlib - A Software Toolkit for the Analysis of Dynamical Systems and Chemical Kinetic Models

CSPlib is an open source software library for analyzing general ordinary differential equation (ODE) systems and detailed chemical kinetic ODE systems. It relies on the computational singular perturbation (CSP) method for the analysis of these systems. The software provides support for: General ODE models (gODE model class) for computing source terms and Jacobians for a generic ODE system; TChem model (ChemElemODETChem model class) for computing source term, Jacobian, other necessary chemical reaction data, as well as the rates of progress for a homogenous batch reactor using an elementary step detailed chemical kinetic reaction mechanism. This class relies on the TChem [2] library; A set of functions to compute essential elements of CSP analysis (Kernel class). This includes computations of the eigensolution of the Jacobian matrix, CSP basis vectors and co-vectors, time scales (reciprocals of the magnitudes of the Jacobian eigenvalues), mode amplitudes, CSP pointers, and the number of exhausted modes. This class relies on the Tines library; A set of functions to compute the eigensolution of the Jacobian matrix using Tines library GPU eigensolver; A set of functions to compute CSP indices (Index Class). This includes participation indices and both slow and fast importance indices.

97 MATHEMATICS AND COMPUTING↗

Preparation of Nuclear Data Libraries for Web Release [Slides] and Tutorial for Generating Correlated Random Samples and Propagation of Uncertainty [Slides]

The first presentation discuses moving distribution of nuclear data to an online platform which allows ore frequent nuclear data updates, greater ease of acquiring nuclear data, and user flexibility in what nuclear data to download. The second presentation illustrates uncertainties without correlation, uncertainties without correlation with negative samples, uncertainties with correlation, uncertainties with a χ-like constraint, uncertainties with a Σ tot -like constraint, sampling using different distributions, and dealing with negative eigenvalues in a covariance matrix.

42 ENGINEERING↗

Advances in Mixed Precision Algorithms: 2021 Edition

Over the last year, the ECP xSDK-multiprecision effort has made tremendous progress in developing and deploying new mixed precision technology and customizing the algorithms for the hardware deployed in the ECP flagship supercomputers. The effort also has succeeded in creating a cross-laboratory community of scientists interested in mixed precision technology and now working together in deploying this technology for ECP applications. In this report, we highlight some of the most promising and impactful achievements of the last year. Among the highlights we present are: Mixed precision IR using a dense LU factorization and achieving a 1.8× speedup on Spock; results and strategies for mixed precision IR using a sparse LU factorization; a mixed precision eigenvalue solver; Mixed Precision GMRES-IR being deployed in Trilinos, and achieving a speedup of 1.4× over standard GMRES; compressed Basis (CB) GMRES being deployed in Ginkgo and achieving an average 1.4× speedup over standard GMRES; preparing hypre for mixed precision execution; mixed precision sparse approximate inverse preconditioners achieving an average speedup of 1.2×; and detailed description of the memory accessor separating the arithmetic precision from the memory precision, and enabling memory-bound low precision BLAS 1/2 operations to increase the accuracy by using high precision in the computations without degrading the performance. We emphasize that many of the highlights presented here have also been submitted to peer-reviewed journals or established conferences, and are under peer-review or have already been published.

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Advances in Mixed Precision Algorithms: 2021 Edition

