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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

An Empirical Quantile Estimation Approach for Chance-Constrained Nonlinear Optimization Problems

We investigate an empirical quantile estimation approach to solve chance-constrained nonlinear optimization problems. Our approach is based on the reformulation of the chance constraint as an equivalent quantile constraint to provide stronger signals on the gradient. In this approach, the value of the quantile function is estimated empirically from samples drawn from the random parameters, and the gradient of the quantile function is estimated via a finite-difference approximation on top of the quantile-function-value estimation. We establish a convergence theory of this approach within the framework of an augmented Lagrangian method for solving general nonlinear constrained optimization problems. The foundation of the convergence analysis is a concentration property of the empirical quantile process, and the analysis is divided based on whether or not the quantile function is differentiable. In contrast to the sampling-and-smoothing approach used in the literature, the method developed in this paper does not involve any smoothing function and hence the quantile-function gradient approximation is easier to implement and there are less accuracy-control parameters to tune. Furthermore, we demonstrate the effectiveness of this approach and compare it with a smoothing method for the quantile-gradient estimation. Numerical investigation shows that the two approaches are competitive for certain problem instances.

Applied Probability↗
DOE OSTI2024

Simulation of gas mixture dynamics in a pipeline network using explicit staggered-grid discretization

Here we develop an explicit staggered finite difference discretization scheme for simulating the transport of highly heterogeneous gas mixtures through pipeline networks. This study is motivated by the proposed blending of hydrogen into natural gas pipelines to reduce end use carbon emissions while using existing pipeline systems throughout their planned lifetimes. Our computational method accommodates an arbitrary number of constituent gases with very different physical properties that may be injected into a network with significant spatiotemporal variation. In this setting, the gas flow physics are highly location- and time- dependent, so that local composition and nodal mixing must be accounted for. The resulting conservation laws are formulated in terms of pressure, partial densities and flows, and volumetric and mass fractions of the constituents. We include non-ideal equations of state that employ linear approximations of gas compressibility factors, so that the pressure dynamics propagate locally according to a variable wave speed that depends on mixture composition and density. We derive compatibility relationships for network edge boundary values that are more complex than for a homogeneous gas. The simulation method is evaluated on initial boundary value problems for a single pipe and a small network, is cross-validated with a lumped element simulation, and used to demonstrate a local monitoring and control policy for maintaining allowable concentration levels.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A provably stable numerical method for the anisotropic diffusion equation in confined magnetic fields

We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive energy estimates of the solution of the continuous initial boundary value problem. A discrete formulation is presented using operator splitting in time with the summation by parts finite difference approximation of spatial derivatives for the perpendicular diffusion operator. Weak penalty procedures are derived for implementing both boundary conditions and parallel diffusion operator obtained by field line tracing. We prove that the fully-discrete approximation is unconditionally stable. Discrete energy estimates are shown to match the continuous energy estimate given the correct choice of penalty parameters. A nonlinear penalty parameter is shown to provide an effective method for tuning the parallel diffusion penalty and significantly minimises rounding errors. Several numerical experiments, using manufactured solutions, the “NIMROD benchmark” problem and a single island problem, are presented to verify numerical accuracy, convergence, and asymptotic preserving properties of the method. Finally, we present a magnetic field with chaotic regions and islands and show the contours of the anisotropic diffusion equation reproduce key features in the field.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Formation and optical properties of indium nanoparticle arrays for deep-UV plasmonics

We utilize a combined computational-experimental approach to examine the influence of indium nanoparticle (NP) array distributions on deep-ultraviolet (UV) plasmon resonances. For photon energies < 5.7 eV, analysis of ellipsometric spectra reveals an increase in silicon reflectance induced by indium NP arrays on silicon. For various energies in the range 5.7–7.0 eV, a decrease in reflectance is induced by the NP arrays. Similar trends in reflectance are predicted from finite-difference time-domain (FDTD) simulations using NP size distributions extracted from atomic-force micrographs as input. In addition, in the energy range of 7.4–9.2 eV, the FDTD simulations reveal reflectance minima, characteristic of localized surface plasmon resonances. Here, electron energy-loss spectroscopy collected from individual indium NPs reveals the presence of LSPR at ≈ 8 eV, further supporting the promise of indium NP arrays on silicon for deep-UV plasmonics.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Application of mesh refinement to relativistic magnetic reconnection

