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DOE OSTI2024

A meshless stochastic method for Poisson–Nernst–Planck equations

A plethora of biological, physical, and chemical phenomena involve transport of charged particles (ions). Its continuum-scale description relies on the Poisson–Nernst–Planck (PNP) system, which encapsulates the conservation of mass and charge. The numerical solution of these coupled partial differential equations is challenging and suffers from both the curse of dimensionality and difficulty in efficiently parallelizing. We present a novel particle-based framework to solve the full PNP system by simulating a drift–diffusion process with time- and space-varying drift. We leverage Green’s functions, kernel-independent fast multipole methods, and kernel density estimation to solve the PNP system in a meshless manner, capable of handling discontinuous initial states. The method is embarrassingly parallel, and the computational cost scales linearly with the number of particles and dimension. We use a series of numerical experiments to demonstrate both the method’s convergence with respect to the number of particles and computational cost vis-à-vis a traditional partial differential equation solver.

Chemistry↗

DOE OSTI2026

An implicit-explicit time splitting strategy for the far SOL plasma fluid model with DG-FEM discretization

We consider a far scrape-off layer (SOL) plasma fluid model of ions that is governed by a Braginskiitype model: a one-dimensional, nonlinear system of advection-diffusion equations coupled with a diffusion equation for neutral particles. Our motivation for studying this system arises from the coupling between the edge plasma and radio-frequency (RF) heating, where solving a far SOL plasma fluid model provides critical insights into edge plasma dynamics. Numerical simulations of plasma fluid models require advanced computational techniques to achieve both efficiency and accuracy, especially when resolving the boundary layer in magnetically confined plasmas. In this work, we propose an implicit-explicit time operator splitting strategy that allows for an efficient solution algorithm, where the diffusive terms are treated semi-implicitly requiring only a linear solve, while the advection part is handled explicitly using a strong-stability-preserving Runge-Kutta (SSP-RK3) scheme. This leads to a fully decoupled system in which the diffusion and advection sub-problems can be solved separately, simplifying the overall solution procedure and allowing for efficient parallelization, which is particularly relevant for exploring the impact of RF heating on the SOL plasma. The main challenge of the discretization is due to the strong coupling between diffusion and advection, particularly through the boundary conditions. This makes implementation of such a scheme in an accurate and stable manner nontrivial. We discuss in detail how to split the equations and manage boundary conditions to maintain stability and well-posedness for each subsystem. We also describe a spatial discretization approach, based on the discontinuous Galerkin finite element method (DG-FEM) and present numerical results for a one-dimensional system.

Burkovska, Olena [ORNL] (ORCID:0000000163101130)↗

DOE OSTI2024

Investigation of Debonding Effect in Internal Replacement Pipe System Under Lateral Loading

The aging pipeline infrastructure around the world necessitates immediate rehabilitation. Internal replacement pipe (IRP) is a trenchless system offering a versatile and cost-effective solution across a variety of industries, including oil, natural gas, water, and wastewater. As a structural pipeline repair system, IRPs are subject to lateral deformation because of surface traffic loading. The present study evaluates the impact of adhesion between the host pipe and the IRP, with a focus on assessing the debonding effect on the behavior of the repair system under lateral deformation and bending. This was achieved using a comprehensive approach, including experimental, numerical, and analytical techniques. Varying levels of adhesive strength resulting from different methods of surface preparation were considered. The effectiveness of the IRP system on both discontinuous host pipes with various crack widths and continuous host pipes was also investigated. The results demonstrate that adhesive strength exerts a significant influence on the repair system, especially in the case of narrow circumferential cracks, while its impact on the continuous system is minimal. For optimal performance, it is essential to choose adhesives that possess sufficient shear strength while also accounting for the required debonding length. This approach ensures that minor discontinuities are effectively controlled, thereby enhancing the system′s fatigue life. The reliable determination of the maximum allowable shear strength for the adhesive or the debonding length can ensure that it does not negatively affect fatigue life. The findings presented in this study offer new insights into the development of trenchless repair techniques that can enhance system performance and extend service life.

