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DOE OSTI2025

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↗
DOE OSTI2025

Conjugate Heat Transfer Modeling of Salt-Filled Fuel Pins for Stable Salt Reactor Safety Analysis

The Stable Salt Reactor (SSR) combines the proven structural design of light water reactor fuel assemblies with the inherent safety and fuel-cycle advantages of molten salt technology. In its fast reactor configuration, the SSR utilizes recycled nuclear waste as fuel, sealed within narrow salt-filled fuel pins and cooled by a surrounding liquid salt coolant. Reliable transfer of heat from the molten fuel salt through the cladding to the external coolant is essential for both reactor safety and performance. This work investigates conjugate heat transfer (CHT) in the SSR’s salt-filled fuel pins using NekRS, a high-fidelity spectral element computational fluid dynamics (CFD) solver. The analyses capture internal natural convection within the molten fuel salt and external forced convection in the coolant, under steady-state and transient operating conditions. Parametric studies evaluate how variations in reactor power and coolant flow rate influence heat transfer distributions and system response. The high-fidelity CFD results are time-averaged and post-processed for direct comparison with moderate-fidelity Reynolds-averaged Navier–Stokes (RANS) models, and for the development of reduced-order models within the SAM system code. These validated models support fast-running safety analyses of normal and off-normal transients, improving predictive capability for key safety margins. By integrating advanced CFD with system-level safety tools, this study strengthens the modeling framework for SSR design, reduces uncertainty in molten salt CHT simulations, and accelerates the engineering and licensing of next-generation nuclear reactors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

2025 Advances in NekRS: Supporting improved performance for nuclear applications

This report presents several 2025 advancements in NekRS, a high-fidelity spectral element CFD code developed at Argonne National Laboratory to support the NEAMS thermal-hydraulics program. The forthcoming v25 release consolidates several of these advances, adding new features for portability across heterogeneous GPU architectures, real-time in situ visualization, improved turbulence modeling, and conjugate heat transfer coupling. Over the past year, NekRS has demonstrated strong scalability and performance on DOE’s leading exascale platforms, including Aurora and Frontier, confirming its readiness for some of the largest and most complex simulations attempted to date. These achievements provide a powerful new platform for high-fidelity data generation, which in turn supports the development and validation of advanced closure models critical for reactor safety and design. Significant algorithmic innovations have also been introduced. A new global runtime h-refinement capability simplifies workflows by reducing mesh preparation burdens and enabling coarse-to-fine restarts. Building on this, a novel multigrid strategy was implemented to accelerate pressure and transport solves at scale, addressing long-standing bottlenecks in exascale CFD. Together, these developments improve both the efficiency and accessibility of high-fidelity simulations for reactor-relevant problems. Collectively, these enhancements represent a major step forward in simulation technology, positioning NekRS as a cornerstone of NEAMS efforts to enable accurate, efficient, and scalable high-fidelity analysis of advanced nuclear systems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Spectroscopic Fourth-order Coronagraph for the Characterization of Terrestrial Planets at Small Angular Separations from Host Stars

We propose a new approach for high-contrast imaging at the diffraction limit using segmented telescopes in a modest observation bandwidth. This concept, named “spectroscopic fourth-order coronagraphy,” is based on a fourth-order coronagraph with a focal-plane mask that modulates the complex amplitude of the Airy disk along one direction. While coronagraphs applying the complex amplitude mask can achieve the theoretical limit performance for any arbitrary pupils, the focal-plane mask severely limits the bandwidth. Here, focusing on the fact that the focal-plane mask modulates the complex amplitude along one direction, we noticed that the mask can be optimized for each spectral element generated by a spectrograph. We combine the fourth-order coronagraph with two spectrographs to produce a stellar spectrum on the focal plane and reconstruct a white pupil on the Lyot stop. Based on the wave-front analysis of an optical design applying an Offner-type imaging spectrograph, we found that the achievable contrast of this concept is 10{sup −10} at 1.2–1.5 times the diffraction limit over the wavelength range of 650–750 nm for the entrance pupil of the LUVOIR telescope. Thus, this coronagraph concept could bring new habitable planet candidates not only around G- and K-type stars beyond 20–30 pc but also around very nearby M-type stars. This approach potentially promotes the characterization of the atmospheres of nearby terrestrial planets with future on- and off-axis segmented large telescopes.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Improving climate model coupling through a complete mesh representation: a case study with E3SM (v1) and MOAB (v5.x)