During relativistic magnetic reconnection, antiparallel magnetic fields undergo a rapid change in topology, releasing a large amount of energy in the form of non-thermal particle acceleration. This work explores the application of mesh refinement to 2D reconnection simulations to efficiently model the inherent disparity in length-scales. We have systematically investigated the effects of mesh refinement and determined necessary modifications to the algorithm required to mitigate non-physical artifacts at the coarse–fine interface. We have used the ultrahigh-order pseudo-spectral analytical time-domain Maxwell solver to analyze how its use can mitigate the numerical dispersion that occurs with the finite-difference time-domain (or “Yee”) method. Absorbing layers are introduced at the coarse–fine interface to eliminate spurious effects that occur with mesh refinement. We also study how damping the electromagnetic fields and current density in the absorbing layer can help prevent the non-physical accumulation of charge and current density at the coarse–fine interface. Using a mesh refinement ratio of 8 for two-dimensional magnetic reconnection simulations, we obtained good agreement with the high-resolution baseline simulation, using only 36% of the macroparticles and 71% of the node-hours needed for the baseline. The methods presented here are especially applicable to 3D systems where higher memory savings are expected than in 2D, enabling comprehensive, computationally efficient 3D reconnection studies in the future.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

A matrix-free hyperviscosity formulation for high-order ALE hydrodynamics

The numerical approximation of compressible hydrodynamics is at the core of high-energy density (HED) multiphysics simulations as shocks are the driving force in experiments like inertial confinement fusion (ICF). In this work, we describe our extension of the hyperviscosity technique, originally developed for shock treatment in finite difference simulations, for use in arbitrarily high-order finite element methods for Lagrangian hydrodynamics. Hyperviscosity enables shock capturing while preserving the high-order properties of the underlying discretization away from the shock region. Specifically, we compute a high-order term based on a product of the mesh length scale to a high power scaled by a hyper-Laplacian operator applied to a scalar field. We then form the total artificial viscosity by taking a non-linear blend of this term and a traditional artificial viscosity term. We also present a matrix-free formulation for computing the finite element based hyper-Laplacian operator. Such matrix-free methods have superior performance characteristics compared to traditional full matrix assembly approaches and offer advantages for GPU based HPC hardware. We demonstrate the numerical convergence of our method and its application to complex, multi-material ALE simulations on high-order (curved) meshes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Error Estimates for the Optimal Control of a Parabolic Fractional PDE

In this work, we consider the integral definition of the fractional Laplacian and analyze a linear-quadratic optimal control problem for the so-called fractional heat equation; control constraints are also considered. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates for the optimal variables. To discretize the state equation we propose a fully discrete scheme that relies on an implicit finite difference discretization in time combined with a piecewise linear finite element discretization in space. We derive stability results and a novel $L^2(0,T;L^2(\Omega))$ a priori error estimate. On the basis of the aforementioned solution technique, we propose a fully discrete scheme for our optimal control problem that discretizes the control variable with piecewise constant functions, and we derive a priori error estimates for it. We illustrate the theory with one- and two-dimensional numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

In-situ Characterizations of Microstructural Degradation of Perovskite Solar Cells

