Results for “Level set methods”

DOE OSTI2026

An efficient level set method for tracking many materials

Here, we present an efficient level set method to track an arbitrary number of materials. The algorithm is optimal in the sense that it only needs to store a single unsigned distance-like function and a single integer indicator function, independent of the number of materials or distinct regions being tracked. Furthermore, for smooth velocity fields and smooth interface shape, arbitrarily high order solutions can be demonstrated. For interfaces that are or become kinked, the solution is limited to second-order convergence rates in the L 1 norm and first-order in the L ∞ norm.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

MOSCATO Development and Integration in Fiscal Year 2025: Implementation of Multiphase, Multiphysics Modeling Capabilities for Molten Salt Systems

MOSCATO (Molten Salt Chemistry and Transport) is a multiphysics code that provides high-fidelity, coupled simulations of fluid flow, heat transfer, mass transfer, chemistry, electrochemical phenomena, and alloy corrosion for molten salt systems. In FY25, significant developments were made to the code package, enhancing its capabilities for modeling all relevant phenomena within operating moltens salt reactors (MSRs). The developments and activities in FY25 included: 1. Implementation of Level-Set methods to enable modeling of single-bubble behavior in molten salts. In FY25, the Level-Set two-phase flow modeling implementation was improved to simulate single bubble behavior with molten salt media. The large density and viscosity ratios between typical gases and molten salt liquids present challenges for these types of numerical solvers. With enhancements to the pressure projection method, MOSCATO’s Level-Set solver was able to be successfully validated to experiments related to helium bubble rise in stagnant molten salt. The simulated bubble rising velocity showed reasonable good agreement with experimental measurements. The bubble shape and dynamics were also visually compared with experimental snapshots, demonstrating a good qualitative match. 2. Generation of mass transfer correlations for multiphase flow systems. To enable calculations of the tritium transport across the interface between gas bubbles and salt, we modeled high- Schmidt-number mass transfer around a sphere across a broad range of Reynolds numbers. The mesh near the sphere surface was highly refined to resolve steep concentration gradients caused by the low diffusion coefficient. Literature-based mass transfer correlations were compared with the numerical results, and modifications were proposed to improve agreement, particularly at higher Schmidt numbers. These mass transfer correlations were subsequently provided to other national laboratories to help enable high quality mass transfer simulations using lower-order solvers under development within the NEAMS program. 3. Preliminary implementation of a bubbly flow solver. To model bubbly flow in molten salt, we implemented a bubbly flow solver for void fractions less than 5%. To do so, an algebraic relative velocity model that assumes small bubbles with rapid momentum equilibration was added to MOSCATO to compute bubble velocities. Preliminary comparisons with experimental data showed reasonable agreement, and further improvements are underway. 4. Generation of mass transfer correlations for MSRE subchannel The Molten-Salt Reactor Experiment (MSRE) was a landmark historical project that demonstrated the feasibility of molten-salt reactor technology. The MSRE campaign also generated a significant body of experimental data and reports that continue to support molten-salt–related research. In this report, the MSRE core subchannel was used as the reference geometry for a mass transfer study performed with MOSCATO. The geometry and computational mesh were adapted from a previous study, providing adequate resolution for the relatively low Reynolds number in this case. Additional mesh refinement was applied to reach higher Schmidt numbers, enabling the derivation of a reliable mass-transfer correlation for the present scenario. 5. Simulations of oxygen ingressions into molten salt. In the previous fiscal year, we initiated a study to simulate oxygen ingression in stagnant salt. As oxygen enters the salt through its surface, it reacts with Ce 3+ to form solid CeO 2 and other reaction products. To more fully capture the complex diffusion-convection-reaction mechanisms, capabilities for modeling natural convection in the salt vessel were added. These were needed as the flow of the ingressed gas induced flow in the salt caused by surface shear and non-isothermal effects. With these updated physics in place, we were able to successfully reproduce the experimental results for the rate of change of CeCl 3 concentrations versus time. 6. Flow corrosion model validation. In FY24, MOSCATO’s corrosion model was validated against static corrosion experiments. In FY25, this work was extended to a flow corrosion experiment, where FLiNaK salt was driven by natural convection, with initial salt impurities to initiate corrosion. Despite uncertainties in parameters such as elemental diffusion coefficients in the alloy and unknown H + concentrations, the simulations achieved good agreement with experimental results, especially in predicting sample mass losses.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Spectrally Stabilized Interface Capturing Formulation and Implementation in Nek5000/NekRS

