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DOE OSTI2026

Coupling Noah-Multiparameterization land-surface Model with Energy Research and Forecasting Model

The Energy Research and Forecasting (ERF) model is a high-performance atmospheric model built on the AMReX adaptive mesh refinement (AMR) framework, enabling efficient simulations on heterogeneous computing platforms that combine multicore processors with hardware accelerators. To support land–atmosphere interactions within ERF’s AMR-based environment, a land-surface model must be capable of operating directly on hierarchically refined meshes. In this work, we present a methodology for coupling the Fortran-based Noah-Multiparameterization (Noah-MP) land-surface model with ERF’s C++ codebase. Rather than rewriting Noah-MP, we construct a Fortran–C interoperability layer using CodeScribe, a tool that leverages large language models (LLMs) to automate the generation of interface code. CodeScribe applies structured prompting techniques to generate bindings that support efficient data exchange and function calls between ERF and Noah-MP. The coupling framework also incorporates AMR-aware data handling strategies, allowing NoahMP to operate seamlessly within ERF’s hierarchical mesh structure. This work provides a structured approach for integrating legacy Fortran models into modern C++-based modeling systems using LLM-assisted code generation.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Comparison of Full-Field and Integrated CFD Convergence Based on Richardson Extrapolation

This work investigated the usefulness of Richardson extrapolation--based discretization error estimates across all points in a solution field to produce a spatial convergence field for a computational fluid dynamics (CFD) simulation. The presented work used previously developed methods for Richardson extrapolation to compute the convergence orders of a CFD simulation at all points of the base (coarsest) mesh solution. Three test cases of increasing complexity were considered: Poiseuille flow, incompressible flow around a sharp corner, and transonic flow over an RAE 2822 airfoil. These test cases highlighted the potential of the proposed method to identify error sources and their relation to the model system-response-quantity convergence orders. However, these test cases also revealed the immaturity of the proposed method stemming from the unreliability of computing observed convergence orders at single points. Nonetheless, the test cases highlighted that the observed convergence orders allow for a more accurate diagnosis of constructive and destructive error transport than mesh pair error estimates. In the long run, the proposed method can be a tool for developing efficient and advanced error management strategies like adaptive mesh refinement.

Weinmeister, Justin↗

DOE OSTI2024

Turbo-Turtle v0.12.1

A collection of solid body modeling tools for 2D sketched, 2D axisymmetric, and 3D revolved models. It also contains general purpose meshing and image generation utilities appropriate for any model, not just those created with this package. Implemented for Abaqus and Cubit as backend modeling and meshing software. Orginal implementation targeted Abaqus so most options and descriptions use Abaqus modeling concepts and language. Turbo-Turtle makes a best effort to maintain common behaviors and features across each third-party software’s modeling concepts. As much as possible, the work for each subcommand is performed in Python 3 to minimize solution approach duplication in third-party tools. The third-party scripting interface is only accessed when creating the final tool specific objects and output. The tools contained in this project can be expanded to drive other meshing utilities in the future, as needed by the user community. This project derives its name from the origins as a sphere partitioning utility following the turtle shell (or soccer ball) pattern.s.

Brindley, Kyle↗

DOE OSTI2024

Meshfree Methods

Meshfree methods have undergone substantial development and have received much attention in the last two decades. This new family of numerical methods is designed to inherit the main advantages of the finite element method such as compact supports of shape functions and good approximation properties while, at the same time, overcome the main disadvantages of the finite element method caused by the mesh dependence. The meshfree methods share a common feature that no mesh is needed and shape functions are constructed from sets of points, thus eliminating the need for time consuming mesh generation. The most significant advantage of meshfree methods is the flexibility in customizing approximation functions for desired regularity and for capturing essential physics and features of the particular problems of interest. Adaptivity formulation and multiple-scale solution strategies also can be implemented with relative ease. It has become clear that the meshfree methods provide considerable advantages over the conventional finite element methods in solving problems involving moving discontinuities, evolving material interfaces, multiple-scale phenomena, large material distortion and structural deformation, and fracture and damage processes. This Chapter gives an overview of many classes of meshfree methods, with more detailed discussions on Smoothed Particle Hydrodynamics (SPH), the Reproducing Kernel Particle Method (RKPM), Peridynamics (PD), the Material Point Method (MPM), as well as their applications in various challenging engineering problems.2