Over the last year, the ECP xSDK-multiprecision effort has made tremendous progress in developing and deploying new mixed precision technology and customizing the algorithms for the hardware deployed in the ECP flagship supercomputers. The effort also has succeeded in creating a cross-laboratory community of scientists interested in mixed precision technology and now working together in deploying this technology for ECP applications. In this report, we highlight some of the most promising and impactful achievements of the last year. Among the highlights we present are • Mixed precision IR using a dense LU factorization and achieving a 1.8× speedup on Spock; • Results and strategies for mixed precision IR using a sparse LU factorization; • A mixed precision eigenvalue solver; • Mixed Precision GMRES-IR being deployed in Trilinos, and achieving a speedup of 1.4× over standard GMRES; • Compressed Basis (CB) GMRES being deployed in Ginkgo and achieving an average 1.4× speedup over standard GMRES; • Preparing hypre for mixed precision execution; • Mixed precision sparse approximate inverse preconditioners achieving an average speedup of 1.2×; • Detailed description of the memory accessor separating the arithmetic precision from the memory precision, and enabling memory-bound low precision BLAS 1/2 operations to increase the accuracy by using high precision in the computations without degrading the performance. We emphasize that many of the highlights presented here have also been submitted to peer-reviewed journals or established conferences, and are under peer-review or have already been published.

97 MATHEMATICS AND COMPUTING↗

Plutonium Production Reactor Progression Problems: Magnox Neutronics Benchmarks

The goal of this document is to provide a set of comprehensive benchmarking neutronics problems for gas-cooled, graphite-moderated reactors. The problems are designed to be representative problems that increase in complexity to test performance of various codes. For the simulation of the benchmarking problems, the Shift Monte Carlo code and MPACT deterministic code are chosen because of their state-of-the-art capabilities, which are optimized for various reactor designs. Because these codes have been developed primarily for light water reactor applications, their application to graphite-moderated, gas-cooled reactors has not been extensively explored. This report attempts to evaluate benchmarks for a Magnox-style reactor, one that is graphite-moderated and gas-cooled. Parameters that are calculated and presented in this benchmark include the eigenvalue, peaking factors, and isotope concentrations. Results show good agreement between Shift and MPACT, and demonstrate the capability of MPACT to model graphite-moderated systems well.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Performance Improvements for the Griffin Transport Solvers

Griffin is a Multiphysics Object-Oriented Simulation Environment based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. Griffin includes a variety of deterministic radiation transport solvers for fixed source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. A code assessment performed in FY-20 identified two significant issues with the transport solvers in Griffin: first, the primary heterogeneous SN (discrete ordinates) transport solver based on continuous finite element methods required significant mesh refinement and higher memory usage compared to solvers based on the method of characteristic for equivalent accuracy. Second, the homogeneous PN (spherical harmonics expansion) transport solver did not adequately support polynomial refinement, which is a feature usually required for problems with spatial homogenization and pronounced streaming, typical in fast or gas-cooled reactor systems. To address the first issue, the development effort focused on the more promising discontinuous finite element method (DFEM)-based SN transport solver in Griffin. The addition of an asynchronous parallel transport sweeper and coarse mesh finite difference (CMFD) acceleration have rendered a superior heterogeneous SN transport capability for multiphysics problems that requires far less computing resources in terms of both CPU time and memory usage. This is demonstrated with typical thermal- and fast-spectrum reactor benchmark problems, including 2D Transient Reactor Test, 3D Advanced Burner Test Reactor (ABTR), and 2D and 3D Empire microreactor. For the second issue, the development effort focused on a new transport solver based on the hybrid finite element PN method (HFEM-PN), equivalent to the variational nodal method, as well as a new diffusion solver based on HFEM-Diffusion. This solver is intended for homogenized domains with multiphysics coupling (i.e., supports mesh displacement, seamless temperature feedback, etc.). Initial calculations with the HFEM-Diffusion implementation show very good parallel efficiency for the residual evaluations with the 2D ABTR benchmark. A future development effort will be centered on further improvements to the CMFD, HFEM-PN, and DFEM diffusion solvers to ensure Griffin meets performance and software quality assurance requirements for advanced reactor design and analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Equations of Motion for the Vertical Rigid-Body Rotor: Linear and Nonlinear Cases

Centuries ago, the prolific mathematician Leonhard Euler (1707–1783) wrote down the equations of motion (EOM) for the heavy symmetrical top with one point fixed. The resulting set of equations turned out to be nonlinear and had a limited number of closed-form solutions. Today, tools such as transfer matrix and finite elements enable the calculation of the rotor dynamic properties for rotor-bearing systems. Some of these tools rely on the “linearized” version of the EOM to calculate the eigenvalues, unbalance response, or transients in these systems. In fact, industry standards mandate that rotors be precisely balanced to have safe operational characteristics. However, in some cases, the nonlinear aspect of the EOM should be considered. The purpose of this paper is to show examples of how the linear vs. nonlinear formulations differ. This paper will also show how excessive unbalance is capable of dramatically altering the behavior of the system and can produce chaotic motions associated with the “jump” phenomenon.