This report documents the formulation of a novel level-set method for incompressible two-phase flows in the continuous Galerkin (CG) high order spectral element framework. The overall method hinges on a novel implementation of the spectral vanishing viscosity (SVV) operator for the stabilization of linear/non-linear hyperbolic problems. The multidimensional SVV convolution kernels, which in essence, have a similar effect as a high pass filter applied to the derivatives, are formulated by exploiting the tensor product form, analogous to the construction of the usual stiffness matrix system. The resulting kernels are directionally decoupled and ensure a linear, symmetric positive definite, elliptic matrix operator. The SVV formulation is demonstrated to provide a robust stabilizing mechanism through challenging linear and non-linear hyperbolic problems, including problems pertinent to the level-set formulation. The two-phase framework conceptualized herein is based on the conservative level-set (CLS) method which represents the interface between the fluids by the 0.5 iso-contour of the smoothed Heaviside function. The CLS method is augmented with a preconditioning procedure for interface normals using the signed distance function which precludes the manifestation of spurious oscillations in the vicinty of the interface. Further, the existing mixed explicit-implicit approach for the solution of Navier-Stokes equations in Nek5000, as described in Tomboulides et al, is augmented with a pressure coefficient splitting approach for the Poisson equation, which greatly accelerated the convergence of pressure solver for two-phase systems with large density ratio. The robustness and accuracy of the overall two-phase method is demonstrated through canonical challenging problems involving high density and viscosity ratios, with and without surface tension. The two-phase formulation is wholly implemented in Nek5000 and the SVV stabilization method is implemented in NekRS, which is the essential precursor to the two-phase framework, undergoing active development.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Pore Resolved Simulations of Joule Heating in Fibrous Media using an Embedded Boundary Method

Joule heating has been regarded as an energy-efficient and sustainable method for heating materials and gases at large scales. The modeling of local temperature effects at pore-resolved scales for such systems, however, has been difficult to achieve due to challenges in coupling thermo-chemical processes in complex porous media and in large representative volume elements (RVEs). To this end, we developed an electro-thermal model at the pore scale to study Joule heating effects in large heterogeneous systems with different microstructures. This was achieved using the level set method to implicitly delineate distinct regions within the domain, and an embedded boundary method to facilitate heat exchange across the fluid-solid interface. Moreover, we applied this method to investigate unsteady non-linear electro-thermal effects in non-woven fibrous graphite conductors for RVEs with characteristic lengths of 2 mm, with different fiber orientations, porosity (80% – 90%) and fiber diameters (10 – 20µm). The coupled equations were solved numerically and they produced peak temperatures greater than 2000 K resulting in heating rates as high as 80,000 K/s. Moreover, the results depended strongly on the microstructure of the fiber skeleton and current density. Geometries with large fibers (∼ 20µm) had the highest average and peak temperatures with the mean temperature increasing by 3.9 % while the peak temperature increased by 9.9 %. Anisotropic domains on the other hand had the lowest mean and peak temperatures with peak and mean temperatures of 2293 K and 1437.7K respectively representing a corresponding 12.1% and 5.1% drop in the temperatures. An increase in porosity from 80% to 90%, however, led to an increase in the peak temperature by 5.1%.