Rapid progress has been achieved in perovskite solar cells (PSCs), and their efficiencies have improved from 3.8 % to 24.2 % in less than a decade. With low-cost processing, PSCs have shown exciting photovoltaic (PV) properties, such as effective optical absorption, a long carrier lifetime, and unique defect tolerance. While recent studies demonstrated improved stability up to 100 days, PSC technology is still challenged to meet the stringent industry requirements for commercialization. Despite considerable efforts, the underlying physical mechanisms for the inferior stability of PSCs are not well understood. One reason for this divergence is that many established measurement techniques (e.g., quantum efficiency, photoluminescence) probe the properties on length scales far greater than that of electronic and/or structural inhomogeneity (i.e., < 1 μm near grain boundaries) and therefore characterize convoluted and/or averaged properties. Ion/electron beam-based techniques have been extensively used to access the microstructures of PSCs, enabling atomic/nanoscale structural, chemical, optical, and electrical characterizations. For example, focused ion beam (FIB) milling produces an atomically smooth surface that minimizes the artifacts attributed to the surface roughness. FIB techniques can also create a well-defined cross-section of PSCs without mechanical damage in a physical cleaving sample preparation. While powerful, there are some concerns about possible beam damage of inorganic-organic perovskites via chemical-bond breakage and local heating. This project aims to comprehensively understand how the microstructural/interfacial properties of PSCs (e.g., Methylammonium Lead Iodide [MAPbI 3 ]) are modified under the irradiating ion beams. Specifically, we investigate the sub-surface properties of PSCs before and after Ar-ion beam injections. Kelvin probe force microscopy (KPFM) measures the contact potential differences (CPDs). Photoluminescence (PL) microscopy in conjunction with Finite-Difference Time-Domain (FDTD) simulations infers the formation of a “dead layer” (< 15 nm) on the subsurface of MAPbI 3 during Ar+ milling processes while preserving the initial bulk properties. The x-ray photoemission spectroscopy (XPS) confirms this modified surface is a lead-rich and iodine-deficient surface. We initiate customizing in-situ measurement setup while measuring the local optical and electrical properties of PSC under thermal (cooling, heating) and light stressors. Our results provide in-depth knowledge of the ion-beam impact on metal-halide perovskites and how this modified sub-surface impacts their properties under accelerated stressors of light and heat. Intensive Monte Carlo simulations of an electron beam interacting with PSCs provide the beam energy distribution in PSCs, proposing possible measurement conditions of using e-beam with minimizing beam damage. Our in-situ measurement platform can accommodate the diverse architecture of PSC devices for studying deterioration mechanisms under mixed environmental stressors.

14 SOLAR ENERGY↗
DOE OSTI2021

Modeling of High-Temperature Corrosion of Zirconium Alloys Using the eXtended Finite Element Method (X-FEM)

Oxidation modeling in modern nuclear fuel performance codes is currently limited by the lack of coupling with mechanics, thus preventing proper description of how high-temperature oxidation impacts mechanical properties. This is mostly due to the fact that the finite difference formalism adopted in corrosion models is incompatible with the direct coupling with mechanics in the finite element modeling employed in modern nuclear fuel performance codes. In this study, a physically based zirconium alloy corrosion model called the Coupled-Current Charge Compensation (C4) model, which was initially developed for operating temperature conditions, has been updated to include high-temperature corrosion in order to provide additional critical information (e.g., oxygen concentration profile) under loss-of-coolant accident (LOCA) conditions—information lacking in existing empirical models. The C4 model was implemented in the MOOSE finite-element framework developed at Idaho National Laboratory, enabling it to be used in the BISON nuclear fuel performance code based on the MOOSE framework. To precisely track the different interfaces at a relatively low computational cost, the eXtended Finite Element Method (X-FEM) was applied in MOOSE. The model’s results were compared to those of existing empirical models as well as metallographic analysis of high-temperature oxidized Zircaloy-4 coupons. Oxygen diffusivities in the a and ß phases resulting from this comparison closely agree with those found in the literature. The C4 model implemented with X-FEM in MOOSE now has the capability to accurately predict oxide, oxygen-stabilized a, and prior ß phase layer growth kinetics under isothermal exposure at high temperature (1000–1500°C). Furthermore, in contrast with the empirical models, the C4 model accounts for the finite thickness of the fuel cladding. It can predict the oxygen concentration profile evolution through the whole cladding, enabling evaluation of the remaining ductile thickness—a crucial variable for modeling the mechanical behavior of the fuel cladding under LOCA. Furthermore, this implementation allows direct coupling with mechanics, at a low computing cost, using finite-element-based nuclear fuel performance codes such as BISON.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Exploring the impact of surface topography on Rayleigh-Bénard dry convection in the Pi cloud chamber using OpenFOAM: In cylindrical and rectangular geometries