Chen, Jiun-Shyan↗

DOE OSTI2025

Advanced Computational Modeling of High-Level Waste Vitrification at the Hanford Site

The U.S. Department of Energy (DOE) has selected vitrification for stabilizing legacy tank waste at the Hanford site, where radioactive waste from plutonium production was historically stored in underground tanks. This waste will be separated into low-activity waste (LAW) and high-level waste (HLW) fractions and processed at the Waste Treatment and Immobilization Plant (WTP). At WTP, glass melters are used for the vitrification of radioactive tank waste, transforming it into a stable borosilicate glass form for safe long-term storage. The melter vessel is constructed from highly durable and heat-resistant materials, where the vitrification process occurs. The main regions that are modeled are the melt pool, plenum, cold cap, riser/discharge chamber, and surrounding structure with insulation layers. Forced convection induced by air bubblers at the base of the melter ensure uniform temperature distribution and provide heat to the cold cap layer. The cold cap is a region of reacting batch feed that floats on top of the molten glass and is where the batch-to-glass reactions occur. Joule heating provided by electrodes mounted along the vertical walls of the melter and immersed directly in the glass, generates the necessary heat for the net endothermic conversion processes that occur in the cold cap. The high temperatures, radioactivity, and opaque nature of the glass prevent direct observation inside the melters. Therefore, computational models are essential for providing insight into factors that affect melter throughput. Thermocouples in the plenum provide operators with plenum temperature measurements. Operational adjustments include bubbling rate, voltage supplied to the electrodes, feed adjustments, and glass removal rate. Different computational fluid dynamics (CFD) models have been developed, each serving a specific purpose. There are CFD models of different scale melters, as well as models that capture the two-phase flow interfaces of rising bubbles in the molten glass or models with a simplified molten glass region so that the surrounding structure and plenum can be feasibly incorporated. Pilot-scale melter models have been developed to serve as validation of the methods employed in the simulation of the full-scale WTP melters. Models incorporating resolved bubbling are used to develop momentum source terms to implement into a single phase, multi-region, steady-state flow model that is being validated by measured process parameters such as glass production rate, voltage, input power, plenum temperatures, etc. The resolved bubbling model uses the multiphase volume of fluid approach to model the system with a high-resolution interface capturing scheme to maintain sharp interfaces between the molten glass and the air phase. The suite of CFD models is continually being improved to incorporate more realistic physics and achieve faster turnaround time. For example, an incremental controller is implemented to automatically adjust electrode voltage within the simulation to a molten glass set point temperature of 1150°C. Newer models feature improved meshes to ensure conformal meshes between regions and eliminate unnecessary mesh refinement in areas that are not of interest (such as boundary layers in offgas ports). Instead of explicitly modeling the structural, refractory, and insulation layers of the melter, a thermal resistance approach is used with published correlations used for boundary conditions. The development of robust and efficient CFD models will be instrumental in enabling the WTP to successfully fulfill its mission of safely stabilizing legacy nuclear waste.

12 - MGMT OF RADIOACTIVE AND NON-RADIOACTIVE WASTE↗

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 OSTI2024

FLARE: field line analysis and reconstruction for 3D boundary plasma modeling

The FLARE code is a magnetic mesh generator that is integrated within a suite of tools for the analysis of the magnetic geometry in toroidal fusion devices. A magnetic mesh is constructed from field line segments and permits fast reconstruction of field lines in 3D boundary plasma codes such as EMC3-EIRENE. Both intrinsically non-axisymmetric configurations (stellarators) and those with symmetry breaking perturbations of an axisymmetric equilibrium (tokamaks) are supported. The code itself is written in Modern Fortran with MPI support for parallel computing, and it incorporates object-oriented programming for the definition of the magnetic field and the material surface geometry. Extended derived types for a number of different magnetohydrodynamic equilibrium and plasma response models are implemented. The core element of FLARE is a field line tracer with adaptive step-size control, and this is integrated into tools for the construction of Poincaré maps and invariant manifolds of X-points. A collection of high-level procedures that generate output files for visualization is build on top of that. The analysis modules are build with Python frontends that facilitate customization of tasks and/or scripting of parameter scans.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Exact signed distance fields using parallel Fast Sweeping Method

