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Verification and Validation of the STAT7 Code

This document presents the verification and validation of the STAT7 Version 1.1 code, which has been developed to perform the steady-state thermal hydraulics (TH) safety calculations required to support conversion of the Massachusetts Institute of Technology Research Reactor from highly enriched uranium fuel to low- enriched uranium fuel. The key capabilities of the code, including statistical processing, water property generation, and TH solution, are verified independently. While the first two capabilities are checked using statistical tests and NIST data tables, each component of the TH solution is verified using simple geometry test problems. The comparison between results obtained by the code and by hand calculations on these problems shows that each of these components works correctly. Additionally, a comprehensive comparison between STAT7 Version 1.1 and PLTEMP/ANL Version 4.3 Revision 162 calculations is performed for the validation. Good agreement is achieved between the results obtained with the two codes for all TH parameters belonging to the fuel core region.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Verification and validation of the Alternative Nonlinear Two-phase Subchannel (ANTS) code

The Alternative Nonlinear Two-phase Subchannel solver (ANTS) code was written to provide a fast-running, steady-state, pin-resolved modeling and simulation tool for analysis of common boiling water reactor (BWR) geometry and common operating conditions. ANTS has been integrated into the Virtual Environment for Reactor Application (VERA) core simulator software, where it can be used to provide a thermal/hydraulic (T/H) subchannel solution that is then used to provide neutronic feedback as well as perform the fuel depletion and temperature solution. Herein, this paper presents the rigorous analysis performed on the ANTS code, which includes both code and solution verification testing, benchmarking with the existing two-phase subchannel capability in VERA, CTF, and validation testing using popular two-phase experiments such as PWR Sub-channel and Bundle Tests (PSBT), BWR Full-size Fine-mesh Bundle Tests (BFBT), Risø, and FRIGG. This assessment was used to qualify ANTS for its intended applications before its use for core-scale, multiphysics BWR simulations. In general, it was found that agreement with experimental data was good; errors were within the range of experimental data uncertainty. Furthermore, code and solution verification confirmed that the governing equations and the most important closure terms were correctly implemented and behaving as expected.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Verification and Validation Activities for the Multi-Fidelity Toolkit

The Multi-Fidelity Toolkit (MFTK) is a simulation tool being developed at Sandia National Laboratories for aerodynamic predictions of compressible flows over a range of physics fidelities and computational speeds. These models include the Reynolds-Averaged-Navier-Stokes (RANS) equations, the Euler equations, and modified Newtonian aerodynamics (MNA) equations, and they can be invoked independently or coupled with hierarchical Kriging to interpolate between high-fidelity simulations using lower-fidelity data. However, as with any new simulation capability, verification and validation are necessary to gather credibility evidence. This work describes formal code- and solution-verification activities as well as model validation with uncertainty considerations. Code verification is performed on the MNA model by comparing with an analytical solution for flat-plate and inclined-plate geometries. Solution-verification activities include grid-refinement studies of HIFiRE-1 wind tunnel measurements, which are used for validation, for all model fidelities. A thorough treatment of the validation comparison with prediction error and validation uncertainty is also presented.

42 ENGINEERING↗

ThinCurr: An open-source 3D thin-wall eddy current modeling code for the analysis of large-scale systems of conducting structures

In this paper we present a new thin-wall eddy current modeling code, ThinCurr, for studying inductively-coupled currents in 3D conducting structures -- with primary application focused on the interaction between currents flowing in coils, plasma, and conducting structures of magnetically-confined plasma devices. The code utilizes a boundary finite element method on an unstructured, triangular grid to accurately capture device structures. The new code, part of the broader Open FUSION Toolkit, is open-source and designed for ease of use without sacrificing capability and speed through a combination of Python, Fortran, and C/C++ components. Scalability to large models is enabled through use of hierarchical off-diagonal low-rank compression of the inductance matrix, which is otherwise dense. Ease of handling large models of complicated geometry is further supported by automatic determination of supplemental elements through a greedy homology approach. Here, a detailed description of the numerical methods of the code and verification of the implementation of those methods using cross-code comparisons against the VALEN code and Ansys commercial analysis software is shown.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Feasibility and performance of the staged Z-pinch: A one-dimensional study with FLASH and MACH2