Joule heating↗

DOE OSTI2024

MOSCATO Development and Integration in Fiscal Year 2024

MOSCATO (Molten Salt Chemistry and Transport) is a multiphysics code that provides high-fidelity, coupled simulations of fluid flow, heat transfer, mass transfer, chemistry, electrochemical phenomena, and alloy evolution for molten salt equipment. In FY24, significant developments were made to the code package, enhancing its capabilities in many aspects. The improvements and advancements can be summarized as follows: 1. Implementation of tritium transport capabilities and validation with experimental data: To enable modeling of tritium and other fission gases within MSRs, we implemented gas transport within MOSCATO via inclusion of couple mass transport equations within the salt and structural alloys. Comparisons to experimental data from literature showed good agreement with respect to tritium release rates. 2. Preliminary implementation of two-phase flow models in MOSCATO: To model tritium and other gases above their solubility limits, we implemented preliminary two-phase flow models within MOSCATO to account for bubble transport. The first model adopted was the Level-Set approach, which can handle the high void fraction regime, but with a requirement for high mesh resolution thus high computational expense. In this report, we present a verification of the Level-Set method using a simple benchmark case. We also performed a demonstration of the code as applied to an experimental case involving cover gas flow through salt in an experimental vessel. The second model adopted was the Eulerian-Eulerian dispersed flow model, which is computationally cheaper but limited to low void fraction regimes, such as bubbly flow. Validation and verification have not yet been performed for the Eulerian-Eulerian approach, but a preliminary implementation was completed. 3. Validation with static corrosion experiments: Static corrosion experimental data for stainless steel coupons within molten salts was used to further validate the corrosion model in MOSCATO. To do so, we leveraged the existing models in MOSCATO and simulated the sample mass loss and mass gain phenomena. Several ion species, including Cr 2+ , Fe 2+ and H + , were simulated in salt using the PNP solver, while Cr 0 and Fe 0 were simulated with a diffusion solver in stainless steel. The mass loss of the samples was compared with experimental data, and good agreement was achieved. These combined activities served to further expand the capabilities of MOSCATO and make it more generally applicable to the full range of phenomena that can control chemistry and corrosion in molten salt reactors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Level-set topology optimization with PDE generated conformal meshes

This paper presents a level-set topology optimization approach that uses conformal meshes for the analysis of the displacement field. The structure’s boundary is represented by the iso-contour of a level-set field discretized on a fixed background design mesh. The conformal mesh is updated for each design iteration via a PDE based mesh morphing process that identifies the set of facets in the background mesh that are homeomorphic to the boundary and relaxes the homeomorphic mesh to conform to the structure’s boundary and ensure high element quality. The conformal mesh allows for a more accurate computation of the response versus density and some level-set based methods which interpolate material properties using the volume fraction. Numerical examples illustrate the proposed approach by optimizing linear-elastic two- and three-dimensional structures, wherein insight into the performance of the mesh morphing process is provided. The examples also highlight the scalability of the approach.

42 ENGINEERING↗

DOE OSTI2024

Adaptive immersed isogeometric level-set topology optimization

Here, this paper presents for the first time an adaptive immersed approach for level-set topology optimization using higher-order truncated hierarchical B-spline discretizations for design and state variable fields. Boundaries and interfaces are represented implicitly by the iso-contour of one or multiple level-set functions. An immersed finite element method, the eXtended IsoGeometric Analysis, is used to predict the physical response. The proposed optimization framework affords different adaptively refined higher-order B-spline discretizations for individual design and state variable fields. The increased continuity of higher-order B-spline discretizations together with local refinement enables direct control over the accuracy of the representation of each field while simultaneously reducing computational cost compared to uniformly refined discretizations. A flexible mesh adaptation strategy enables local refinement based on geometric measures or physics-based error indicators. These adaptive discretization and analysis approaches are integrated into gradient-based optimization schemes, evaluating the design sensitivities using the adjoint method. Numerical studies illustrate the features of the proposed framework with static, linear elastic, multi-material, two- and three-dimensional problems. The examples provide insight into the effect of refining the design variable field on the optimization result and the convergence rate of the optimization process. Using coarse higher-order B-spline discretizations for level-set fields promotes the development of smooth designs and suppresses the emergence of small features. Moreover, adaptive mesh refinement for state variable fields results in a reduction of overall computational cost. Higher-order B-spline discretizations are especially interesting when evaluating gradients of state variable fields due to their higher inter-element continuity.