Signed distance fields are often used in multiphysics simulations to track material interfaces. We present a simple methodology based on the fast sweeping method to generate the exact signed distance from triangular meshes and linear paths on Cartesian grids. The methodology propagates the closest primitive to the boundary to the rest of the domain following the characteristics. A local upwind criterion is used to decide between the new and existing closest primitive at each grid point while capturing the correct sign of the global function. The methodology has optimal computational complexity and runs efficiently in distributed-memory architectures. We include 2D and 3D test cases along with a resolution study up to 0.512 trillion zones and 1,000 computer cores. The solution strategy can also be applied to other types of meshes or collections of primitives.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Improvements to MOOSE user workflow through polyhedral elements, automation, and concise physics syntax

The MOOSE framework is a foundational capability used by the NEAMS program to create over 15 different simulation tools for advanced nuclear reactors. Due to MOOSE's broad use, improvements to the framework in support of modeling and simulation goals are critical to the program. Such improvements can take many forms, including optimization, improved user experience, streamlined application programming interfaces (APIs), parallelism, and new capabilities. The work described in this report was conducted in direct support of NEAMS tools and includes: addition of support for polyhedral elements, incorporation of mesh smoothers for mesh repair, integration of the Physics and ActionComponents systems, expansion of the Convergence system, and exploration of automated input file generation. These five areas of development are fundamental capabilities that will be leveraged by many NEAMS applications.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Concurrent two-way coupling of global and local models across internal boundaries with non-matching discretizations

Coupling local and global models enables efficient simulation of multiscale systems, where global models capture large-scale behavior and local models, with enhanced physics, resolve finer details over a smaller region. Here, this paper presents a mathematically consistent method for coupling physics-based models of varying fidelity across adjacent, non-overlapping subdomains, even when discretizations do not match at the immersed interdomain interfaces. Incompressible Navier-Stokes equations (NSE) constitute the global model while residual-based turbulence model serves as the local high-fidelity model. In addition, a scalar advection-diffusion equation that models the convection of an active scalar field is appended to the turbulence model in the local domain. This scalar field does not have its complement in the global model, giving rise to unequal number of equations at the immersed boundary between local and global models. Interdomain coupling terms are derived via the Variational Multiscale Discontinuous Galerkin (VMDG) method with new developments in scale representation and efficient fine-scale estimation. While transient laminar flows modeled with NSE in the global domain can be resolved with relatively coarse mesh, turbulent flow calculations in the local model require much finer spatial discretizations as well as smaller time-step for appropriately resolving the turbulent flow physics. The proposed framework also accommodates non-matching meshes at the immersed boundaries. Test problems in 2D and 3D numerically showcase the concurrent two-way coupling of unknown fields across the immersed boundaries. The 3D test presents a case with an unequal number of equations, where the scalar field represents the convection of contaminant concentration. This provides more detailed physics in the local region and highlights its application in climate modeling and atmospheric sciences.

Variational Multiscale Discontinuous Galerkin (VMD↗

DOE OSTI2024

Zapiary: Creating Visibility in IOT Networks

Zigbee and Z-Wave are the main networking protocols used by low-power Internet of Things (IOT) devices. These protocols use low frequencies. Mesh architecture, and unique address formats that make them not compatible with traditional network traffic tools like IX-Discovery Tools. Zapiary is a software that takes CSV files with Zigbee and Z-Wave traffic and generates Structured Threat Information eXpression (STIX) JSON bundles illustrating the communication within IOT networks. The bundles can then be viewed within Structured Threat Intelligence Graph (STIG) or used with AI/ML models to provide deeper visibility into nodes that make up the network and the ability to trend the mesh network over time.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Numerical integration in the virtual element method with the scaled boundary cubature scheme

Abstract The virtual element method (VEM) is a stabilized Galerkin method on meshes that consist of arbitrary (convex and nonconvex) polygonal and polyhedral elements. A crucial ingredient in the implementation of low‐ and high‐order VEM is the numerical integration of monomials and nonpolynomial functions over such elements. In this article, we apply the recently proposed scaled boundary cubature (SBC) scheme to compute the weak form integrals in various virtual element formulations over polygonal and polyhedral meshes. In doing so, we demonstrate the flexibility of the approach and the accuracy that it delivers on a broad suite of boundary‐value problems in 2D and 3D over polytopes with affine faces as well as on elements with curved boundaries. In addition, the use of the SBC scheme is exemplified in an enriched Poisson formulation of the VEM in which weakly singular functions are required to be integrated. This study establishes the SBC method as a simple, accurate and efficient integration scheme for use in the VEM.