Z-pinch platforms constitute a promising pathway to fusion energy research. Here, we present a one-dimensional numerical study of the staged Z-pinch (SZP) concept using the FLASH and MACH2 codes. We discuss the verification of the codes using two analytical benchmarks that include Z-pinch-relevant physics, building confidence on the codes' ability to model such experiments. Then, FLASH is used to simulate two different SZP configurations: a xenon gas-puff liner (SZP1*) and a silver solid liner (SZP2). The SZP2 results are compared against previously published MACH2 results, and a new code-to-code comparison on SZP1* is presented. Using an ideal equation of state and analytical transport coefficients, FLASH yields a fuel convergence ratio (CR) of approximately 39 and a mass-averaged fuel ion temperature slightly below 1 keV for the SZP2 scheme, significantly lower than the full-physics MACH2 prediction. For the new SZP1* configuration, full-physics FLASH simulations furnish large and inherently unstable CRs (>300) but achieve fuel ion temperatures of many kilo-electron volts. While MACH2 also predicts high temperatures, the fuel stagnates at a smaller CR. The integrated code-to-code comparison reveals how magnetic insulation, heat conduction, and radiation transport affect platform performance and the feasibility of the SZP concept.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Verification of MOOSE/Bison's Heat Conduction Solver Using Combined Spatiotemporal Convergence Analysis

Bison is a computational physics code that uses the finite element method to model the thermo-mechanical response of nuclear fuel. Since Bison is used to inform high-consequence decisions, it is important that its computational results are reliable and predictive. One important step in assessing the reliability and predictive capabilities of a simulation tool is the verification process, which quantifies numerical errors in a discrete solution relative to the exact solution of the mathematical model. One step in the verification process—called code verification—ensures that the implemented numerical algorithm is a faithful representation of the underlying mathematical model, including partial differential or integral equations, initial and boundary conditions, and auxiliary relationships. In this paper, the code verification process is applied to spatiotemporal heat conduction problems in Bison. Simultaneous refinement of the discretization in space and time is employed to reveal any potential mistakes in the numerical algorithms for the interactions between the spatial and temporal components of the solution. For each verification problem, the correct spatial and temporal order of accuracy is demonstrated for both first- and second-order accurate finite elements and a variety of time-integration schemes. Furthermore, these results provide strong evidence that the Bison numerical algorithm for solving spatiotemporal problems reliably represents the underlying mathematical model in MOOSE. The selected test problems can also be used in other simulation tools that numerically solve for conduction or diffusion.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Wind Turbine Noise Code Benchmark: A Comparison and Verification Exercise: Preprint

In a number of institutions and companies, researchers and engineers are developing modeling numerical frameworks that are used to predict the aerodynamic noise emission from a wind turbine rotor. The simulation codes vary from empirically-tuned engineering models to high-fidelity computational ones. Their common feature is the fact that they all specifically model the main aerodynamic noise mechanisms occurring at the rotating blades, namely trailing edge noise and turbulent inflow noise. Nevertheless, it can be expected that these different modeling frameworks will produce different results for a same given rotor design, and identical operating conditions. Trailing edge noise is put at the forefront of the study as it is recognized as the main audible source of noise from wind turbines. The present benchmark aims at comparing the results from the different modeling approaches, and drawing some conclusions from these comparisons. This effort, denoted as Wind Turbine Noise Code benchmark, was initiated in 2019 as a joint-activity between the IEA Wind Task 39 (Quiet Wind Turbine Technology) and Task 29 (Detailed Aerodynamics of Wind Turbines, now Task 47). In addition to the investigation of the noise emissions themselves, the rotor aerodynamic characteristics are investigated as they have a significant impact on the noise generation mechanisms. A number of test cases are defined and the aerodynamic and aeroacoustic predictions from the various models are compared. There exist some discrepancies between the different methods, but it is difficult to conclude if one methodology is better than another in order to design a wind turbine with noise as a constraint.

aeroacoustics↗

Developing Ultrahigh-Resolution E3SM Land Model for GPU Systems

Designing and refactoring complex scientific code, such as the E3SM land model (ELM), for new computing architectures is challenging. This paper presents design strategies and technical approaches to develop a data-oriented, GPU-ready ELM model using compiler directives (OpenACC/OpenMP). We first analyze the datatypes and processes in the original ELM code. Then we present design considerations for ultrahigh-resolution ELM (uELM) development for massive GPU systems. These techniques include the global data-oriented simulation workflow, domain partition, code porting and data copy, memory reduction, parallel loop restructure and flattening, and race condition detection. We implemented the first version of uELM using OpenACC targeting the NVidia GPUs in the Summit supercomputer at Oak Ridge National Laboratory. During the implementation, we developed a software tool (named SPEL) to facilitate code generation, verification, and performance tuning using these techniques. The first uELM implementation for Nvidia GPUs on Summit delivered promising results: 1) over 98% of the ELM code was automatically generated and tuned by scripts. Most ELM modules had better computational performances than the original ELM code for CPUs. The GPU-ready uELM is more scalable than the CPU code on fully-loaded Summit nodes. Example profiling results from several modules are also presented to illustrate the performance improvements and race condition detection. The lessons learned and toolkit developed in the study are also suitable for further uELM deployment using OpenMP on the first US exascale computer, Frontier, equipped with AMD CPUs and GPUs.