One of the fundamental factors contributing to the spatiotemporal inaccuracy in climate modeling is the mapping of solution field data between different discretizations and numerical grids used in the coupled component models. The typical climate computational workflow involves evaluation and serialization of the remapping weights during the preprocessing step, which is then consumed by the coupled driver infrastructure during simulation to compute field projections. Tools like Earth System Modeling Framework (ESMF) and TempestRemap offer capability to generate conservative remapping weights, while the Model Coupling Toolkit (MCT) that is utilized in many production climate models exposes functionality to make use of the operators to solve the coupled problem. However, such multistep processes present several hurdles in terms of the scientific workflow and impede research productivity. In order to overcome these limitations, we present a fully integrated infrastructure based on the Mesh Oriented datABase (MOAB) library, which allows for a complete description of the numerical grids and solution data used in each submodel. Through a scalable advancing-front intersection algorithm, the supermesh of the source and target grids are computed, which is then used to assemble the high-order, conservative, and monotonicity-preserving remapping weights between discretization specifications. The Fortran-compatible interfaces in MOAB are utilized to directly link the submodels in the Energy Exascale Earth System Model (E3SM) to enable online remapping strategies in order to simplify the coupled workflow process. We demonstrate the superior computational efficiency of the remapping algorithms in comparison with other state-of-the-science tools and present strong scaling results on large-scale machines for computing remapping weights between the spectral element atmosphere and finite volume discretizations on the polygonal ocean grids.

58 GEOSCIENCES↗
DOE OSTI2022

Metrics for Intercomparison of Remapping Algorithms (MIRA) protocol applied to Earth system models

Abstract. Strongly coupled nonlinear phenomena such as those described by Earth system models (ESMs) are composed of multiple component models with independent mesh topologies and scalable numerical solvers. A common operation in ESMs is to remap or interpolate component solution fields defined on their computational mesh to another mesh with a different combinatorial structure and decomposition, e.g., from the atmosphere to the ocean, during the temporal integration of the coupled system. Several remapping schemes are currently in use or available for ESMs. However, a unified approach to compare the properties of these different schemes has not been attempted previously. We present a rigorous methodology for the evaluation and intercomparison of remapping methods through an independently implemented suite of metrics that measure the ability of a method to adhere to constraints such as grid independence, monotonicity, global conservation, and local extrema or feature preservation. A comprehensive set of numerical evaluations is conducted based on a progression of scalar fields from idealized and smooth to more general climate data with strong discontinuities and strict bounds. We examine four remapping algorithms with distinct design approaches, namely ESMF Regrid (Hill et al., 2004), TempestRemap (Ullrich and Taylor, 2015), generalized moving least squares (GMLS) (Trask and Kuberry, 2020) with post-processing filters, and WLS-ENOR (Li et al., 2020). By repeated iterative application of the high-order remapping methods to the test fields, we verify the accuracy of each scheme in terms of their observed convergence order for smooth data and determine the bounded error propagation using challenging, realistic field data on both uniform and regionally refined mesh cases. In addition to retaining high-order accuracy under idealized conditions, the methods also demonstrate robust remapping performance when dealing with non-smooth data. There is a failure to maintain monotonicity in the traditional L2-minimization approaches used in ESMF and TempestRemap, in contrast to stable recovery through nonlinear filters used in both meshless GMLS and hybrid mesh-based WLS-ENOR schemes. Local feature preservation analysis indicates that high-order methods perform better than low-order dissipative schemes for all test cases. The behavior of these remappers remains consistent when applied on regionally refined meshes, indicating mesh-invariant implementations. The MIRA intercomparison protocol proposed in this paper and the detailed comparison of the four algorithms demonstrate that the new schemes, namely GMLS and WLS-ENOR, are competitive compared to standard conservative minimization methods requiring computation of mesh intersections. The work presented in this paper provides a foundation that can be extended to include complex field definitions, realistic mesh topologies, and spectral element discretizations, thereby allowing for a more complete analysis of production-ready remapping packages.