42 ENGINEERING↗

BWR Progression Problems

Under the Consortium for the Advanced Simulation of Light Water Reactors (CASL) Program, the Virtual Environment for Reactor Applications (VERA) was developed with the primary focus to model pressurized water reactors (PWRs). Recently, a new project was started to extend the modeling capability in VERA to model boiling water reactors (BWRs). The new project is called “Modeling and Analysis of Exelon BWRs for Eigenvalue and Thermal Limits Predictability,” and it is led by Oak Ridge National Laboratory (ORNL) and Exelon with participation from Global Nuclear Fuel and three universities: North Carolina State University (NCSU), the University of Michigan, and the University of Illinois.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Cross Section Generation Capability in Griffin

The Griffin code is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. The code includes a variety of steady-state solvers for fixed-source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. The code reads multigroup cross sections in the ISOXML format generated from external deterministic or Monte Carlo cross section generation codes. The implementation of the cross section generation capability in Griffin was initiated last year by plugging in the cross section application programming interface (CSAPI) and reviewing the methodologies for treating particulate fuels. The focus this year was on improving the CSAPI integration and implementing advanced self-shielding methods for applications to advanced reactor problems with TRISO fuels. First, the process for cross section library generation was updated to accurately and rigorously produce isotopic cross section data. Second, the equivalent Dancoff factor cell method performing slowing down calculations on the fly for the resonance treatment was implemented in CSAPI to improve the accuracy of effective multigroup cross sections in the resonance energy range. Third, the iterative local spatial self-shielding method was implemented under the calculation framework of the equivalent Dancoff factor cell method to accurately deal with the double heterogeneity effect of particulate fuel. The updated CSAPI with the advanced self-shielding methods, together with the cross section libraries generated based on the improved process, were tested for pin-cell, unit-cell, and fuel assembly problems with various resonance self-shielding conditions based on very high temperature reactor, high temperature test reactor, and Empire benchmark cores, indicating that the updated CSAPI in Griffin is able to produce multigroup cross sections accurately and efficiently. We also showed that the methodology worked well for pebble bed fuel from HTR-10, but the capability still needs to be fully integrated into CSAPI. In the future, further benchmark tests will be performed for various thermal reactor core problems, including particulate fuel-based pebble bed reactors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Griffin Software Development Plan

Griffin is a MOOSE-based reactor physics application for advanced reactor multiphysics modeling and simulation. The application is developed in a consistent multiphysics environment with strong software quality assurance. Griffin inherited most of the capabilities of MAMMOTH/Rattlesnake and is adopting the capabilities from PROTEUS that are needed in the code. The toolset includes a variety of deterministic radiation transport solvers for fixed source, k-eigenvalue, ad-joint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. The code contains the cross-section preparation capabilities applicable to fast and thermal reactors, including TRISO-fueled reactors. Core management capabilities include core performance, fuel depletion and shuffling, equilibrium core calculation, pebble-bed reactor run-in and equilibrium core, molten-salt reactor delayed neutron precursor drift, and control rod and drum movement with cusping correction. This software development plan presents the current and future capabilities and features in Griffin for the design and analysis of non-light-water reactor systems in steady-state and transient conditions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Final Design of a New Pulsed-Neutron Die-Away Experimental Testbed for Thermal Scattering Law Benchmarks (PNDA) (IER-501 CED-2)