Schwartz, Peter↗

Calculation of neutron flux spectra of the VVER-1000 mock-up shielding benchmark with Monte Carlo code MCS utilizing mesh-based weight window

The measurements of neutron spectra compiled inside the NEA-1517/82 package from the Shielding Integral Benchmark Archive and Database (SINBAD) are chosen as benchmark cases to validate the variance reduction technique based on weight window in Monte Carlo Code MCS. A full 3D model for fixed source mode calculation with hexagonal lattice source definition is developed to simulate total of 6 points of measurements at the vicinity of the reactor and the reactor pressure vessel region. A code/code comparison against MCNP6 code is first conducted as verification element for the mesh-based weight window capability in MCS. Finally, the validation results are presented against measurements. The verification against MCNP6 code gives good agreement in addition of the insight to the importance of user understanding to determine proper reference point and reference lower weight bound for scaling which is not required in MCS code due to its capability of automatic scaling. The comparison of neutron spectra between MCS and measurements shows good agreement within 3 standard deviations for all of six detector positions.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Software Quality Assurance for the MOOSE-Based Open-Source Multiphysics Code Cardinal - An Expanded CI Testing Suite

Cardinal is a wrapping of the GPU-oriented spectral element Computational Fluid Dynamics (CFD) code NekRS and the Monte Carlo particle transport code OpenMC within the Multiphysics Object-Oriented Simulation Environment (MOOSE). Cardinal provides high-resolution thermal-hydraulics and/or radiation transport feedback to MOOSE multiphysics simulations. Multiphysics feedback is implemented in a geometry-agnostic manner which eliminates the need for rigid one-to-one mappings. A generic data transfer implementation also allows NekRS and OpenMC to couple to any MOOSE application, enabling a broad set of multiphysics capabilities. Cardinal simulations can also leverage combinations of MPI, OpenMP, and GPU resources. Cardinal continuous development and improvement efforts have led to the software being considered as a high-fidelity design and licensing tool for key areas of nuclear reactor relevant physics, including neutron transport, fluid flow, heat transfer, and mechanical processes. The fast development and expansion of the software from a pure R&D framework towards its application in the nuclear industry and regulation require a focus on developing, enhancing and, maintaining Cardinal’s software quality through strict adherence to a Software Quality Assurance (SQA) framework and SQA program. To facilitate compliance with SQA standards, the Cardinal SQA Program has been initiated during Fiscal Year 2023 (FY23). During the development of the Cardinal SQA Program, multiple gaps have been identified. These gaps are primarily related to model verification and code pedigree as they relate to the use of Cardinal as a safety analysis tool. These gaps have been captured in a report published in 2023. A second report highlighted the progress made during Fiscal Year 2024 (FY24) and described Argonne’s effort to document and integrate software verification within Cardinal’s software development process. This report documents a snapshot of the verification test cases currently available for Cardinal and NekRS in their assimilation into a Continuous Integration (CI) platform. Following the CI practice permits the integrating of source code changes frequently and ensuring that the integrated codebase clears the verification testing for the software. It should be noted that the SQA program itself, including the program plans, procedures, configuration management, and testing strategies, need to be developed in a future step of this task.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Results of the Micromorphic Upscaling Workflow for the PSAAP III Year 3 Report

Predicting the mechanical response and failure of heterogeneous materials has proven difficult. Multiscale numerical methods based in higher order continuum theories attempt to bridge the gap between microscale and macroscale structural behavior. Micromorphic continuum theories have shown promise. The Tardigrade software package is an implementation of Eringen’s micromorphic continuum theory with capabilities to support multiscale material modeling workflows. These include homogenization through the Micromorphic Filter, calibration of micromorphic material models, and macroscale simulation in Tardigrade-MOOSE. This work discusses micromorphic upscaling efforts of the University of Colorado Boulder PSAAP III multidisciplinary simulation center (MSC). Verification studies are presented that compare the accuracy of the upscaling workflow with analytical solutions for a trivial stress state and homogeneous material using direct numerical simulations (DNS) conducted in the Ratel finite element method (FEM) and GEOS material point method (MPM) codes. These verification studies consider upscaling using the Micromorphic Filter for a “single filter domain”. Finally, DNS of a heterogeneous composite material is upscaled using a “multiple filter domain” method.

