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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 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Effect of workpiece curvature on the tool influence function during hemispherical sub-aperture tool glass polishing

The influence of workpiece curvature on the tool influence function spot during polishing of fused silica glass with cerium oxide slurry, while using a rotating hemispherical pad-foam tool for a wide variety of process conditions (tool displacement, inclination angle, and rotation rate), has been investigated. (Workpiece curvature ranged from 500 mm radius concave to 43 mm radius convex.) The TIF spot decreases in diameter and increases in the peak removal rate on more convex workpieces. In contrast, the TIF spot increases both in diameter and peak removal rate on more concave workpieces. For the range of workpiece curvatures investigated, both the spot size and the peak removal rate changed significantly, as much as 2 times. An elastic sphere–sphere contact mechanics model, which utilizes both a modified displacement (that leads to a change in the applied load) as well as a mismatch factor (that influences the pressure distribution shape), has been developed. Furthermore, the model was validated using both offline load-displacement measurements and finite-element analysis simulations. The model quantitatively describes the measured change in the relative contact diameter and relative pressure distribution, as well as semiquantitively describes the change in the relative volumetric removal rate on a large variety of TIF spots. The change in the volumetric removal rate for convex workpieces is a result of the balance between a decreasing spot size (reducing removal) and an increasing peak pressure (increasing removal), which usually results in relatively small changes in volumetric removal. In the case of concave workpieces, the volumetric removal rate change is also governed by a similar balance, but the spot size increase contribution dominates, resulting in a significant increase in volumetric removal rate. Understanding these trends can enable methods to add greater determinism during the fabrication of freeform optics by adjusting polishing parameters (such as dwell time) while the tool translates along a workpiece surface with different local curvatures.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Analysis of spent nuclear fuel multipurpose canister dynamics during rail transportation

The primary mode of spent nuclear fuel transportation within the United States will be by railcar. One such system is the Atlas railcar, which is designed to transport 17 different spent nuclear fuel cask systems, including bare fuel systems and canister fuel systems. In the latter configuration, multipurpose canisters containing spent nuclear fuel may be placed within an overpack for storage, or within a cask for transportation. Compared to bare fuel systems, canister fuel systems have additional degrees of freedom for motion during transportation, because clearance between the cask and canister allows for some motion of the canister to occur relative to the cask. This work investigates the effect of canister motion on the shock and vibration imparted to the spent nuclear fuel within. Structural dynamic analyses have been conducted to identify the effects of canister to cask clearance, presence and type of dunnage, and loading direction and frequency. This modeling study calculates anticipated cask motion, canister motion, and spent nuclear fuel structural dynamic response to normal conditions of transportation railcar motion using finite element analysis methods that were developed to model the rail segment of the ENSA/DOE (Equipos Nucleares S.A., U.S. Department of Energy) multimodal transportation test of 2017.

SNF, UNF, LS-DYNA, dynamics, kinematics, shock, vi↗
DOE OSTI2023

Guidelines for predicting stress in cemented doublets undergoing temperature change

This work explores quick predictive methods for calculating potentially risky stresses and deflections in cemented doublets experiencing temperature change that agree well with finite element analysis. There are three failure modes of interest: cohesive failure of the adhesive, delamination (surface bond failure or debonding), and glass fracture. Adhesive theory, confirmed by finite element analysis, predicts stress singularities that complicate interpretation of the stress calculations. The presence of a stress singularity indicates the breakdown of linear elastic assumptions, but damage initiation and stress singularities are related. The authors find that geometry details near a bond edge can exacerbate or minimize damage initiation and stress concentrations. Because the interpretation of the stress results is complicated, the authors investigated predicted stresses in doublets that have been successfully tested between -40 and 85 °C. This study found that the product (ΔT ∙ Δα) should be less than 189 ppm, where ΔT is the temperature excursion and Δα is the difference in glass coefficient of thermal expansion. If the product (ΔT ∙ Δα) is equal to or greater than 189 ppm, further analysis and testing is warranted. But the authors also show that the fabrication process can significantly influence stress failure, particularly with large diameter doublets.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Guidelines for predicting stress in cemented doublets undergoing temperature change

