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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Sylvester-preconditioned adaptive-rank implicit time integrators for advection-diffusion equations with variable coefficients

Here, we consider the adaptive-rank integration of multi-dimensional time-dependent advection-diffusion partial differential equations (PDEs) with variable coefficients. We employ a standard finite-difference method for spatial discretization coupled with high-order diagonally implicit Runge-Kutta temporal schemes. The discrete equation is a generalized Sylvester equation (GSE), which we solve with a projection-based adaptive-rank algorithm structured around two key strategies: (i) constructing dimension-wise subspaces using a novel atypical extended Krylov strategy, and (ii) efficiently solving the basis coefficient matrix with a preconditioned GMRES solver. The low-rank decomposition is performed in 2D using SVD and with high-order SVD (HOSVD) in 3D to represent the tensor in a compressed Tucker format. For d-dimensional problems (here, d = 2 or 3), the computational complexity and memory storage of the approach are found numerically to scale as and $\mathscr{O}(Nr^2) + \mathscr{O} (r^{d+1})$ and $\mathscr{O}(Nr) + \mathscr{O} (r^{d})$, respectively, with the one-dimensional resolution and the maximal rank during the Krylov iteration (which we find to be largely independent of on our numerical examples). We present numerical examples that illustrate the advertised properties of the algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Highly confined epsilon-near-zero and surface phonon polaritons in SrTiO 3 membranes

Recent theoretical studies have suggested that transition metal perovskite oxide membranes can enable surface phonon polaritons in the infrared range with low loss and much stronger subwavelength confinement than bulk crystals. Such modes, however, have not been experimentally observed so far. Here, using a combination of far-field Fourier-transform infrared (FTIR) spectroscopy and near-field synchrotron infrared nanospectroscopy (SINS) imaging, we study the phonon polaritons in a 100 nm thick freestanding crystalline membrane of SrTiO 3 transferred on metallic and dielectric substrates. We observe a symmetric-antisymmetric mode splitting giving rise to epsilon-near-zero and Berreman modes as well as highly confined (by a factor of 10) propagating phonon polaritons, both of which result from the deep-subwavelength thickness of the membranes. Theoretical modeling based on the analytical finite-dipole model and numerical finite-difference methods fully corroborate the experimental results. Our work reveals the potential of oxide membranes as a promising platform for infrared photonics and polaritonics.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Derivative-free stochastic optimization via adaptive sampling strategies

In this paper, we present a novel derivative-free framework for solving unconstrained stochastic optimization problems. Many problems in fields ranging from simulation optimization to reinforcement learning to quantum computing involve settings where only stochastic function values are obtained via a zeroth-order oracle, which has no available gradient information and necessitates the usage of derivative-free optimization methodologies. Our approach includes estimating gradients using stochastic function evaluations and integrating adaptive sampling techniques to control the accuracy in these stochastic approximations. Our framework encapsulates several gradient estimation techniques, including standard finite-difference, Gaussian smoothing, sphere smoothing, randomized coordinate finite-difference, and randomized subspace finite-difference methods. We provide theoretical convergence guarantees for our framework and analyze the worst-case iteration and sample complexities associated with each gradient estimation method. Finally, we demonstrate the empirical performance of the methods on logistic regression and nonlinear least squares problems.

Adaptive sampling↗
DOE OSTI2025

Atmospheric Profile Builder

APBuilder is a software tool designed to generate atmospheric profiles for use with AC2Dr by downloading weather model data and transforming it into 1D or 2D binary profiles. These binary profiles serve as required inputs for AC2Dr, an LLNL-developed, open source, two-dimensional numerical solver for the acoustic wave equation based on the finite difference method.

Kim, Keehoon [Lawrence Livermore National Laborato↗
DOE OSTI2025

Seismic H2: Version 1.0

Seismic-H2 is an integrated software package for geological hydrogen reservoir simulation, optimization, and leakage monitoring. The package includes multiple components: (1) code used for modeling seismic wave propagation in 3D heterogeneous elastic media based on finite-difference method to support detection of geological hydrogen storage reservoir leakage; (2) 3D reservoir simulations of leaks from an underground reservoir and 3D simulations of saline aquifers and depleted gas reservoirs; (3) seismic monitoring costs of passive and active seismic monitoring required for UHS; (4) rock physics calculations and interpolations for converting the reservoir simulations from part (2) into the elastic media models in part (1); (5) pre-processing seismic data; and lastly (6), a GUI interface that combines these different components.