36 MATERIALS SCIENCE↗

Progress Towards NQA-1 for Cardinal in FY25

Cardinal is a wrapping of the GPU-oriented spectral element Computational Fluid Dynamics (CFD) code NekRS and the Monte Carlo particle transport code OpenMC within the Multiphysics Object-Oriented Simulation Environment (MOOSE). Cardinal provides high-resolution thermal-hydraulics and/or radiation transport feedback to MOOSE multiphysics simulations. Multiphysics feedback is implemented in a geometry-agnostic manner which eliminates the need for rigid one-to-one mappings. A generic data transfer implementation also allows NekRS and OpenMC to couple to any MOOSE application, enabling a broad set of multiphysics capabilities. Cardinal simulations can also leverage combinations of MPI, OpenMP, and GPU resources. Cardinal continuous development and improvement efforts have led to the software being considered as a high-fidelity design and licensing tool for key areas of nuclear reactor relevant physics, including neutron transport, fluid flow, heat transfer, and mechanical processes. The fast development and expansion of the software from a pure R&D framework towards its application in the nuclear industry and regulation require a focus on developing, enhancing,and maintaining Cardinal’s software quality through strict adherence to a Software Quality Assurance (SQA) framework and SQA program. To facilitate compliance with SQA standards, the Cardinal SQA Program was initiated during Fiscal Year 2023 (FY23). During the development of the Cardinal SQA Program, multiple gaps have been identified. These gaps are primarily related to model verification and code pedigree as they relate to the use of Cardinal as an analysis tool. These gaps were captured in a report published in 2023. A second report highlighted the progress made during Fiscal Year 2024 (FY24) and described Argonne’s effort to document and integrate software verification within Cardinal’s software development process. This report documents the progress made towards NQA-1 for Cardinal in the Fiscal Year 2025 (FY25). All cases in the expanded Continuous Integration (CI) suite of NekRS are included in this report which test the solvers and modules available in NekRS exhaustively. The NekRS tests are integrated with the Cardinal CI suite and made available in publicly accessible Github documentation. Following the CI practice permits integrating of source code changes frequently and ensuring that the integrated codebase clears the verification testing for the software. Also in this report is a brief overview of the development of the Cardinal Software Quality Assurance Plan (SQAP) that was done in FY25, though it should be noted that the rest of the documentation for the SQA program needs to be developed in a future step of this task.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Verification and Validation of the PLTEMP/ANL Code for Thermal-Hydraulic Analysis of Experimental and Test Reactors, Volume 1

This is Volume 1 of a two-volume document that collects the verification and validation (V&V) works done for the PLTEMP/ANL code during the years of its development and improvement. Volume 1 describes the V&V of sixteen capabilities of the PLTEMP/ANL code that were identified by research reactor analysts as frequently used in their thermal-hydraulic analysis. Volume 2 describes the V&V of developments and improvements since the release of PLTEMP/ANL Version 4.3. Each chapter of the document focuses on verifying or validating a specific part of the software that calculates a specific phenomenon, e.g., channel flow calculation, coolant property calculation, heat transfer calculation, and flow instability calculation. Software verification is performed by comparing the code with hand calculation, Microsoft spreadsheet calculation, Mathematica calculation, or MATLAB calculation. The software validation is done by comparing the code with experimental data or a widely tested code like the RELAP5 code. In addition, some PLTEMP/ANL V&V works that are available in the open literature are simply cited in Volume 1 of the document. PLTEMP/ANL has been used in the safety analysis reports of several US and foreign research reactors licensed and converted from highly enriched uranium fuel to low-enriched uranium fuel. A list of such reactors is given in Volume 1 of the document.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Verification and Validation of the PLTEMP/ANL Code for Thermal-Hydraulic Analysis of Experimental and Test Reactors, Volume 2