36 MATERIALS SCIENCE↗

DOE OSTI2025

The Remarkable I 2 O 3 Molecule: A New View from Theory

Atmospheric iodine chemistry has garnered increasing attention as a result of increased iodine emissions. A key subset of this chemistry involves iodine oxides (I 2 O 2–5 ), which serve as precursors to particle formation. Among these, I 2 O 3 is the simplest iodine oxide involved in particle formation, but it has remained undetected in the atmosphere. Previous theoretical studies have characterized this peculiar molecule, primarily using energies to refine geometries obtained at low levels of theory. Due to the reemerging interest in I 2 O 3 , this study presents geometries optimized at the CCSD(T)/aug-cc-pwCVTZ-PP level of theory─marking the first instance, to the best of our knowledge, where this system has been studied exclusively with CCSD(T). Harmonic vibrational frequencies were computed at the same level of theory. Final energetics were obtained using the very high level CCSDT(Q) method with basis sets up to quintuple-zeta cardinality (aug-cc-pwCV5Z-PP) and extrapolated to the CBS limit to yield CCSDT(Q)/CBS//CCSD(T)/aug-cc-pwCVTZ-PP energies. These energies include harmonic zero-point vibrational energy corrections and scalar relativistic energy corrections. Additionally, this study discovers new isomers along the I 2 O 3 potential energy surface, a novel contribution to the field. The performance of different computational methods and DFT functionals commonly used in atmospheric chemistry is also assessed relative to high-level theoretical methods.

basis sets↗

DOE OSTI2025

A simple and highly efficient protocol for 13 C-labeling of plant cell wall for structural and quantitative analyses via solid-state nuclear magnetic resonance

Plant cell walls are made of a complex network of interacting polymers that play a critical role in plant development and responses to environmental changes. Thus, improving plant biomass and fitness requires the elucidation of the structural organization of plant cell walls in their native environment. The 13 C-based multi-dimensional solid-state nuclear magnetic resonance (ssNMR) has been instrumental in revealing the structural information of plant cell walls through 2D and 3D correlation spectral analyses. However, the requirement of enriching plants with 13 C limits the applicability of this method. To our knowledge, there is only a very limited set of methods currently available that achieve high levels of 13 C-labeling of plant materials using 13 CO 2 , and most of them require large amounts of 13 CO 2 in larger growth chambers. In this study, a simplified protocol for 13C-labeling of plant materials is introduced that allows ca 60% labeling of the cell walls, as quantified by comparison with commercially labeled samples. This level of 13 C-enrichment is sufficient for all conventional 2D and 3D correlation ssNMR experiments for detailed analysis of plant cell wall structure. The protocol is based on a convenient and easy setup to supply both 13 C-labeled glucose and 13 CO 2 using a vacuum-desiccator. The protocol does not require large amounts of 13 CO 2 . This study shows that our 13 C-labeling of plant materials can make the accessibility to ssNMR technique easy and affordable. The derived high-resolution 2D and 3D correlation spectra are used to extract structural information of plant cell walls. This helps to better understand the influence of polysaccharide-polysaccharide interaction on plant performance and allows for a more precise parametrization of plant cell wall models.

09 BIOMASS FUELS↗

DOE OSTI2025

Multiclass Classification Using Bayesian Multivariate Adaptive Regression Splines

We present a new Bayesian model for the problem of multiclass classification. In this model, the probabilities of class membership of a given observation are determined by the mean of a latent Gaussian distribution. The mean functions of this latent distribution consist of combinations of highly flexible basis functions of the inputs: multivariate adaptive regression splines (MARS), first developed for multiple regression. We use reversible jump Markov chain Monte Carlo to make inference on the classification model, including the number of basis functions. We compare the probabilistic classification performance of our proposed approach to existing methods on simulated and benchmark data, and compare uncertainty estimates on simulated data. Our proposed method compares favorably with existing Bayesian and frequentist multiclass classification methods in out-of-sample probabilistic classification, and uncertainty estimation of these probabilistic classifications. We examine the fit of the proposed method to a data set of hurricane storm surge levels near Delaware Bay, US, and conclude that sea level rise is a key contributor to damage delivered by storm surge.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Power Profile Monitoring and Tracking Evolution of System-Wide HPC Workloads