Creasy, Neala↗
DOE OSTI2025

Hydrogen Diffusion Through Stainless Steel

SAND2025-14430O Hydrogen Diffusion Through Stainless Steel is a tool that employs a finite difference method algorithm to solve Fick's law and other mass transport models pertinent to the diffusion of hydrogen through stainless steel. Additionally, the software uses particle swarm optimization to determine physical parameters based on experimental data. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Mason, Tyler [Sandia National Lab. (SNL-CA), Liver↗
DOE OSTI2024

Pore-scale visualization of natural hydrate-bearing sediments

Accurate modeling of gas hydrate reservoir productivity and geomechanical risks associated with subsurface dissociation of natural gas hydrates (NGH) requires the determination of model parameters through physical testing on natural hydrate-bearing sediments (HBS). This involves investigating the hydro-mechanical behavior of undisturbed hydrate samples from nature under in situ conditions using pressure core characterization and analysis, which provides a unique opportunity for research. By employing state-of-the-art micro computed tomography imagery on cryogenically preserved, hydrate-bearing sediment samples, we can determine hydrate saturation as well as permeability with and without the presence of hydrates in the sediment. Furthermore, utilizing a machine learning based image segmentation technique, it is possible to extract pore space and grain information. Subsections of the entire image volume were used to determine anisotropic permeabilities using a finite-difference method Stokes solver (FDMSS). Additionally, permeability measurements on whole pressure and temperature preserved hydrate-bearing core were analyzed by utilizing the National Energy Technology Laboratory’s (NETL) Pressure Core Characterization and X-ray CT Visualization Tool (PCXT) to manipulate, cut, and analyze pressure preserved sediment. Permeabilities were measured under a broad range of vertical stress states to simulate expected pressure changes during production scenarios, and the results show that permeabilities derived from images are in agreement with those from traditional core derived experiments. The collected stress-dependent permeability, permeability anisotropy, and corresponding gas hydrate saturations provide valuable input into numerical simulations of reservoir productivity. These properties have been proven to be key parameters determining a long-term reservoir response under depressurization.

Liu, Mengwei [Oak Ridge Institute for Science and ↗
DOE OSTI2024

Solidification and crystallographic texture modeling of laser powder bed fusion Ti-6Al-4V using finite difference-monte carlo method

Laser powder bed fusion (LPBF) additive manufacturing makes near-net-shaped parts with reduced material cost and time, rising as a promising technology to fabricate Ti-6Al-4V, a widely used titanium alloy in aerospace and medical industries. However, LPBF Ti-6Al-4V parts produced with 67° rotation between layers, a scan strategy commonly used to reduce microstructure and property inhomogeneity, have varying grain morphologies and weak crystallographic textures that change depending on processing parameters. Here, this study predicts LPBF Ti-6Al-4V solidification at three energy levels using a finite difference-Monte Carlo method and validates the simulations with large-area electron backscatter diffraction (EBSD) scans. The developed model accurately shows that a <001> texture forms at low energy and a <111> texture occurs at higher energies parallel to the build direction but with a lower strength than the textures observed from EBSD. A validated and well-established method of combining spatial correlation and general spherical harmonics representation of texture is developed to calculate a difference score between simulations and experiments. The quantitative comparison enables effective fine-tuning of nucleation density (N 0 ) input, which shows a nonlinear relationship with increasing energy level. Future improvements in texture prediction code and a more comprehensive study of N 0 with different energy levels will further advance the optimization of LPBF Ti-6Al-4V components. These developments contribute a novel understanding of crystallographic texture formation in LPBF Ti-6Al-4V, the development of robust model validation and calibration pipeline methodologies, and provide a platform for mechanical property prediction and process parameter optimization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

A sweeping positivity-preserving high-order finite difference WENO scheme for Euler equations

We develop a simple, high-order, conservative and robust positivity-preserving sweeping procedure for the density and the nonlinear pressure function in the compressible Euler equations. Using the scaling limiter in Zhang and Shu (J Comput Phys 229:3091–3120, 2010), we obtain a non-trivial extension of the scalar sweeping technique in Liu et al. (J Sci Comput 73:1028–1071, 2017) for the positivity of pressure. The sweeping procedure developed in this paper is a post-processing technique, which can be applied to any concave functions of the conserved variables in hyperbolic conservation law systems. Thus, it has applications beyond the Euler equations. This procedure preserves positivity and conservation of physical quantities without destroying the accuracy of the underlying scheme. The algorithm works for general schemes including finite difference, finite volume and discontinuous Galerkin methods; however, in this paper we focus on finite difference weighted essentially non-oscillatory (WENO) methods. As a result, we provide numerical tests of the fifth-order finite difference WENO scheme to demonstrate the accuracy and robustness of the technique.