This is Volume 2 of a two-volume document that collects the verification and validation (V&V) works done for the PLTEMP/ANL code during the years of its development and improvement. Volume 1 describes the V&V of sixteen capabilities of the PLTEMP/ANL code that were identified by research reactor analysts as frequently used in their thermal-hydraulic analysis. Volume 2 describes the V&V of developments and improvements since the release of PLTEMP/ANL Version 4.3. Each chapter of the document focuses on verifying or validating a specific part of the software that calculates a particular phenomenon, e.g., channel flow calculation, coolant property calculation, heat transfer calculation, and flow instability calculation. Software verification is performed by comparing the code with a hand calculation, Microsoft spreadsheet calculation, Mathematica calculation, or MATLAB calculation. The software validation is achieved by comparing the code with experimental data or a widely tested code like the RELAP5 code. In addition, some PLTEMP/ANL V&V works that are available in the open literature are simply referenced in Volume 1 of the document. PLTEMP/ANL has been used in safety analysis reports of several US and foreign research reactors licensed and converted from highly enriched uranium fuel to low-enriched uranium fuel. A list of such reactors is given in Volume 1 of the document.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Verification of a specialized hydrodynamic simulation code for modeling deflagration and detonation of high explosives

A specialized hydrodynamic simulation code has been developed and verified for the simulation of one-dimensional unsteady problems involving the detonation and deflagration of high explosives. To model all the relevant physical processes in these problems, a code is required to simulate compressible hydrodynamics, unsteady thermal conduction, and chemical reactions with complex rate laws. Several verification exercises are presented which test the implementation of these capabilities. The code also requires models for physics processes such as equations of state and conductivity for pure materials and mixtures as well as rate laws for chemical reactions. Additional verification tests are required to ensure that these models are implemented correctly. Though this code is limited in the types of problems it can simulate, its computationally efficient formulation allows it to be used in calibration studies for reactive burn models for high explosives. Furthermore, this study demonstrates how a series of verification tests can be used to ensure that the various physics processes needed to simulate complex phenomenon can be tested to ensure that they are correctly implemented.

97 MATHEMATICS AND COMPUTING↗

Variational, stable, and self-consistent coupling of 3D electromagnetics to 1D transmission lines in the time domain

This work presents a new multiscale method for coupling the 3D Maxwell's equations to the 1D telegrapher's equations. While Maxwell's equations are appropriate for modeling complex electromagnetics in arbitrary-geometry domains, simulation cost for many applications (e.g. pulsed power) can be dramatically reduced by representing less complex transmission line regions of the domain with a 1D model. By assuming a transverse electromagnetic (TEM) ansatz for the solution in a transmission line region, we reduce the Maxwell's equations to the telegrapher's equations. Here, we propose a self-consistent finite element formulation of the fully coupled system that uses boundary integrals to couple between the 3D and 1D domains and supports arbitrary unstructured 3D meshes. Additionally, by using a Lagrange multiplier to enforce continuity at the coupling interface, we allow for an absorbing boundary condition to also be applied to non-TEM modes on this boundary. We demonstrate that this feature reduces non-physical reflection and ringing of non-TEM modes off of the coupling boundary. By employing implicit time integration, we ensure a stable coupling, and we introduce an efficient method for solving the resulting linear systems. We demonstrate the accuracy of the new method on two verification problems, a transient O-wave in a rectilinear prism and a steady-state problem in a coaxial geometry, and show the efficiency and weak scalability of our implementation on a cold test of the Z-machine MITL and post-hole convolute.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Generalized thermo-mechanical framework for heterogeneous materials through asymptotic homogenization

Abstract A fundamental understanding of the interaction between microstructure and underlying physical mechanisms is essential, especially for developing more accurate multi-physics models for heterogeneous materials. Effects of microstructure on the material response at the macroscale are modeled by using the generalized thermomechanics. In this study, strain gradient theory is employed as a higher-order theory on the macroscale with thermodynamics modeled as a first-order theory on the microscale. Hence, energy depends only on the temperature such that we circumvent an extension of Fourier’s law and analyze the “simplest” thermo-mechanical model in strain gradient elasticity. Developing multiphysics models for heterogeneous materials is indeed a challenge and even this “simplest” model in generalized thermomechanics creates dozens of parameters to be determined. We develop a thermo-mechanical framework, in which microstructure is modeled as a periodic structure and through asymptotic homogenization approach, higher-order parameters at macroscopic scale are calculated. To illustrate the importance of higher-order parameters in overall thermo-mechanical response of a heterogeneous materials, finite element method (FEM) is employed with the aid of open-source codes (FEniCS). Verification example of a bulk system and several case studies of porous structures demonstrate how such numerical framework can be beneficial in the design of materials with tailored microstructures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

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↗