Chin, Eric B.↗

DOE OSTI2025

Characterizing GPU Energy Usage in Exascale-Ready Portable Science Applications

We characterize the GPU energy usage of two widely adopted exascale-ready applications representing two classes of particle and mesh solvers: (i) QMCPACK, a quantum Monte Carlo package, and (ii) AMReX-Castro, an adaptive mesh astrophysical code. We analyze power, temperature, utilization, and energy traces from double-/single (mixed)-precision benchmarks on NVIDIA’s A100 and H100 and AMD’s MI250X GPUs using queries in NVML and rocm_smi_lib, respectively. We explore application-specific metrics to provide insights on energy vs. performance trade-offs. Our results suggest that mixed-precision energy savings range between 6–25% on QMCPACK and 45% on AMReX-Castro. Also, we found gaps in the AMD tooling used on Frontier GPUs that need to be understood, while query resolutions on NVML have little variability between 1 ms-1 s. Overall, application level knowledge is crucial to define energy-cost/science-benefit opportunities for the codesign of future supercomputer architectures in the post-Moore era.

Godoy, William [ORNL] (ORCID:0000000225905178)↗

DOE OSTI2025

McCormick envelopes in mixed-integer PDE-constrained optimization

McCormick envelopes are a standard tool for deriving convex relaxations of optimization problems that involve polynomial terms. Such McCormick relaxations provide lower bounds, for example, in branch-and-bound procedures for mixed-integer nonlinear programs but have not gained much attention in PDE-constrained optimization so far. This lack of attention may be due to the distributed nature of such problems, which on the one hand leads to infinitely many linear constraints (generally state constraints that may be difficult to handle) in addition to the state equation for a pointwise formulation of the McCormick envelopes and renders bound-tightening procedures that successively improve the resulting convex relaxations computationally intractable. We analyze McCormick envelopes for a model problem class that is governed by a semilinear PDE involving a bilinearity and integrality constraints. We approximate the nonlinearity and in turn the McCormick envelopes by averaging the involved terms over the cells of a partition of the computational domain on which the PDE is defined. This yields convex relaxations that underestimate the original problem up to an a priori error estimate that depends on the mesh size of the discretization. These approximate McCormick relaxations can be improved by means of an optimization-based bound-tightening procedure. We show that their minimizers converge to minimizers to a limit problem with a pointwise formulation of the McCormick envelopes when driving the mesh size to zero. We provide a computational example, for which we certify all of our imposed assumptions. The results point to both the potential of the methodology and the gaps in the research that need to be closed. Our methodology provides a framework first for obtaining pointwise underestimators for nonconvexities and second for approximating them with finitely many linear inequalities in an infinite-dimensional setting.

Approximations and Expansions↗

DOE OSTI2025

A mixed-integer PDE-constrained optimization formulation for constructing electromagnetic cloaks with multiple materials

We study the design of an electromagnetic cloak from multiple materials with an additional constraint on the mass of the cloak. Our problem is an example of a topology optimization problem, and we formulate this problem as a mixed-integer partial-differential equation constrained optimization (MIPDECO) problem, where Maxwell’s equation models the propagation of the wave through the cloak and surrounding medium. We use binary variables to model the assignment of the different materials, and their relevant properties (permittivity and density). The mass constraint adds a nontrivial constraint to this problem. We propose a two-phase strategy to solve this problem. In the first phase, we solve a continuous relaxation, and then propose a new variant of the feasibility pump that exploits the structure of the PDE to obtain an initial integral solution candidate. In the second phase, we use a trust-region approach to improve this incumbent. We also consider a continuation or mesh-sequencing approach to find better solutions faster on consecutively finer meshes. We present detailed numerical results to illustrate the effectiveness of our approaches for constructing multi-material cloaks with a mass constraint.