58 GEOSCIENCES↗
DOE OSTI2023

A mountain-induced moist baroclinic wave test case for the dynamical cores of atmospheric general circulation models

Idealized test cases for the dynamical cores of atmospheric general circulation models are informative tools to assess the accuracy of the numerical designs and investigate the general characteristics of atmospheric motions. A new test case is introduced that is built upon a baroclinically unstable base state with an added orographic barrier. The topography is analytically prescribed and acts as a trigger of both baroclinic Rossby waves and inertia–gravity waves on a rotating, regular-sized planet. Both dry and idealized moist configurations are suggested. The latter utilizes the Kessler warm-rain precipitation scheme. The test case enhances the complexity of the existing test suite hierarchy and focuses on the impacts of two midlatitudinal mountain ridges on the circulation. Selected simulation examples from four dynamical cores are shown. These are the Spectral Element and Finite Volume dynamical cores, which are part of the National Center for Atmospheric Research (NCAR) Community Earth System Model (CESM), versions 2.1.3 and 2.2, and the Cubed-Sphere Finite Volume dynamical cores, which is new to CESM version 2.2. In addition, the Model for Prediction Across Scales (MPAS) is tested. The overall flow patterns agree well in the four dynamical cores, but the details can vary greatly. The examples highlight the broad palette of use cases for the test case and reveal physics–dynamics coupling issues.

58 GEOSCIENCES↗
DOE OSTI2023

Quantitative uranium elemental reconstruction using spectral x-ray radiography

X-ray radiography offers the ability to noninvasively inspect the internal structure and material composition of objects. Dual-energy radiography allows material discrimination but is limited in quantitative material measurements due to the broad nature of the interrogating x-ray spectrum. Spectral radiography detectors provide an observation of not just the number of x rays that are transmitted through a sample but also the spectrum. Here, experimental validations of a method to use spectral x-ray radiography to accurately quantify the uranium mass in a powder are presented. An accurate system response model was developed, which includes a model of the incident x-ray source spectrum and a pixel-wise detector response that describes how the transmitted x rays were observed. Further, a calibration to account for the effect of partial x-ray attenuation was developed. As a result, the method is demonstrated to be capable of estimating the uranium mass in a variety of uranium oxide powders to a bias of –0.01±0.62%.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2022

Multi-element flow-driven spectral chaos (ME-FSC) method for uncertainty quantification of dynamical systems

The flow-driven spectral chaos (FSC) is a recently developed method for tracking and quantifying uncertainties in the long-time response of stochastic dynamical systems using the spectral approach. The method uses a novel concept called enriched stochastic flow maps as a means to construct an evolving finite-dimensional random function space that is both accurate and computationally efficient in time. In this paper, we present a multi-element version of the FSC method (the ME-FSC method for short) to tackle (mainly) those dynamical systems that are inherently discontinuous over the probability space. In ME-FSC, the random domain is partitioned into several elements, and then the problem is solved separately on each random element using the FSC method. Subsequently, results are aggregated to compute the probability moments of interest using the law of total probability. To demonstrate the effectiveness of the ME-FSC method in dealing with discontinuities and long-time integration of stochastic dynamical systems, four representative numerical examples are presented in this paper, including the Van-der-Pol oscillator problem and the Kraichnan-Orszag three-mode problem. Results show that the ME-FSC method is capable of solving problems that have strong nonlinear dependencies over the probability space, both reliably and at low computational cost.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Spectral Equivalence of Low-Order Discretizations for High-Order H(curl) and H(div) Spaces

In this paper, we present spectral equivalence results for high-order tensor product edge- and face-based finite elements for the H(curl) and H(div) function spaces. Specifically, we show for certain choices of shape functions that the mass and stiffness matrices of the high-order elements are spectrally equivalent to those for an assembly of low-order elements on the associated Gauss--Lobatto--Legendre mesh. Based on this equivalence, efficient preconditioners can be designed with favorable computational complexity. Numerical results are presented which confirm the theory and demonstrate the benefits of the equivalence results for overlapping Schwarz preconditioners.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Establishing an isoelectronic line ratio temperature diagnostic for soft X-ray absorption spectroscopy

For diagnosing temperatures of high-energy-density plasmas, relying on the ratio of a pair of isoelectronic spectral lines provides the alternative of ‘‘matched charge-state transits in different elements’’ to the more conventional, ‘‘unmatched charge-state transits in the same-element’’ spectral-line-ratio technique. In contrast to a novel previous establishment of isoelectronic emission-line ratio determination of plasma temperature, this report determines plasma temperature from the ratio of isoelectronic absorption spectral line pairs. Here, the feasibility of this technique is assessed from experimentally acquired transmission spectra, spanning the 7– 15 Å range, through a 0.4 μm MgO-NaF foil, tamped with CH, x-ray-radiation heated by a z-pinch dynamic hohlraum (ZPDH), and backlit by the brief X-ray burst upon imploding-wire stagnation on the Z pulsed-power facility at Sandia National Laboratories. As expected from the slight difference between interstage and isoelectronic absorption processes, a quantitative comparison between the value of isoelectronic-absorption-derived temperature and the value of inter-stage-absorption-derived temperature is shown to yield a well correlated, slight difference in inferred values of plasma temperature associated with local thermodynamic equilibrium.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Measurement of L-shell emission from mid-Z targets under non-LTE conditions using Transmission Grating Spectrometer and DANTE power diagnostics