Tien, Tri C. M.↗

DOE OSTI2025

Microstructural, Oxidation, and Mechanical Behavior of NbTi-Based Refractory Alloys with 5 to 10 Pct Co, Cr, and Ni Additions

NbTi-based refractory alloys with additions of Co, Cr, and Ni represent an interesting medium-entropy alloy system with potential for protective oxide film formation, high strength, and ductility. This study investigates the microstructural evolution, oxidation behavior, and mechanical properties of NbTi-based alloys containing 5 to 10 at. pct Co, Cr, and Ni. CALPHAD predictions suggest that this composition range can be heat treated to obtain a predominantly body-centered cubic matrix phase. Mechanical properties, including microhardness, yield strength, maximum strength, and specific strength are evaluated through isothermal compression tests conducted between room temperature and 800 °C. The oxidation kinetics of these alloys are assessed through discontinuous oxidation tests. Parabolic oxidation kinetics were observed for NbTi–10Ni and NbTi–5Co, while linear oxidation kinetics were found for NbTi–10Cr and NbTi–10(CoCrNi). Microstructures and oxide layers are characterized using X-ray diffraction, electron backscatter diffraction, energy-dispersive X-ray spectroscopy, and scanning electron microscopy. All alloys exhibit significant mechanical softening between room temperature and 800 °C, with elastic-perfectly plastic flow observed at 800 °C. The addition of 10 pct Cr to NbTi resulted in two BCC phases up to 1050 °C, conflicting with CALPHAD predictions of a single-phase solid solution at this temperature, and resulting in higher flow stress at 800 °C. NbTi–10(CoCrNi) exhibited the lowest flow stress at 800 °C despite having more ‘cocktail effect’ potential and insufficient molar fractions of Co, Cr, or Ni to form a desirable protective oxide film.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Sovereign Credit Rating Processes Adapted to Critical Infrastructure Cyber Risk Assessment

United States critical infrastructure entities are increasingly targeted by motivated and capable threat actors and must be prepared to assess and treat a diverse range of cyber risks. Consequently, this necessitates some form of analytical process to evaluate risks and inform cyber security investment decisions. A potential solution for structuring cyber risk evaluation exists within the field of sovereign credit ratings – where agencies employ mature approaches that integrate quantitative and qualitative data to produce a singular value of assessment. Adapting such approaches, we present a novel criterion and methodology for measuring and communicating the likelihood element of cyber risk. The methodology is composed of three sequential phases: a quantitative baseline organized by distinct capability frames, a bounded qualitative adjustment per frame, and a greater-bounded qualitative adjustment spanning the entire process. The process culminates in publication of a cyber capability rating that communicates a critical infrastructure entity’s ability and willingness to mitigate discontinuous function due to cyberattack.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2026

Elucidating the Microscale Behavior and Phase Separation Kinetics of Thermally Responsive Ionic Liquid–Water Mixtures

Thermally responsive ionic liquids (ILs) exhibit liquid-liquid phase separation into a water-rich (WR) and ionic-liquid-rich (ILR) phase when heated above a lower critical solution temperature (LCST). This phase behavior has been leveraged for applications ranging from forward osmosis (FO) desalination, where the IL acts as a draw solute, to refrigeration and dehumidification cycles, where the IL acts as a liquid desiccant. While significant effort has been devoted to characterizing the thermodynamic and thermophysical properties of LCST ILs, their phase separation kinetics have not been investigated. In this work, we describe the macroscale phase separation kinetics (phase separation time) by gleaning insight into the microscale colloidal behavior of aqueous mixtures of four different materials, P 4444 TFA (tetrabutylphosphonium-2,4-trifluoroacetate), P 4444 DMBS (tetrabutylphosphonium-2,4-dimethyl-benzenesulfonate), N 4444 Sal (tetrabutylammonium salicylate), and P 4444 Sal (tetrabutylphosphonium salicylate) as a function of IL concentration at a separation temperature of 70 °C. We report the discontinuous microscale size distributions for each material and correlate their theoretical settling velocities to experimental phase separation times. The results indicate that a simple Stokes' law model can predict the phase separation time within reasonable accuracy. Overall, this work lays the foundation for understanding the micro- to macroscale phase separation behavior and kinetics of LCST ILs for various water-energy applications.

