Search NASA⌕ Search

SEARCH · Search NASA

Results for “finite difference method”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 973 records · Page 54
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Momentum distribution of the uniform electron gas at finite temperature: Effects of spin polarization

We carry out extensive direct path integral Monte Carlo (PIMC) simulations of the uniform electron gas (UEG) at finite temperature for different values of the spin-polarization ξ. This allows us to unambiguously quantify the impact of spin effects on the momentum distribution function n(k) and related properties. We find that interesting physical effects like the interaction-induced increase in the occupation of the zero-momentum state n(0) substantially depend on ξ. Our results further advance the current understanding of the UEG as a fundamental model system, and are of practical relevance for the description of transport properties of warm dense matter in an external magnetic field. All PIMC results are freely available online and can be used as a benchmark for the development of methods and applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

(U) Estimating the Photonics Budget, Resolution, and Signal Requirements for a Multi-Monochromatic X-ray Imager

This document examines the performance of a generic flat-mirror multimonochromatic imager (MMI), with special emphasis on existing instruments at NIF and Omega. We begin by deriving the standard equation for the mean number of photons detected per resolution element. The pinhole energy bandwidth is a contributing factor; this is dominated by the finite size of the source and may be considerable. The most common method for estimating the spatial resolution of such a system (quadrature addition) is, technically, mathematically invalid for this case. However, under the proper circumstances it may produce good estimates compared to a rigorous calculation based on the convolution of point-spread functions. Diffraction is an important contribution to the spatial resolution. Common approximations based on Fraunhofer (farfield) diffraction may be inappropriate and misleading, as the instrument may reside in multiple regimes depending upon its configuration or the energy of interest. It is crucial to identify the correct diffraction regime; Fraunhofer and Fresnel (near-field) diffraction profiles are substantially different, the latter being considerably wider. Finally, we combine the photonics and resolution analyses to derive an expression for the minimum signal level such that the resulting images are not dominated by photon statistics. This analysis is consistent with observed performance of the NIF MMI.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2017

A micro-scale cutting model for UD CFRP composites with thermo-mechanical coupling

Cutting a unidirectional carbon fiber-reinforced polymer (UD CFRP) structure is the basic unit for CFRP machining, which is a complex thermal-mechanically coupled process. To reveal the deformation mechanism and predict cutting force in UD CFRP micro cutting, a micro-scale fracture model for UD CFRP cutting with thermal-mechanical coupling is demonstrated in this paper, which captures the failure modes for fibers, matrix and the interface based on a micro-level RVE using a relatively simple damage based fracture method. The thermal-mechanical coupling model at the micro scale is developed on the basis of the plastic energy dissipation and frictional heating during cutting. Failure models for the fiber, matrix and interface region are applied depending on the material properties of each of these three phases. Numerical simulations based on the above model with different fiber orientations were performed to predict the deformation and forces of different components in UD CFRP. Cutting experiments with the same fiber orientations as considered in the simulations were carried out to validate the force and deformation results. The predicted force and deformation patterns match well with evidence from our experiments. In general, the cutting force is larger than the thrust force regardless of fiber orientation. The cutting force reaches a maximum as the fiber orientation approaches 90 , but thrust forces do not vary substantially across cases. When the fiber orientation is acute, the deformation of fibers is much smaller than when the cutting angle is obtuse. Surface roughness follows the same trend with cutting angle as fiber deformation.

42 ENGINEERING↗
DOE OSTI2020

Fast GPU 3D diffeomorphic image registration

3D image registration is one of the most fundamental and computationally expensive operations in medical image analysis. Here, we present a mixed-precision, Gauss–Newton–Krylov solver for diffeomorphic registration of two images. Our work extends the publicly available CLAIRE library to GPU architectures. Despite the importance of image registration, only a few implementations of large deformation diffeomorphic registration packages support GPUs. Our contributions are new algorithms to significantly reduce the run time of the two main computational kernels in CLAIRE: calculation of derivatives and scattered-data interpolation. Additionally, we deploy (i) highly-optimized, mixed-precision GPU-kernels for the evaluation of scattered-data interpolation, (ii) replace Fast-Fourier-Transform (FFT)-based first-order derivatives with optimized 8th-order finite differences, and (iii) compare with state-of-the-art CPU and GPU implementations. As a highlight, we demonstrate that we can register clinical images in less than 6 s on a single NVIDIA Tesla V100. This amounts to over 20 speed-up over the current version of CLAIRE and over 30 speed-up over existing GPU implementations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