This report presents the final design (CED-2) of IER-501, a testbed for pulsed-neutron die-away (PNDA) experiments at Lawrence Livermore National Laboratory (LLNL). The PNDA experiments will be high-quality benchmarks that serve to optimize and validate thermal neutron scattering laws (TSLs), which are high-priority nuclear data for the Department of Energy’s Nuclear Criticality Safety Program (NCSP). This CED-2 was guided by experimental results gathered from a prototype experimental set-up rather than with detailed simulations as is typically done for criticality experiments. The report presents the PNDA design and its equipment, and it documents the methodology used to postprocess the measured data. It discusses how experimental configurations influenced the decay-constant eigenvalue, or the integral parameter, of the experiment. The studied variations included the distance from the target to the generator, the orientation of the generator relative to the box, the orientation of the target to the generator, the effect of HDPE lining in the shielding box, the settings of the generator, and finally the benefits of using a low-scatter facility. From these results, a final configuration for the target, detectors, shielding box, and neutron generator was chosen. Two factors particularly influenced the chosen configuration: the reproducibility of the experiment’s geometry for benchmark modeling, and the minimization of measured neutrons scattered off the shielding box.

42 ENGINEERING↗

Fission Matrix Processing Using the MCNP6.3 HDF5 Restart File

This paper describes an approach to interrogating the fission matrix available in the HDF5-formatted restart file (also known as the “runtape” file), which is produced by the upcoming public release of the MCNP R code, version 6.3. The fission matrix, its eigenvalues, and its eigenvectors, are important tools for characterizing fissile systems such as research and power reactors and for accelerating the convergence of the Monte Carlo fission-source site distribution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Verification of the DIF3D Software to Support Fast Reactor Analysis

Ongoing design activities at Argonne National Laboratory are requiring a thorough verification of the Argonne Reactor Computation codes be performed. DIF3D is central to this system. The driver for this effort requires the 3D Cartesian, triangular-Z, and hexagonal-Z core geometry options of DIF3D be verified. Previous work identified the DIF3D features required to be verified to support current design activities, features of which are generally applicable to hexagonal-Z fast reactor designs. The scope of this verification effort includes verifying DIF3D’s ability to correctly translate the user’s model in to DIF3D’s preferred format, verifying that options planned for use have the desired effect, and verifying the correctness of the eigenvalue, fixed-source, forward, and adjoint solvers in DIF3D-FD and DIF3D-VARIANT. This manuscript provides the verification tasks and their results with respect to the features needed for current design activities. Since analytic solutions of the neutron diffusion and transport equations are either limited in scope or not possible, multiple tiers of problems unique to each solver and geometry type were implemented. Each of these tiers tests features independent and complementary arguments for why the separate testing of functionalities is acceptable. Finally, this separate testing was also supplemented with a high-level integral check of each the diffusion and transport capabilities and applicable geometries. To accommodate cases which an analytic solution is not feasible, MCNP6.2 was relied upon to provide a higher-order reference solution. This therefore required that the capabilities within MCNP6.2 which were relied upon for this work are also verified in this work. No MCNP discrepancies were noted in this effort. Note that the MCNP6.2 verification included in this work does not stand as a full verification of MCNP6.2, but merely verifies the features used in verifying DIF3D. The verification effort identified no issues that are debilitating or otherwise impactful to design usage of DIF3D, and thus DIF3D version 11.0, release 3012 is considered verified. As some additional changes have been made to the ARC software since this point all versions between release 3012 and 3266 can be considered verified as version 3253 was used for all updates in this revision. The types of issues that were identified were predominantly in the areas of: unclear documentation, software bugs which were inconsequential to final results, editing options which were ignored in favor of printing more information than requested, bugs in the outputs of intermediate results, or secondary output binary file information which was not present. While not a bug, this verification report also identified that the algorithm used to evaluate the peak fast flux in a nodal transport solution can be quite unreliable due to the methodology used and the location of the peak within the mesh. The authors of the report therefore recommend the usage of the EvaluateFlux software (distributed with ARC) as a more robust alternative noting that DIF3D will properly notify the user when the peaking values it is providing are potentially incorrect.