The Pi convection-cloud chamber can generate steady-state turbulence in both rectangular and cylindrical shapes via Rayleigh-Bénard convection (RBC) by maintaining warm bottom and cold top surfaces. Although most experiments in the Pi chamber were conducted in cylindrical shapes, all previous Pi chamber simulations were conducted in a rectangular shape due to the limitations of those models to discretize a cylindrical domain when using the finite difference method therein. Here, we use OpenFOAM, an open-source finite-volume-based Computational Fluid Dynamics (CFD) software package, to conduct Large-Eddy Simulation (LES) of dry RBC in the Pi chamber at high Rayleigh numbers (10 8 to 10 9 ). Results show that large-scale circulation (LSC) direction varies in the chamber with a constant side wall temperature. Imposing a slight temperature imbalance at the side wall ranging from 0.1 to 0.7 degrees can lock the LSC, aligning better with Pi chamber observations, particularly at higher Rayleigh numbers. In addition, we examine the impact of surface topography on LSC and heat transfer in RBC systems within cylindrical and rectangular shapes under varying conditions. Results show that roughing top/bottom surfaces by adding bars of a few tens millimeters height can strengthen thermal plumes and enhance temperature fluctuations in the chamber. Furthermore, we observe that different bar height configurations lead to notable changes in LSC orientation and thermal stratification, highlighting the complex interactions between surface features and convection patterns. This finding highlights how surface topography and chamber geometry affect Rayleigh-Bénard convection, improving understanding of turbulent heat transfer and atmospheric boundary-layer processes. Direct Numerical Simulations (DNS) are also conducted to validate LES results. In conclusion, while LES effectively captures qualitative behaviors seen in DNS, it tends to underestimate velocity variances near walls, illustrating a trade-off between computational efficiency and accuracy.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Extended Applications of Subgrid Representation in the 2D/1D Method

Recent efforts in MPACT have focused on improving the performance of the 2D/1D subplane implementation to help target computational performance goals. Here, we build on previous efforts that targeted the use of subgrid treatments to improve the accuracy of control rod representation, presenting three additional applications of subgrid treatments with the goal of reducing the computational burden of simulations. These subgrid applications include treatment of spacer grids, thermal feedback, and axial reflector material representation. With these approaches, a single method of characteristics (MOC) plane can contain several different materials axially that are represented explicitly via subgrids on the coarse mesh finite difference (CMFD) mesh but are axially homogenized on the MOC mesh. This allows for a substantial reduction in the number of MOC planes needed in the calculation through the introduction of an approximate treatment, particularly with regard to the self-shielded cross sections and MOC-informed radial current coupling coefficients in CMFD. Several test problems ranging from single rod to quarter core are used to assess the solution accuracy and performance of these various subgrid representations. Overall, the accuracy of the approximations seems very reasonable, with extremely small differences in eigenvalue observed and maximum pin power errors in the 0.5% to 1.0% range. Several cases show substantial value in the compromise between accuracy and computational performance. Others highlight the new computational hurdles that future research will aim to resolve.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Optimal surface-tension isotropy in the Rothman-Keller color-gradient lattice Boltzmann method for multiphase flow