This work explores quick predictive methods for calculating potentially risky stresses and deflections in cemented doublets experiencing temperature change that agree well with finite element analysis. There are three failure modes of interest: cohesive failure of the adhesive, delamination (surface bond failure or debonding), and glass fracture. Adhesive theory, confirmed by finite element analysis, predicts stress singularities that complicate interpretation of the stress calculations. The presence of a stress singularity indicates the breakdown of linear elastic assumptions, but damage initiation and stress singularities are related. The authors find that geometry details near a bond edge can exacerbate or minimize damage initiation and stress concentrations. Because the interpretation of the stress results is complicated, the authors investigated predicted stresses in doublets that have been successfully tested between -40 and 85 °C. This study found that the product (∆T ∙ ∆α) should be less than 189 ppm, where ∆T is the temperature excursion and ∆α is the difference in glass coefficient of thermal expansion. If the product (∆T ∙ ∆α) is equal to or greater than 189 ppm, further analysis and testing is warranted. But the authors also show that the fabrication process can significantly influence stress failure, particularly with large diameter doublets

42 ENGINEERING↗
DOE OSTI2021

Sparse Approximate Multifrontal Factorization with Butterfly Compression for High-Frequency Wave Equations

In this work, we present a fast and approximate multifrontal solver for large-scale sparse linear systems arising from finite-difference, finite-volume or finite-element discretization of high-frequency wave equations. The proposed solver leverages the butterfly algorithm and its hierarchical matrix extension for compressing and factorizing large frontal matrices via graph-distance guided entry evaluation or randomized matrix-vector multiplication-based schemes. Complexity analysis and numerical experiments demonstrate $\mathcal{O}(N\log^2 N)$ computation and $\mathcal{O}(N)$ memory complexity when applied to an $N\times N$ sparse system arising from 3D high-frequency Helmholtz and Maxwell problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Time-dependent variational principle for mixed matrix product states in the thermodynamic limit

Here, we describe a time evolution algorithm for quantum spin chains whose Hamiltonians are composed of an infinite uniform left and right bulk part, and an arbitrary finite region in between. The left and right bulk parts are allowed to be different from each other. The algorithm is based on the time-dependent variational principle (TDVP) of matrix product states. It is inversion-free and very simple to adapt from an existing TDVP code for finite systems. The importance of working in the projective Hilbert space is highlighted. We study the quantum Ising model as a benchmark and an illustrative example. The spread of information after a local quench is studied in both the ballistic and the diffusive case. We also offer a derivation of TDVP directly from symplectic geometry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Precision study of the massive Schwinger model near quantum criticality

We perform a numerical analysis of the massive Schwinger model in the presence of a background electric field. Using the Density Matrix Renormalization Group approach, we efficiently compute the spectrum of the Schwinger model on a staggered lattice with up to 3000 qubits. As a result, we achieve a precise computation of the critical mass of the massive Schwinger model to five digits using four different “criticality criteria,” observing perfect agreement among them Additionally, we discuss the effect of a four-fermion operator deformation of the Schwinger model and compute the critical mass for various values of the deformation parameter.

Critical phenomena↗
DOE OSTI2021

Shell-structure and asymmetry effects in level densities

Level density [Formula: see text] is derived for a nuclear system with a given energy [Formula: see text], neutron [Formula: see text], and proton [Formula: see text] particle numbers, within the semiclassical extended Thomas–Fermi and periodic-orbit theory beyond the Fermi-gas saddle-point method. We obtain [Formula: see text], where [Formula: see text] is the modified Bessel function of the entropy [Formula: see text], and [Formula: see text] is related to the number of integrals of motion, except for the energy [Formula: see text]. For small shell structure contribution one obtains within the micro–macroscopic approximation (MMA) the value of [Formula: see text] for [Formula: see text]. In the opposite case of much larger shell structure contributions one finds a larger value of [Formula: see text]. The MMA level density [Formula: see text] reaches the well-known Fermi gas asymptote for large excitation energies, and the finite micro-canonical limit for low excitation energies. Fitting the MMA [Formula: see text] to experimental data on a long isotope chain for low excitation energies, due mainly to the shell effects, one obtains results for the inverse level density parameter [Formula: see text], which differs significantly from that of neutron resonances.

Physics↗
DOE OSTI2025

Feasibility of an Accelerometer-Based Structural Health Monitoring System for the LANL Blast Tube

A modeling- and simulation-based study was conducted on the feasibility of implementing an accelerometer-based SHM system on the Los Alamos National Laboratory blast tube. A blast tube experiment was modeled using the Abaqus explicit finite element solver. A custom user subroutine was written to apply test-like pressure loading to the inside surface of the blast tube. The subroutine applies analytically defined pressure loads derived from tracer output taken from a Compressible Flow Computational Fluid Dynamics Solver model of the blast tube. Five unique versions of the model were created: an undamaged reference model at 65°F was used as the baseline and compared to equivalent models at 10°F and 100°F. These three models were compared to models with small damage at the reference temperature. The two types of damage considered were a radial (circumferential) crack in the main tube body and a longitudinal crack in the supports. Acceleration outputs were extracted from accelerometer bodies included in the model and were post processed using a variety of standard SHM techniques. Different potential features signaling failure were extracted and compared using statistical methods in the time and frequency domains. A method was identified that clearly shows that differences in structural response resulting from the modeled damage can be differentiated from the structural response resulting from changing environmental conditions. However, the amount of damage applied to create observable differences in the accelerometer data was so large that simpler methods of damage detection would be more cost effective in locating damage.

