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Results for “Finite Difference Methods”

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 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Multigrid methods and high order finite difference for flow in transition - Effects of isolated and distributed roughness elements

The high order finite difference and multigrid methods have been successfully applied to direct numerical simulation (DNS) for flow transition in 3D channels and 3D boundary layers with 2D and 3D isolated and distributed roughness in a curvilinear coordinate system. A fourth-order finite difference technique on stretched and staggered grids, a fully-implicit time marching scheme, a semicoarsening multigrid method associated with line distributive relaxation scheme, and a new treatment of the outflow boundary condition, which needs only a very short buffer domain to damp all wave reflection, are developed. These approaches make the multigrid DNS code very accurate and efficient. This makes us not only able to do spatial DNS for the 3D channel and flat plate at low computational costs, but also able to do spatial DNS for transition in the 3D boundary layer with 3D single and multiple roughness elements. Numerical results show good agreement with the linear stability theory, the secondary instability theory, and a number of laboratory experiments.

Liu, C.↗
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↗
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 ↗