LCST↗

DOE OSTI2024

Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method

Abstract An interface-modified reproducing kernel particle method (IM-RKPM) is introduced in this work to allow for a direct model construction from image pixels of heterogeneous polycrystalline Li-ion battery microstructures. The interface-modified reproducing kernel (IM-RK) approximation is constructed through scaling of a kernel function by a regularized distance function in conjunction with strategic placement of interface node locations. This leads to RK shape functions with either weak or strong discontinuities across material interfaces, suitable for modeling various interface mechanics. With the placement of a triple junction node and distance-based scaling of kernel functions, the resulting IM-RK shape function also possesses proper discontinuities at the triple junctions. This IM-RK approximation effectively remedies the well-known Gibb’s oscillation in the smooth approximation of discontinuities. Different from the conventional meshfree approaches for interface discontinuities, this IM-RK approach is done without additional degrees of freedom associated with the enrichment functions, and it is formulated with the standard procedures in the RK shape function construction. This work focuses on identifying the accuracy and convergence properties of IM-RKPM for modeling the coupled electro-chemo-mechanical system. A linear patch test is formulated and numerically tested for the electro-chemo-mechanical coupled problem with a Butler–Volmer boundary condition representing the physical conditions in Li-ion battery microstructures. This is followed by verification of the optimal rates of convergence of IM-RKPM for solving the coupled problem with higher order solutions. The image-based modeling of Li-ion battery microstructures in the numerical examples demonstrates the applicability of the proposed method to realistic Li-ion battery materials modeling.

25 ENERGY STORAGE↗

DOE OSTI2024

Limiting current in a collisional crossed-field gap

Crossed-field devices are often used in pulsed power and high-power microwave applications. Previous studies derived closed-form solutions for the limiting current of a vacuum crossed-field system, corresponding to the maximum permissible current for laminar flow, below and above the Hull cutoff B H for magnetic insulation. We extend these studies by introducing collision frequency into the electron force law as a friction term to derive the limiting current in a collisional crossed-field gap. The resulting solution recovers the vacuum crossed-field case in the limit of no collisions and the collisional space-charge limited current with general initial velocity for magnetic field B → 0. In the limit of infinite collisions, we obtain a crossed-field equivalent to the Mott–Gurney law for the maximum current permissible in a collisional, nonmagnetic diode. When the collision frequency ν is less than the electron cyclotron frequency Ω, increasing initial velocity makes the critical current nonmonotonic with increasing ν with the critical current higher at B = B H for ν = Ω. As for a misaligned crossed-field gap where a component of the magnetic field was introduced parallel to the electric field across the gap, magnetic insulation is eliminated and the discontinuity at B = B H for limiting current observed in a vacuum crossed-field gap vanishes. As B → ∞, the limiting current approaches a constant that depends on the initial velocity and the collision frequency.