The power & energy demands of HPC machines have grown significantly. Modern exascale HPC systems require tens of megawatts of combined power for computing resources and cooling facilities at full capacity. The current energy trend is not sustainable for future HPC systems, and there is a need to work toward the energy efficiency aspect of HPC performance. Energy awareness of the HPC applications at the job level is essential for running an efficient HPC system. This work aims to develop a pipeline to provide a production-level system-wide overview of the HPC workloads' power profile while handling evolving workloads exhibiting new power trends. We developed an open-set classification model for HPC jobs based on the properties of power profiles to continuously provide a system-wide holistic view of recently completed jobs. The pipeline helps continuously monitor the job-level power usage pattern of HPC and enables us to capture the new trends in applications' power behavior. We employed a comprehensive set of techniques to generate job-level data, custom-designed feature extraction methods to extract critical features from jobs' power profiles, clustering techniques powered by generative modeling, and open-set classification for identifying job profiles into known classes or an unknown set. With extensive evaluations, we demonstrate the effectiveness of each component in our pipeline. We provide an analysis of the resulting clusters that characterize the power profile landscape of the Summit supercomputer from more than 60K jobs executed in a year. The open-set classification classifies the known data sets into known classes with high accuracy and identifies unknown data noints with over 85% accuracy.

Karimi, Ahmad Maroof↗

DOE OSTI2025

Learning with Adaptive Conservativeness for Distributionally Robust Optimization: Incentive Design for Voltage Regulation

Information asymmetry between the Distribution System Operator (DSO) and Distributed Energy Resource Aggregators (DERAs) obstructs designing effective incentives for voltage regulation. To capture this effect, we employ a Stackelberg game-theoretic framework, where the DSO seeks to overcome the information asymmetry and refine its incentive strategies by learning from DERA behavior over multiple iterations. We introduce a model-based online learning algorithm for the DSO, aimed at inferring the relationship between incentives and DERA responses. Given the uncertain nature of these responses, we also propose a distributionally robust incentive design model to control the probability of voltage regulation failure and then reformulate it into a convex problem. This model allows the DSO to periodically revise distribution assumptions on uncertain parameters in the decision model of the DERA. Finally, we present a gradient-based method that permits the DSO to adaptively modify its conservativeness level, measured by the size of a Wasserstein metric-based ambiguity set, according to historical voltage regulation performance. The effectiveness of our proposed method is demonstrated through numerical experiments.

adaptation models↗

DOE OSTI2024

Learning with Adaptive Conservativeness for Distributionally Robust Optimization: Incentive Design for Voltage Regulation: Preprint

Information asymmetry between the Distribution System Operator (DSO) and Distributed Energy Resource Aggregators (DERAs) obstructs designing effective incentives for voltage regulation. To capture this effect, we employ a Stackelberg game-theoretic framework, where the DSO seeks to overcome the information asymmetry and refine its incentive strategies by learning from DERA behavior over multiple iterations. We introduce a model-based online learning algorithm for the DSO, aimed at inferring the relationship between incentives and DERA responses. Given the uncertain nature of these responses, we also propose a distributionally robust incentive design model to control the probability of voltage regulation failure and then reformulate it into a convex problem. This model allows the DSO to periodically revise distribution assumptions on uncertain parameters in the decision model of the DERA. Finally, we present a gradient-based method that permits the DSO to adaptively modify its conservativeness level, measured by the size of a Wasserstein metric-based ambiguity set, according to historical voltage regulation performance. The effectiveness of our proposed method is demonstrated through numerical experiments.

distribution system operator↗

DOE OSTI2026

Third moments of nucleon unpolarized, polarized, and transversity parton distribution functions from physical-point lattice QCD

Using forward matrix elements of local leading-twist operators, we present a determination of the isovector third Mellin moments ⟨𝑥 2 ⟩ of nucleon unpolarized, polarized, and transversity parton distribution functions. Two lattice QCD ensembles at the physical pion mass are used, which were generated using a tree-level Symanzik-improved gauge action and 2+1 flavor tree-level improved Wilson Clover fermions coupling via 2-level HEX-smearing. Leveraging a wide set of operators, two extraction methods for the matrix elements, and the automatic inclusion of model uncertainties via bootstrapped model averages, we extract values of the third Mellin moments. Furthermore, this is the first direct calculation of these observables performed at the physical pion mass.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Machine Learning Classification Strategy to Improve Streamflow Estimates in Diverse River Basins in the Colorado River Basin