Compressible Euler equations↗
DOE OSTI2026

Sparsity Applications for Gradient‐Based Optimization of Wind Farms

Optimizing wind farms is essential for designing efficient energy systems, especially as farms grow larger and span multiple sites. However, this optimization becomes increasingly challenging due to the rising computational cost associated with more turbines. Gradient‐based optimization methods scale better than gradient‐free approaches for large problems, but the most computationally expensive component remains the calculation of gradients for the objective function and constraint Jacobians. To address this, we propose leveraging sparsity to accelerate gradient evaluations and reduce the size of the constraint Jacobian. Wind farms naturally exhibit sparsity—many turbines do not influence each other under certain wind directions. However, unlike traditional sparse problems with fixed patterns, wind farm sparsity is dynamic, requiring new strategies to handle changing interactions efficiently. This paper presents a study of sparsity in wind farm optimization and introduces several methods to exploit it. These strategies are tested on multiple farms using the analytic Cumulative Curl model, with gradients computed via automatic differentiation (AD). The same sparsity‐aware techniques are also applicable to finite difference (FD) methods, where they can yield even greater speedups due to the high cost of directional evaluations. Results show that sparse methods achieve up to a 10x speedup with less than ± 5% variance in optimized wake losses compared to traditional methods. These findings suggest that sparsity‐aware optimization not only maintains solution quality but also scales efficiently with farm size, enabling more comprehensive design exploration at reduced computational cost.

17 WIND ENERGY↗
DOE OSTI2024

Efficient sensitivity analysis of the thermal profile in powder bed fusion of metals using hypercomplex automatic differentiation finite element method

Rapid cyclic temperature fluctuation occurring in powder bed fusion of metals using a laser beam (PBF-LB/M) influences the formation of flaws in printed parts. Consequently, there is a pressing need to enhance the quality of printed parts by developing innovative methodologies that can predict thermal histories and help uncover the intricate relationships between process parameters and thermal profiles. Sensitivity Analysis (SA) emerges as an essential tool for this, offering the potential for process optimization and enhanced quality control. Nonetheless, conventional SA methodologies often incur in excessive computational costs and potential numerical approximation errors. Here, to address this technical challenge, we present a novel method for SA that integrates the HYPercomplex-based Automatic Differentiation (HYPAD) technique with transient thermal simulations conducted via the finite element method (FEM). Leveraging this methodology, we efficiently and accurately perform SA for PBF-LB/M processes in a post-processing step. Compared to traditional methods like Finite Differences (FD), HYPAD-FEM required 96 % less computational time for obtaining sensitivities for 22 process parameters, under a comparative study conducted within the context of the 2018–02 AM benchmark of the National Institute of Standards and Technology. In summary, HYPAD-FEM offers superior efficiency and accuracy in SA over conventional methods, delivering the best sensitivity of a model without the need for step-size selection and problem or parameter-based implementations.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Finite-element-based simulations of electrodes for CO 2 cascade reduction reactions

The multielectron reduction of CO 2 to liquid fuels could be a path to scalable energy storage, but reaching this goal requires major advances in catalysis and systems engineering. Cascade catalysis, which couples sequential reactions without isolating intermediates, has emerged as a promising route to enhance selectivity and efficiency in CO 2 reduction (CO 2 R). In this review, we examine how finite-element-based simulations of continuum model [finite element method (FEM)] approaches are being used to analyze and guide CO 2 R cascade systems. We first outline the fundamentals of cascade catalysis and recent advances in catalytic materials (metallic, molecular, and hybrid architectures). We then focus on FEM developments at the electrode and device scales, emphasizing how these models capture transport phenomena, local microenvironments, and geometry-dependent effects. To clarify design principles, we present case studies of cascade electrodes organized in systems without and with integrated semiconductors. We further emphasize the integration of FEM with multiscale frameworks (density functional theory, molecular dynamics, kinetic Monte Carlo) and its role in bridging atomic-level insights with device-level performance. Finally, we identify current limitations and future prospects, including improved boundary conditions, coupling with operando experiments, and machine learning-accelerated model development. Together, these insights provide design principles for next-generation CO 2 R cascade systems for efficient solar fuel production.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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 OSTI2024

Rotordynamic Analysis and Comparative Study of High-Speed Outer Rotor Permanent Magnet Motor Designs

High–power density electric motor designs are a requirement in aerospace and automotive applications. Outer rotor permanent magnet motors can offer high power density but have mechanical challenges such as structural stability and rotodynamic issues. In this work, a rotodynamic study was performed for two outer rotor permanent magnet motor designs. The first design was a cantilever design in which the rotor was suspended at one end, supported by four bearings; in the second design, the rotor was simply supported by two bearings in each end. Two different finite element method–based approaches, solid rotor and beam rotor methods, were used to extract the critical speed.

Barua, Himel↗
DOE OSTI2025

Estimation of extreme temperatures in direct solar methane pyrolysis within a porous medium

Porous media have wide application in renewable energy conversion processes, such as solar-thermal fuels production and decarbonization. Heat transport mechanisms within porous media can be highly complex, particularly under extreme conditions encountered in concentrated solar thermal reactors in which direct measurement of temperature is challenging. Here, we implement and report an inverse heat conduction model to estimate the temperature distribution throughout a porous substrate domain in a direct solar methane pyrolysis process. By solving a two-dimensional heat transfer problem and applying an inverse optimization algorithm, we estimate the quasi-steady state spatial temperature distribution in a fibrous porous carbon substrate. The results are validated indirectly by experimentally measured graphite deposition and a simplified reaction kinetic model.

finite difference method↗