Breen, Lorin I.↗

DOE OSTI2024

Hybridized Discontinuous Galerkin Methods for Computational Fluid Dynamics

Hybridizable Discontinuous Galerkin (HDG) methods hold promise for any applications with significant advection character, including thermal hydraulics in light water reactors and advanced reactor concepts and fluid models of plasmas in magnetic confinement fusion. Its features include natural upwinding, local element conservation, and extensibility to arbitrarily high order accuracy. In the last fiscal year we have implemented HDG in the Multiphysics Object-Oriented Simulation Environment (MOOSE). We developed a first-of-its-kind automatic static condensation system in MOOSE’s underlying finite element library libMesh which can condense out arbitrarily many internal variables. Finally, we developed the first preconditioner for HDG discretizations of the Navier-Stokes equations which shows robust performance across a wide range of problem sizes and Reynolds numbers. This preconditioner yields solution times that are equivalent to the fastest developed for industry standard finite volume methods. Moreover, the arbitrarily high-order nature of HDG makes it a prime candidate for acceleration via graphical processing units (GPUs). We believe these developments will hold significant importance for future DOE Nuclear Energy (NE) and Fusion Energy Science (FES) programs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Benchmarking CO₂ storage simulations: Results from the 11 th Society of Petroleum Engineers Comparative Solution Project

The 11 th Society of Petroleum Engineers Comparative Solution Project (shortened SPE11 herein) benchmarked simulation tools for geological carbon dioxide (CO 2 ) storage. A total of 45 groups from leading research institutions and industry across the globe signed up to participate, with 18 ultimately contributing valid results that were included in the comparative study reported here. This paper summarizes the SPE11 results. A comprehensive introduction and qualitative discussion of the submitted data are provided, together with an overview of online resources for accessing the full depth of data. A global metric for analyzing the relative distance between submissions is proposed and used to conduct a quantitative analysis of the submissions. This analysis attempts to statistically resolve the key aspects influencing the variability between submissions. The study shows that the major qualitative variation between the submitted results is related to thermal effects, dissolution-driven convective mixing, and resolution of facies discontinuities. Moreover, a strong dependence on grid resolution is observed across all three versions of the SPE11. However, our quantitative analysis suggests that the observed variations are predominantly influenced by factors not documented in the technical responses provided by the participants. We therefore identify that unreported variations due to human choices within the process of setting up, conducting, and reporting on the simulations underlying each SPE11 submission are at least as impactful as the computational choices reported.

Nordbotten, Jan M. [Univ. of Bergen (Norway); Norw↗

DOE OSTI2026

Assessment of the hydromechanical higher-order MPM for the simulation of geotechnical problems

The Material Point Method (MPM) has been increasingly used to simulate large strain deformations. Linear interpolation functions are commonly used to perform the spatial integration. It is well-known that the discontinuities in the interpolation function derivatives induce shock-like artifacts known as ‘cell-crossing’ error. These errors compound with volumetric locking errors when used with hydromechanical formulations for porous media, where different velocity fields are used for each phase. The capabilities of higher-order MPM frameworks have not been explored for real-scale geotechnical problems. As such, this paper aims to assess, validate, and further discuss a higher-order B-spline MPM (BS-MPM) framework. First, the BS-MPM framework is verified against the large-strain oedometer consolidation problem. Second, the framework is validated against a real-scale slope failure experiment triggered by pore water pressure recharge. Landslide features that are captured using the higher-order framework are specifically highlighted, and results (e.g., pore water pressure and deformation) are validated with field measurements. A generally convergent numerical solution is observed when using cubic interpolation functions. Third, a footing penetration problem is simulated using the multi-patch BS-MPM. Trends are examined with respect to penetration velocity and variation in hydraulic conductivity. The BS-MPM framework ultimately presents a stabilized numerical solution that captures plausible hydromechanical interaction trends important in geotechnical engineering applications.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Symmetry Determining Equations of the Rankine-Hugoniot Equations for Variable Velocity Shock Waves