42 ENGINEERING↗
DOE OSTI2025

Modeling the formation of Sedan Crater using the FLAG and HOSS codes

Numerical modeling of explosion crater formation requires accounting for complex physical processes. Numerical validation of explosion cratering is an important step in modeling and requires experimental data for comparison. Models using discrete elements and continuum models have both benefits and drawbacks to their approaches. In this work, we consider both an arbitrary Lagrangian–Eulerian (ALE) hydrocode and a finite discrete element method (FDEM) approach to modeling the formation of the Sedan crater, the largest human-made crater in the United States. The Sedan crater formed from an underground nuclear detonation in the Nevada desert as part of Project Plowshare. Our models show that the continuum approach of the hydrocode matched well compared to early test time prior to the mound rupture and subsequent fireball venting, when most of the alluvium exhibited fluid behavior. Our FDEM approach matched the final crater dimensions well, after material had settled back into the crater, when material strength and solid mechanics play key roles. Our work shows how leveraging the benefits of multiple numerical approaches can lead to better understanding of complex physical problems, especially problems with limited experimental data. By using a continuum approach to early-time hydrodynamics and an FDEM approach to later-time solid mechanics, we can better understand the different physical regimes of explosion crater formation.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Full-Field Strain Measurement Integrated with Two Dimension Regression Analysis to Evaluate the Bi-Modulus Elastic Properties of Isotropic and Transversely Isotropic Materials

Background: Measuring the physical properties of shale is critical for optimizing engineering activities such as geothermal energy generation and hydraulic fracturing. Shale is a transversely isotropic material. Furthermore, this material can also include micro and macro cracks at different locations and orientations that cause it to behave differently under tensile or compressive loading. Objective: In this work, a combined experimental–numerical approach is proposed to evaluate the bi-modulus elastic properties of isotropic and transversely isotropic materials. Methods: Full-field strain measurements for a circular disk under diametral compression are integrated with a regression analysis technique to evaluate the elastic properties of bi-modulus materials subjected to tensile and compressive loads using two loading configurations on the same specimen. Digital Image Correlation (DIC) is used to measure the full-field strains. Subsequently, in the case of an isotropic material, a linear least-squares approach is utilized to process the experimentally determined strains in conjunction with analytical expressions of the stress fields (in terms of far-field loading) to determine the elastic modulus E, the shear modulus G, and the Poisson’s ratio $v$. In the case of a transversely isotopic material, such as shale, a finite element model is implemented to determine the stress fields (again in terms of far-field loading), which is followed by repeating the previous regression analysis in an iterative process to estimate the elastic parameters. Results: The results show that the proposed technique successfully provides a complete set of elastic properties as a function of both the loading condition and the principal material directions. The technique is validated by measurements on a known isotropic material and then applied to determine the properties of shale. Conclusion: In this work, the proposed approach is successfully used to calculate the bi-modulus elastic response of poly(methyl meth- acrylate) (PMMA) and shale. As expected, PMMA exhibits an isotropic response with no bi-modulus effect, however, shale exhibits both transverse isotropy and a bi-modulus effect. Therefore, this approach holds promise for investigating the elastic properties of materials like rocks and fiber-reinforced composite laminates as functions of the principal material directions and the loading conditions.

42 ENGINEERING↗
DOE OSTI2025

Exotic phases in finite-density ℤ 3 theories

Lattice ℤ 3 theories with complex actions share many key features with finite- density QCD including a sign problem and $\mathcal{CK}$ symmetry. Complex ℤ 3 spin and gauge models exhibit a generalized Kramers-Wannier duality mapping them onto chiral ℤ 3 spin and gauge models, which are simulatable with standard lattice methods in large regions of parameter space. The Migdal-Kadanoff real-space renormalization group (RG) preserves this duality, and we use it to compute the approximate phase diagram of both spin and gauge ℤ 3 models in dimensions one through four. Chiral ℤ 3 spin models are known to exhibit a Devil’s Flower phase structure, with inhomogeneous phases that can be thought of as ℤ 3 analogues of chiral spirals. Out of the large class of models we study, we find that only chiral spin models and their duals have a Devil’s Flower structure with an infinite set of inhomogeneous phases, a result we attribute to Elitzur’s theorem. We also find that different forms of the Migdal-Kadanoff RG produce different numbers of phases, a violation of the expectation for universal behavior from a real-space RG. We discuss extensions of our work to ℤ N models, SU(N) models and nonzero temperature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Revisiting Multi-Material Composite Structures with Homogenized Composite Properties