The Rothman-Keller color-gradient (CG) lattice Boltzmann method is a popular method to simulate two-phase flow because of its ability to deal with fluids with large viscosity contrasts and a wide range of interfacial tensions. Here, two fluids are labeled red and blue, and the gradient in the color difference is used to compute the effect of interfacial tension. It is well known that finite-difference errors in the color-gradient calculation lead to anisotropy of interfacial tension and errors such as spurious currents. Here, we investigate the accuracy of the CG calculation for interfaces between fluids with several radii of curvature and find that the standard CG calculations lead to significant inaccuracy. Specifically, we observe significant anisotropy of the color gradient of order 7% for high curvature of an interface such as when a pinchout occurs. We derive a second order accurate color gradient and find that the diagonal nearest neighbors can be weighted differently than in the usual color-gradient calculation such that anisotropy is minimized to a fraction of a percent. The optimal weights that minimize anisotropy for the smallest radius of curvature interface are found to be w = (0.298, 0.284, 0.275) for diagonal nearest neighbors for the cases of the interface smoothing parameter β = (0.5, 0.7, 0.99), somewhat higher than the w = 0.25 value derived by Leclaire et al. [Leclaire, Reggio, and Trepanier, Computers and Fluids 48, 98 (2011)] based on obtaining isotropic errors to second order. We find that use of these optimal w values yields over a factor of 10 decrease in anisotropy and over a factor of 30 decrease in mean anisotropy relative to using the standard w = 1 value. And we find a factor of about 2 decrease in the anisotropic error and up to factor 15 decrease in mean anisotropic error relative to the choice of w = 0.25 for small radius of curvature interfaces. The improved CG calculations will allow the method to be more reliably applied to studies of phenomenology and pore scale processes such as viscous and capillary fingering, and droplet formation where surface-tension isotropy of narrow fingers and small droplets plays a crucial role in correctly capturing phenomenology. We present an example illustrating how different phenomena can be captured using the improved color-gradient method. Namely, we present simulations of a wetting fluid invading a fluid filled pipe where the viscosity ratio of fluids is unity in which droplets form at the transition to fingering using the improved CG calculations that are not captured using the standard CG calculations. We present an explanation of why this is so which relates to anisotropy of the surface tension, which inhibits the pinchouts needed to form droplets.

58 GEOSCIENCES↗
DOE OSTI2025

Extending TOUGH + HYDRATE with a parallel particle transport simulator: numerical investigation of sand production during gas production from hydrate deposits

A new parallel code for simulating particle transport in porous media is integrated with the TOUGH + HYDRATE simulator to investigate sand production associated with gas production from unconsolidated gas hydrate-bearing sediments (HBS). Here, the parallel coupled simulator is named THMPT and uses the integral finite difference method to describe the Darcian and non-Darcian flow of fluids and heat transport, the finite element method to describe the associated geomechanical changes, and the discrete element method to track the trajectory of individual sand particles within the HBS. The THMPT simulator is written in Fortran, incorporates multiple optimized algorithms, and can comprehensively address the coupled flow, thermal, chemical, geomechanical, and particle transport processes that characterize the system behaviors during gas production from HBS. The simulator can capture all processes involved in sand particle transport in porous media, including sand detachment, collision, clogging (i.e., bridging), and migration. A benchmark case study of sand production in the course of depressurization-induced gas production from a representative HBS reveals various distinct microscopic particle migration mechanisms and the adverse impact of sand particle detachment, transport, and clogging. The numerical investigation also examines the effect of bottomhole pressure on mitigating sand production. The simulation results indicate that sand clogging near the wellbore significantly reduces permeability, decreasing gas production by at least 50%. Lastly, the efficiency of gravel packing in mitigating sand production is numerically evaluated, revealing that the structure of the porous media appears to profoundly influence the macroscopic motion behavior of sand particles and sand clogging characteristics.

discrete element method↗
DOE OSTI2026

Benchmarking of massively parallel phase-field codes for directional solidification