Streamflow in the Colorado River Basin (CRB) is significantly altered by human activities including land use/cover alterations, reservoir operation, irrigation, and water exports. Climate is also highly varied across the CRB which contains snowpack-dominated watersheds and arid, precipitation-dominated basins. Recently, machine learning methods have improved the generalizability and accuracy of streamflow models. Previous successes with LSTM modeling have primarily focused on unimpacted basins, and few studies have included human impacted systems in either regional or single-basin modeling. We demonstrate that the diverse hydrological behavior of river basins in the CRB are too difficult to model with a single, regional model. We propose a method to delineate catchments into categories based on the level of predictability, hydrological characteristics, and the level of human influence. Lastly, we model streamflow in each category with climate and anthropogenic proxy data sets and use feature importance methods to assess whether model performance improves with additional relevant data. Overall, land use cover data at a low temporal resolution was not sufficient to capture the irregular patterns of reservoir releases, demonstrating the importance of having high-resolution reservoir release data sets at a global scale. On the other hand, the classification approach reduced the complexity of the data and has the potential to improve streamflow forecasts in human-altered regions.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Virtual Engineering: Python framework for engineering process design

Virtual Engineering (VE) is a Python software framework designed to accelerate the research and development of engineering processes that are fundamentally defined by multiple unit operations executed in series. VE supports a wide variety of different multi-physics models and integrates them to simulate a complete end-to-end process. To automate the execution of this model sequence, VE provides (i) a robust method to communicate between models, (ii) a high-level, user-friendly interface to set model parameters and enable optimization, and (iii) an overall model-agnostic approach that allows new computational units to be swapped in and out of workflows. Although the VE framework was developed to support the biochemical conversion of biomass to fuel, we have designed each component to easily accommodate new domains and unit models.

09 BIOMASS FUELS↗

DOE OSTI2024

Formally Verified ZTA Requirements for OT/ICS Environments with Isabelle/HOL

The clean energy transformation includes the integration of distributed energy resources with the power grid, which has led to a substantial increase in the complexity of power grids infrastructure and the underlying operational technology environment. Power grids infrastructure represents an operational technology environment that has become a system of systems, integrating heterogeneous devices which are both software-and hardware-intensive; as a result, there are increasing demands to exploit advances in the commodity of software-hardware infrastructures to improve energy systems requirements such as cybersecurity and resilience. In such a setting, system requirements at different levels mix, which leads to vulnerabilities and undesirable outcomes. The use of formal methods to characterize and prove system requirements removes ambiguity, increases automation, and provides high levels of assurance and reliability. In this paper, we contribute a methodology and a framework for the system-level verification of zero trust architecture requirements in operational technology environments. We define a formal specification for the core functionalities of operational technology environments, the corresponding invariants, and security proofs. Of particular note is our modular approach for the formal verification of asynchronous interactions in operational technology environments. The formal specification and the proofs have been mechanized using the interactive theorem proving environment Isabelle/HOL.

formal methods↗

DOE OSTI2026

North Slope of Alaska XSAPR b1 Data Processing Report: May 2025-April 2026

The U.S. Department of Energy’s Atmospheric Radiation Measurement (ARM) User Facility operates an X-band Scanning ARM Precipitation Radar (XSAPR) at the North Slope of Alaska (NSA) atmospheric observatory in Utqiaġvik. This radar provides year-round dual-polarization measurements of snow and ice in an arctic environment. Over the past few years, there has been greater focus on the NSA XSAPR, and recent efforts by ARM staff have resulted in quality-controlled, b-level data (Rocque et al. 2026b). This report outlines the processing of the second set of b-level data released for this radar from May 2025 through April 2026 following similar methods from Rocque et al. (2026b).

54 ENVIRONMENTAL SCIENCES↗