In this work, we present the measurement of L-band emission from buried Sc/V targets in experiments performed at the OMEGA laser facility. The goal of these experiments was to study non-local thermodynamic equilibrium plasmas and benchmark atomic physics codes. The L-band emission was measured simultaneously by the time resolved DANTE power diagnostic and the recently fielded time integrated Soreq-Transmission Grating Spectrometer (TGS) diagnostic. The TGS measurement was used to support the spectral reconstruction process needed for the unfolding of the DANTE data. The Soreq-TGS diagnostic allows for broadband spectral measurement in the 120 eV–2000 eV spectral band, covering L- and M-shell emission of mid- and high-Z elements, with spectral resolution λ/Δλ = 8–30 and accuracy better than 25%. The Soreq-TGS diagnostic is compatible with ten-inch-manipulator platforms and can be used for a wide variety of high energy density physics, laboratory astrophysics, and inertial confinement fusion experiments.

Fraenkel, M. (ORCID:0000000291939544)↗
DOE OSTI2021

Spectral Equivalence Properties of Higher-Order Tensor Product Finite Elements and Applications to Preconditioning

In this study, we present spectral equivalence results for higher-order tensor product edge-, face- and interior-based finite elements. Specifically, we show for certain choices of shape functions that the mass and stiffness matrices of the higher-order elements are spectrally equivalent to those for an assembly of lowest-order elements on the associated Gauss-Lobatto-Legendre mesh. Based on this equivalence, efficient preconditioners can be designed with favorable computational complexity. Numerical results are presented which confirm the theory and demonstrate the benefits of the equivalence results for overlapping Schwarz preconditioners.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Spectral Peak Enhancement by Combining Trusted Response Elements via Machine Learning (SPECTRE-ML) v0.8.0

SPECTRE-ML (Spectral Peak Enhancement by Combining Trusted Response Elements via Machine Learning) is a machine learning based program for finding optimal clusters of radiation detector segments (i.e., pixels or voxels) in order to improve spectral performance. It provides facilities for pre-processing and analyzing training datasets, running ML algorithms, and evaluating and visualizing outputs. SPECTRE-ML outperforms simpler ad-hoc segmentation methods such as uniform depth clusters, learning detector performance trends such as dead layers, edge effects, and gain shifts. Although extensible to arbitrary highly-segmented spectroscopic radiation detectors, SPECTRE-ML currently focuses on improving spectral performance in highly-segmented CdZnTe (CZT) detectors for International Atomic Energy Agency (IAEA) non-destructive assay (NDA) safeguards tasks.

Vavrek, Jayson↗
DOE OSTI2020

High energy yield bifacial spectrum-splitting photovoltaic system

In this paper a photovoltaic system is proposed that achieves high energy yield by integrating bifacial silicon cells into a spectrum-splitting module. Spectrum splitting is accomplished using volume holographic optical elements to spectrally divide sunlight onto an array of photovoltaic cells with different bandgap energies. Light that is reflected from the ground surface onto the rear side of the module is converted by the bifacial silicon cells. The energy yield of the system is optimized by tuning the volume holographic element parameters, such as film thickness, index modulation, and construction point source positions. An example is presented for utility-scale illumination parameters in Tucson, Arizona, that attains an energy yield of 1010 k w ⋅ <#comment/> h r y r ⋅ <#comment/> m 2 , which is 32.8% of the incident solar insolation.

Chrysler, Benjamin D. (ORCID:0000000186250147)↗
DOE OSTI2021

A Fast Solver for the Fractional Helmholtz Equation

The purpose of this paper is to study a Helmholtz problem with a spectral fractional Laplacian, instead of the standard Laplacian. Recently, it has been established that such a fractional Helmholtz problem better captures the underlying behavior in Geophysical Electromagnetics. In this work, we establish the well-posedness and regularity of this problem. We introduce a hybrid spectral-finite element approach to discretize it and show well-posedness of the discrete system. In addition, we derive a priori discretization error estimates. Finally, we introduce an efficient solver that scales aswell as the best possible solver for the classical integer-order Helmholtz equation. We conclude withseveral illustrative examples that confirm our theoretical findings.

97 MATHEMATICS AND COMPUTING↗