The “constant velocity piston” problem (Fig. 1), also known as the “piston problem,” is a standard model for a one dimensional, in our case linear, symmetric shock wave moving through an inviscid, perfect gas. The model can be divided into two regions - a perturbed section on the left and an unperturbed section on the right - by a moving shock wave moving left to right. Both the perturbed and unperturbed sections, i.e. the shocked and unshocked regions, respectively, obey the Eulerian conservation equations; however, at the exact location of the shock, there is a mathematical discontinuity not satisfied by the Euler equations. To ensure continuity and conservation of certain quantities when crossing between the unshocked and shocked regions, we evoke a series of equations derived from the Eulerian conservation equations, called the Rankine-Hugoniot equations, or “jump” equations as it is often referred to in the literature on the topic. The classical constant-velocity piston problem assumes the piston features a constant driving velocity (among many other willing suspensions of belief required in the pursuit of a first principles equation model); consequent to this assumption is a constant-velocity shock and a constant-velocity shocked flow state. However, using Lie Group Theory (LGT), also known as symmetry analysis, we can attempt to reinterpret the model with a shock wave of variable velocity in time and space. An extension of the model in this way opens up the possibility for obtaining new analytical solutions to the piston problem for certain shock velocity models. In this report, we use LGT to derive the symmetry determining equations (SDEs), whose solutions are Lie groups, which permit analytical solutions. In the future, we can then use the SDEs to define constraint equations on the shock velocity model and what the successive solutions to the Euler equations might be based off such constraints. This report is structured as follows: Section 2 provides a brief derivation of the Rankine-Hugoniot (“jump”) equations; Section 3 gives an overview of Lie group theory; Section 4 derives the SDEs of the jump equations; Section 5 derives the Euler conservation equations for fluids; and Section 6 presents concluding remarks and opportunities for future studies.

42 ENGINEERING↗

DOE OSTI2026

Comparative Study of Zinc Cold-Spray Coating and Pre-treatments for Magnesium Alloys

Magnesium (Mg) alloys are appealing for automotive lightweighting owing to their high specific strength. However, their susceptibility to corrosion in harsh environments remains a major challenge. Conventional industrial pre-treatment coatings, including zinc phosphate, chromate conversion, and non-chromate conversion, often exhibit discontinuities and microcracks, leading to localized corrosion near fasteners and parting lines. Here, this study investigates cold-sprayed zinc (Zn) coatings as a novel pre-treatment alternative for high-pressure die cast (HPDC) AZ91 Mg alloys, demonstrating significant improvements in wear and corrosion performance. Cold spray produces uniform and robust coatings, reducing wear rate by over 50% and reducing corrosion rate by over 99.3%, as measured by evolved hydrogen release, compared to traditional pre-treatments. Multimodal corrosion testing reveals that Zn cold-spray coatings form a protective layer during exposure, minimizing general and filiform corrosion, and exhibiting corrosion potential (E corr ) that is nobler by ~ 400 mV than the surfaces of both pre-treated and uncoated AZ91. Scalability of cold spray for selective application around multimaterial joints further strengthens their industrial viability. This work establishes Zn cold-spray coatings as highly effective pre-treatment solutions for the advancement of corrosion resistant Mg alloy components in automotive applications.

multimodal corrosion↗

DOE OSTI2025

ULTIMATE Phase I project: Development of Niobium-based alloys for Turbine Applications