Composite structures inherently develop residual stresses during their curing process. Driven predominately by mismatched thermal strains between differing materials or ply orientations, but also affected by curing process phenomena like polymer shrinkage, these residual stresses can lead to failure within composite structures. There are several methods varying in complexity that can be used to model the development of residual stresses, all of which are capable of capturing sufficient detail to understand the residual stress state at the ply level. However, explicitly modeling all plies of a layup in a composite structure can be prohibitively expensive based on the number of plies, structure size, and required element size. The computational cost can be reduced through the homogenization of the composite layup without losing much fidelity of the overall response of the structure. The homogenization process reduces the many plies of a laminate to a single lamina that reduces complexity and increases the mesh size where a single element can span multiple plies. This report focuses on verification and validation efforts for a homogenization process using a suite of finite element simulations rather than an analytic solution derived from classical laminate theory. Initial verification using representative element volumes indicated there was minimal error in the homogenization process; however, this compounded to a small, but acceptable error in strip and split ring experimental composite structures. The error does under predict the residual stress state in the strip and split ring and should be accounted for when simulating composite structures with homogenized properties.

36 MATERIALS SCIENCE↗
DOE OSTI2021

A Study on Computational Cost Reduction of Simulations of Phase-Change Material (PCM) Embedded Heat Exchangers

Thermal storage can be implemented using Phase-Change Materials (PCM), which absorb significant latent heat with a relatively small temperature change. PCM phase-change processes are transient and are driven by thermal diffusion and natural convection – the latter, especially for melting process. Modeling and simulation of PCM heat exchangers (HX’s) is typically computationally intensive due to the relatively complex time-dependent physics. Most of the PCM modeling work in the literature uses high-order modeling tools such as Computational Fluid Dynamics (CFD) and Lattice-Boltzmann Method (LBM). For design purposes, the existing PCM modeling approaches are not practical, limiting researchers in their ability to investigate new ideas and different PCM’s with faster turnarounds. This paper presents a study investigating the reduction of computational cost of PCM embedded HX’s CFD models by evaluating the feasibility of spatial reduction without losing accuracy. The analysis consists of comparing full and partial domain under full melting conditions. The subject of this study is a single straight tube with circular transverse fins in the vertical orientation, using PCM’s with 35oC nominal melting temperature. Different tube and fin dimensions are investigated. Results indicate that the reduced domain reproduces - in half the run time - the same behavior as the full domain since the buoyancy effects are localized and patterned. The outputs from the partial domain simulation were used to build a non-general correlation for the PCM heat transfer characteristics and demonstrated how it can be implemented in a Finite Control Volume Reduced Order Model (ROM). The ROM can accurately reproduce the CFD simulations at 4 to 5 orders of magnitude faster.

25 ENERGY STORAGE↗
DOE OSTI2025

Physical-mass calculation of ρ ( 770 ) and K * ( 892 ) resonance parameters via π π and K π scattering amplitudes from lattice QCD

We present our study of the ρ ( 770 ) and K * ( 892 ) resonances from lattice quantum chromodynamics (QCD) employing domain-wall fermions at physical quark masses. We determine the finite-volume energy spectrum in various momentum frames and obtain phase-shift parametrizations via the Lüscher formalism and as a final step the complex resonance poles of the π π and K π elastic scattering amplitudes via an analytical continuation of the models. By sampling a large number of representative sets of underlying energy-level fits, we also assign a systematic uncertainty to our final results. This is a significant extension to data-driven analysis methods that have been used in lattice QCD to date, due to the two-step nature of the formalism. Our final pole positions, M + i Γ / 2 , with all statistical and systematic errors exposed, are M K * = 893 ( 2 ) ( 8 ) ( 54 ) ( 2 ) MeV and Γ K * = 51 ( 2 ) ( 11 ) ( 3 ) ( 0 ) MeV for the K * ( 892 ) resonance and M ρ = 796 ( 5 ) ( 15 ) ( 48 ) ( 2 ) MeV and Γ ρ = 192 ( 10 ) ( 28 ) ( 12 ) ( 0 ) MeV for the ρ ( 770 ) resonance. The four differently grouped sources of uncertainties are, in the order of occurrence: statistical, data-driven systematic, an estimation of systematic effects beyond our computation (dominated by the fact that we employ a single lattice spacing), and the error from the scale-setting uncertainty on our ensemble. Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