We present a detailed benchmark comparing two state-of-the-art phase-field implementations for simulating alloy solidification under experimentally relevant conditions. The study investigates the directional solidification of Al-3wt%Cu under high-velocity solidification conditions and SCN-0.46wt% camphor under microgravity conditions from National Aeronautics and Space Administration (NASA) DECLIC-DSI-R experiments. Both codes, one employing finite-difference discretization with uniform mesh and GPU-acceleration (GPU-PF) and the other one employing finite-element discretization with adaptive-mesh and CPU-parallelization (PRISMS-PF), solve the same quantitative phase-field formulation that incorporates an anti-trapping current for the solidification of dilute alloys. We evaluate the predictions of each code for dendritic morphology, primary spacing, and tip dynamics in both 2D and 3D, as well as their numerical convergence and computational performance. While existing benchmark problems have primarily focused on simplified or small-scale simulations, they do not reflect the computational and modeling challenges posed by employing experimentally relevant time and length scales. Our results provide a practical framework for assessing phase-field code performance as well as validating and facilitating their application in integrated computational materials engineering (ICME) workflows that require integration with realistic experimental data.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A transient near to far field transformation method and verification benchmarking procedure

The numerical calculation of electromagnetic far fields in the time-domain requires a near to far field transformation (NTFF) method. While time-domain NTFF methods for popular finite-difference time-domain (FDTD) approaches are well established, there is little discourse on NTFF methods for finite-element time-domain (FETD) codes. Here, this work is concerned with the development of an NTFF method for the Empire FETD code, which utilizes curl and divergence conforming elements. This discretization presents a difficulty in obtaining the equivalent electric current for the NTFF. Straightforward finite element interpolation of the fields is shown to give poor accuracy. Alternative interpolation methods are recommended. An expanding magnetic quadrupole pulse benchmark problem, which is fully developed in the appendices, provides the basis for quantitative comparison.

FETD↗
DOE OSTI2024

Difference equations and integral families for Witten diagrams

We show that tree-level and one-loop Mellin space correlators in anti-de Sitter space obey certain difference equations, which are the direct analog to the differential equations for Feynman loop integrals in the flat space. Finite-difference relations, which we refer to as “summation-by-parts relations”, in parallel with the integration-by-parts relations for Feynman loop integrals, are derived to reduce the integrals to a basis. We illustrate the general methodology by explicitly deriving the difference equations and summation-by-parts relations for various tree-level and one-loop Witten diagrams up to the four-point bubble level.

AdS-CFT Correspondence↗
DOE OSTI2024

A computational study of the effects of graphene additions on electrical properties of polycrystalline copper

The addition of graphene has recently shown promise as a route for the significant improvement of the bulk electrical properties of metallic materials. Here, we explore the effects these additions have on the net electrical conductivity of fabricated copper-graphene (Cu-Gr) nanocomposites as a function of grain structure and grain boundary properties. Synthetic 3D microstructures were generated to represent polycrystalline copper with different average grain diameters and twinned grain boundary fractions. Then, the Poisson equation of electrical transport was solved using a finite difference method in order to predict the net electrical conductivity of each microstructure. In this context, the potential effect of graphene on the conductivity of the composite was evaluated as a function of the number of affected grain boundaries. The results of these calculations indicate that 1.) as supported by literature, net electrical conductivity decreases with decreasing grain size, 2.) the presence of twinned grain boundaries results in smaller loss of conductivity than would otherwise be expected, and 3.) the presence of graphene on the grain boundaries can be expected to lead to improvements in net electrical conductivity. However, we also find that 4.) when the Cu grain structure becomes sufficiently refined, the addition of graphene could conceivably result in significant improvements in electrical conductivity over and above coarse-grained Cu. It is estimated from our calculations that, assuming microstructures with average grain sizes between 100 nm and 100 μm and graphene conductivity 1000 to 10,000 that of a typical Cu grain boundary, an improvement in electrical conductivity of approximately 17% over that of bulk Cu may be attainable. Therefore, by performing this study we suggest a possible route for the improvement of Cu electrical properties through the addition of graphene.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