Current Ni-based alloys used in turbine blade applications are operating at 1100°C which is approximately 90% of the solidus of Ni-based alloys. Further increases in temperature can be achieved only through the use of alloys with higher solidus temperatures such as refractory alloys which include Mo, Nb, W, Ta alloys. Niobium has a unique combination of physical properties that include a high melting point (2468°C), lowest density (8.57 g/cc), and the lowest modulus amongst refractory alloys, a good thermal conductivity that increases from 45 W/mK at room temperature to 62 W/mK at 1093°C, good ductility with fabricability using traditional techniques, high strength, good creep resistance, and general chemical inactivity. Hence niobium alloys offer many advantages for use at the desired temperature of 1300°C. One of the major deterrents to the use of niobium and its alloys at high temperatures is achieving good oxidation resistance. In addition, achieving balanced properties of room temperature strength, ductility, fracture toughness, high temperature strength, and creep resistance required for 1300°C operation at a density of 9 g/cm 3 is extremely challenging since the addition of W which is a potent strengthener increases the density of the alloy. This project seeks to enable the development of a tri-layered turbine blade that can operate continuously at 1300°C with the core of the turbine blade providing good creep resistance, the second layer providing improved oxidation resistance over the core layer, and the third layer being an environmental barrier providing oxidation resistance. The objective of this Phase 1 project was to use computational modeling and advanced characterization tools to develop two classes of Nb alloys which could be used as the core layer and the transition layer. The first class of alloys developed in this project was a Nb-alloy designed to serve as the turbine blade core with excellent room temperature strength, ductility, and high temperature strength and creep resistance required for 1300°C operation. These alloys were designed to contain sufficient solute solution strengthening elements (W, Mo) but constrained by the density of alloy, along with the addition of elements such as Zr, Hf, Ta, C, and N to achieve a combination of primary and secondary carbide precipitation. A total of 38 “creep-resistant” alloys were designed and cast during the duration of the project. Processing techniques were developed to keep the oxygen contents as low as possible with typical oxygen contents less than 250 ppm. One alloy with a density of < 9.5 g/cc was successful in meeting the Phase 2 intermediate project mechanical property milestone requirements of room temperature ductility greater than 1.0%, 1200°C creep strain of less than 3% at 150 MPa and 100 hours in vacuum, and with solidus temperature greater than 1500ᵒC. The second class of alloys was designed to be a Nb-rich alloy with improved oxidation resistance when compared to the core layer and was designed specifically to be compatible with the core layer and the outer environmental barrier coating. This Nb- alloy will be specifically designed to be microstructurally stable at these temperatures when in contact with the core alloy and provide protection against catastrophic failure of the barrier coating. Two alloys were cast and processed but further development was discontinued to focus on the development of the creep resistant alloy.

36 MATERIALS SCIENCE↗

DOE OSTI2025

LDRD Abbreviated report: High-Order General-Discrete-Ordinates Method Enabling Efficient Deterministic Transport in Hydrodynamic Simulations

Deterministic transport simulations for national-security and energy applications often operate in high-dimensional phase-space, where accuracy and cost both become major challenges. A common numerical artifact in such problems is the “ray-effect,” which appears as unphysical streaks. Beyond misinterpretation, these artifacts can contaminate tightly coupled physics, such as fluid dynamics, radiation-hydrodynamics, and laser-plasma interactions, eroding the predictive capability of entire multiphysics workflows. Our objective was to make high-dimension studies practical on modern hardware while mitigating the ray-effect without relying on prohibitively expensive sampling approaches such as Monte Carlo methods. We developed the Generic Discretization Library (GenDiL), a Graphics Processing Unit (GPU)-first framework that uses high-order Discontinuous Galerkin (DG) methods and matrix-free algorithms to reduce memory usage and improve computational efficiency, critical for phase-space simulations. GenDiL supports phase-space adaptivity in both mesh size and polynomial order (hp-adaptivity) to place resolution only where it is needed. A central capability is Local Dimensional Refinement (LDR), which couples lower-dimension continuum models to higher-dimension kinetic models through stable and conservative interfaces, so that high-fidelity physics is applied only in regions where it is essential. Building on the GenDiL framework, we developed the General SN (GSN) family of algorithms as a true generalization of the polar SN approach (discrete ordinates, often denoted SN). Rather than tying discrete ordinates to a specific polar change of coordinates, GSN formulates transport on an arbitrary change of coordinates chosen to reduce ray-effect. We studied two complementary variants: an analytic variant, where the coordinate map is prescribed in advance by a closed-form function; and a data-driven variant, where a quantity of interest, such as the net flux, guides the coordinate system. GenDiL provides the library infrastructure for efficient GPU execution, but the GSN concept is algorithmic and independent of any one library. Across representative high-dimension tests, including non-symmetric solutions, both variants delivered strong ray-effect mitigation at practical cost, moving four- to six-dimensional analysis toward repeatable, routine studies.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