A multi-dimensional Child–Langmuir law for any diode geometry

While prior theoretical studies of multi-dimensional space-charge limited current (SCLC) assumed emission from a small patch on infinite electrodes, none have considered emission from an entire finite electrode. In this paper, we apply variational calculus (VC) and conformal mapping, which have previously been used to derive analytic solutions for SCLC density (SCLCD) for nonplanar one-dimensional geometries, to obtain mathematical relationships for any multi-dimensional macroscopic diode with finite cathode and anode. We first derive a universal mathematical relationship between space-charge limited potential and vacuum potential for any diode and apply this technique to determine SCLCD for an eccentric spherical diode. We then apply VC and the Schwartz–Christoffel transformation to derive an exact equation for SCLCD in a general two-dimensional planar geometry with emission from a finite emitter. Particle-in-cell simulations using VSim agreed within 4%–13% for a range of ratios of emitter width to gap distance using the thinnest electrodes practical for the memory constraints of our hardware, with the difference partially attributed to the theory's assumption of infinitesimally thin electrodes. After generalizing this approach to determine SCLCD for any orthogonal diode as a function of only the vacuum capacitance and vacuum potential, we derive an analytical formulation of the three-dimensional Child–Langmuir law for finite parallel rectangular and disk geometries. These results demonstrate the utility for calculating SCLCD for any diode geometry using vacuum capacitance and vacuum potential, which are readily obtainable for many diode geometries, to guide experiment and simulation development.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

A combined experimental and crystal plasticity study of grain size effects in magnesium alloys

This work presents a method to incorporate the micro Hall-Petch equation into the crystal plasticity finite element (CPFE) framework accounting for the microstructural features to understand the coupling between grain size, texture, and loading direction in magnesium alloys. The effect of grain size and texture is accounted for by modifying the slip resistances of individual basal and prismatic systems based on the micro Hall-Petch equation. The modification based on the micro Hall-Petch equation endows every slip system at each microstructural point with a slip system-level grain size and maximum compatibility factor, which are in turn used to modify the slip resistance. While the slip-system level grain size is a measure of the grain size, the maximum compatibility factor encodes the effect of the grain boundary on the slip system resistance modification and is computed based on the Luster-Morris factor. The model is calibrated using experimental stress-strain curves of Mg-4Al samples with three different grain sizes from which the Hall-Petch coefficients are extracted and compared with Hall-Petch coefficients predicted using original parameters from previous work. The predictability of the model is then evaluated for a Mg-4Al sample with different texture and three grain sizes subjected to loading in different directions. The calibrated parameters are then used for some parametric studies to investigate the variation of Hall-Petch slope for different degrees of simulated spread in basal texture, variation of Hall-Petch slope with loading direction relative to basal poles for a microstructure with strong basal texture, and variation of yield strength with change in grain morphology. The proposed approach to incorporate the micro Hall-Petch equation into the CPFE framework provides a foundation to quantitatively model more complicated scenarios of coupling between grain size, texture and loading direction in the plasticity of Mg alloys.

Crystal plasticity↗
DOE OSTI2022

Iterative subspace algorithms for finite-temperature solution of Dyson equation

One-particle Green’s functions obtained from the self-consistent solution of the Dyson equation can be employed in the evaluation of spectroscopic and thermodynamic properties for both molecules and solids. However, typical acceleration techniques used in the traditional quantum chemistry self-consistent algorithms cannot be easily deployed for the Green’s function methods because of a non-convex grand potential functional and a non-idempotent density matrix. Moreover, the optimization problem can become more challenging due to the inclusion of correlation effects, changing chemical potential, and fluctuations of the number of particles. In this paper, we study acceleration techniques to target the self-consistent solution of the Dyson equation directly. We use the direct inversion in the iterative subspace (DIIS), the least-squared commutator in the iterative subspace (LCIIS), and the Krylov space accelerated inexact Newton method (KAIN). We observe that the definition of the residual has a significant impact on the convergence of the iterative procedure. Based on the Dyson equation, we generalize the concept of the commutator residual used in DIIS and LCIIS and compare it with the difference residual used in DIIS and KAIN. The commutator residuals outperform the difference residuals for all considered molecular and solid systems within both GW and GF2. For a number of bond-breaking problems, we found that an easily obtained high-temperature solution with effectively suppressed correlations is a very effective starting point for reaching convergence of the problematic low-temperature solutions through a sequential reduction of temperature during calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