97 MATHEMATICS AND COMPUTING↗

A Note on the Probability of Initiation Problem

The purpose of this note is to draw attention to Pál for his derivation of the Pál-Bell equation which is used by LLNL and LANL to model Probability of Initiation (POI) problems. Both laboratories credit the equation to Bell and Lee. Although the equation formulated by Bell and Lee and the equation derived by Pál appear to be the same, the equation by Bell and Lee is flawed. Scattering, which was absent in Bell’s original formulation of a POI problem, was later introduced by Bell and Lee by replacing a fission term with a scattering term. Such a replacement, however, leads to an incorrect average number $\overline{v}$ of neutrons that is produced in a fission event. By approaching a POI problem from probabilistic point of view, Pál formulates the problem as a branching process that i) describes the growth of a population of neutrons in a fissile medium, and ii) predicts $\overline{v}$ correctly. There are five reasons for writing this report. The first is to clarify the failing in Bell and Lee’s derivation. The second is to establish the origin of the equation used by the laboratories. The third is to elucidate the fixed point technique formulated by Mokhtar-Kharroubi to solve the Pál-Bell equation. The fourth is to derive the α eigenvalue that is associated with a super-critical situation. The fifth is to describe in the Appendix a second order positivity preserving technique that accelerates the convergence of the first order fixed point method developed by Mokhtar-Kharroubi.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

(U) SENSMG: First-Order Sensitivities of Neutron Reaction Rates, Reaction-Rate Ratios, Leakage, k eff , α , and Subcritical Multiplication Using PARTISN

SENSMG is a tool for computing first-order sensitivities of neutron reaction rates, reaction-rate ratios, leakage, k eff , α, and subcritical multiplication using the PARTISN multigroup discrete-ordinates code. SENSMG computes sensitivities to all of the transport cross sections and data (total, fission, a nu, chi, and all scattering moments), two edit cross sections (absorption and capture), and the density for every nuclide and energy group. It also computes sensitivities to the mass density for every material and derivatives with respect to all interface locations and outer boundaries. It computes sensitivities to user specified reactions whose cross sections are available in a user-supplied NJOY output file. The tool can be used for one-dimensional spherical and slab (r) and two-dimensional cylindrical (r-z) geometries. The tool can be used for fixed-source and eigenvalue problems. For most responses, the tool implements Generalized Perturbation Theory (GPT) as discussed by Williams and Stacey. The tool is thus limited to computing sensitivities only for GPT-allowable responses. For subcritical multiplication, the tool implements sensitivities derived by O’Brien and Clark. SENSMG has a similar role as the old SWANLAKE (Ref. 8), FORSS (Ref. 9), and SENSIT (Ref. 10) codes. It has capabilities similar to those of SUSD3D (Refs. 11 and 12), which also uses PARTISN. Section II of this report describes the theory behind adjoint-based sensitivities, gives the equations that SENSMG solves, and defines the sensitivities that are output. Section III describes the user interface, including the input file and command line options. Section IV describes the output. Section V gives some notes about the coding that may be of interest. Section VI presents some sample problems and discusses verification, which is ongoing. Section VII lists needs and ideas for future work. Appendix A lists most of the input files whose results are presented in Sec. VI. Appendix B provides some useful details on one of the cross-section libraries that SENSMG supports.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

MPACT User’s Manual (V.4.3)

The MPACT code is designed to perform high-fidelity light-water reactor (LWR) analysis using whole-core pin-resolved neutron transport calculations on modern parallel-computing hardware. The code consists of several libraries which provide the functionality necessary to solve steady-state eigenvalue problems. Several transport capabilities are available within MPACT including both 2-D and 3-D Method of Characteristics (MOC). A three-dimensional whole core solution based on the 2D-1D solution method provides the capability for full core depletion calculations.

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