Calculus of Variations and Optimization↗

DOE OSTI2024

Assessment of the CTF subchannel code for modeling a large-break loss-of-coolant accident reflood transient

With increased industry interest in extending reactor operating cycles, the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program has been investigating the behavior of high-burnup fuel during design basis accidents such as the large-break loss-of-coolant accident (LBLOCA) with consideration for risk of fuel fragmentation, relocation, and dispersal (FFRD). As part of that activity, the NEAMS subchannel thermal/ hydraulics (T/H) code, CTF, is being used for modeling of LBLOCA and to determine the impact of subchannel resolution on results. Although CTF includes a wide range of models for LBLOCA conditions, the code has not been used for this application while maintained at Oak Ridge National Laboratory (ORNL) until now. Therefore, here, in this work, a preliminary assessment of several of these models was performed using openly available reflood experimental data from the Flooding Experiments in Blocked Arrays (FEBA) tests. One coarse mesh and one fine mesh model were set up in CTF for high and low flooding rate tests performed in the unblocked FEBA facility. A coarse TRACE model was set up to be as consistent as possible with the coarse CTF model to allow for code-to-code benchmarking. The assessment shows a tendency of the codes to over-predict peak cladding temperature (PCT) near the top of the bundle and to quench early. Advanced spacer grid models were shown to improve upper bundle predictions in CTF. The resolved CTF model over-predicted PCT by a larger degree in the center channels in the low-flooding rate test, and it is believed that the radiative heat transfer model, which was not used in this study, may be needed to correct this over-prediction. Finally, this work demonstrates the importance of the droplet model in determining quench time and vapor temperature and PCT prediction, which necessitates a more in-depth validation of these models in the future.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2024

A B-spline based gradient-enhanced micropolar implicit material point method for large localized inelastic deformations

The quasi-brittle response of cohesive-frictional materials in numerical simulations is commonly represented by softening plasticity or continuum damage models, either individually or in combination. However, classical models, particularly when coupled with non-associated plasticity, often suffer from ill-posedness and a lack of objectivity in numerical simulations. Moreover, the performance of the finite element method significantly degrades in simulations involving finite strains when mesh distortion reaches excessive levels. This represents a challenge for modeling cohesive-frictional materials, given their tendency to experience strongly localized deformations, such as those occurring during shear band dominated failure. Hence, accurate modeling of the response of cohesive-frictional solids is a demanding task. To address these challenges, we present an extension of the material point method (MPM) for the unified gradient-enhanced micropolar continuum, aiming at the analysis of finite localized inelastic deformations in cohesive-frictional materials. The generalized gradient-enhanced micropolar continuum formulation is employed to tackle challenges related to localization and softening material behavior, while the MPM addresses issues arising from excessive deformations. The method utilizes a B-spline formulation for the rigid background mesh to mitigate the well-known cell crossing errors of the MPM. To demonstrate the performance of the method, 2D and 3D numerical studies on localized failure in sandstone in plane strain compression and triaxial extension tests are presented. A comparison with finite element results confirms the suitability of the formulation. Moreover, an efficient numerical implementation of the formulation is presented, and it is demonstrated that the additional MPM specific overhead is negligible.

B-spline↗

DOE OSTI2024

Tackling the curse of dimensionality in fractional and tempered fractional PDEs with physics-informed neural networks

Fractional and tempered fractional partial differential equations (PDEs) are effective models of long-range interactions, anomalous diffusion, and non-local effects. Traditional numerical methods for these problems are mesh-based, thus struggling with the curse of dimensionality (CoD). Physics-informed neural networks (PINNs) offer a promising solution due to their universal approximation, generalization ability, and mesh-free training. In principle, Monte Carlo fractional PINN (MC-fPINN) estimates fractional derivatives using Monte Carlo methods and thus could lift CoD. However, this may cause significant variance and errors, hence affecting convergence; in addition, MC-fPINN is sensitive to hyperparameters. In general, numerical methods and specifically PINNs for tempered fractional PDEs are under-developed. Herein, we extend MC-fPINN to tempered fractional PDEs to address these issues, resulting in the Monte Carlo tempered fractional PINN (MC-tfPINN). To reduce possible high variance and errors from Monte Carlo sampling, we replace the one-dimensional (1D) Monte Carlo with 1D Gaussian quadrature, applicable to both MC-fPINN and MC-tfPINN. We validate our methods on various forward and inverse problems of fractional and tempered fractional PDEs, scaling up to 100,000 dimensions. Our improved MC-fPINN/MC-tfPINN using quadrature consistently outperforms the original versions in accuracy and convergence speed in very high dimensions.

42 ENGINEERING↗