EMPIRE-PIC: A Performance Portable Unstructured Particle-in-Cell Code

In this study we introduce EMPIRE-PIC, a finite element method particle-in-cell (FEM-PIC) application developed at Sandia National Laboratories. The code has been developed in C++ using the Trilinos library and the Kokkos Performance Portability Framework to enable running on multiple modern compute architectures while only requiring maintenance of a single codebase. EMPIRE-PIC is capable of solving both electrostatic and electromagnetic problems in two- and three-dimensions to second-order accuracy in space and time. In this paper we validate the code against three benchmark problems — a simple electron orbit, an electrostatic Langmuir wave, and a transverse electromagnetic wave propagating through a plasma. We demonstrate the performance of EMPIRE-PIC on four different architectures: Intel Haswell CPUs, Intel's Xeon Phi Knights Landing, ARM Thunder-X2 CPUs, and NVIDIA Tesla V100 GPUs attached to IBM POWER9 processors. This analysis demonstrates scalability of the code up to more than two thousand GPUs, and greater than one hundred thousand CPUs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Experimentally Validated Computational Modeling of Creep and Creep-Cracking for Nuclear Concrete Structures

In a Nuclear Power Plant, one of the most important components is the concrete nuclear reactor cavity, which serves both a structural and protective function as the biological radiation shield. Given that creep has been identified as a major knowledge gap in the assessment of nuclear structures (NUREG/CR-7153), this work helps to further the understanding of creep behavior of massive concrete containment structures for decades to enable safe and long-term operation of these facilities. This project has developed a robust, experimentally validated model to predict creep in nuclear concrete structures for up 60 years using short-term creep data thereby enabling a longer service life of critical facilities and early detection of structural failure. The work presented in this report is a pairing of computational and experimental methods. For the first time, the time temperature superposition (TTS) principle was successfully used to generate a uniaxial creep compliance master curve to predict mortar creep response for up to 22,500 days (nearly 60 years) at a reference temperature of 20°C. These data were used as input into finite element analysis (FEA) codes that use highly realistic random, 3D concrete microstructures from reconstructed coarse limestone aggregates. Finite element analysis performed provides the ability to quickly upscale mortar viscoelastic behavior to long-term concrete creep/relaxation data. A master creep compliance curve, constructed from the TTS principle, spanning 27 years, was used to validate two and a half decades of simulated concrete creep. Concurrently, three different simulated wall specimens were designed to mimic the behavior of post-tensioned concrete nuclear containment facility vessel walls over time as a result of concrete creep. The specimens were designed with different thicknesses, transverse and longitudinal reinforcement ratios, and level of post-tensioning stress. Each specimen contained various instrumentation to measure internal concrete temperature, concrete strain, and post-tensioning strain hourly for over 3 years. The concrete creep model developed in this project, based on the FEA concrete simulations, was applied to simulate the structural-scale experiments of prestressed concrete walls conducted in this project using the Grizzly code. These models can represent the effects of reinforcing and prestressing. Although there are some discrepancies with the experimental data, the model can predict the overall trends of the creep response in these experiments. One of these experimental models was also applied to an extended time to demonstrate how the findings from this study can be used to predict the behavior of actual structures of interest that have been in service for extended periods of time.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

On convergent finite difference schemes for variational–PDE-based image processing

We study an adaptive anisotropic Huber functional-based image restoration scheme. Using a combination of L2–L1 regularization functions, an adaptive Huber functional-based energy minimization model provides denoising with edge preservation in noisy digital images. We study a convergent finite difference scheme based on continuous piecewise linear functions and use a variable splitting scheme, namely the Split Bregman (In: Goldstein and Osher, SIAM J Imaging Sci 2(2):323–343, 2009) algorithm, to obtain the discrete minimizer. Experimental results are given in image denoising and comparison with additive operator splitting, dual fixed point, and projected gradient schemes illustrates that the best convergence rates are obtained for our algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Symmetric spectrum current drive due to finite radial drift effects

We report the drift surfaces of minority heated ions differ from flux surfaces due to finite poloidal gyroradius effects. As the minority poloidal gyroradius approaches radial scale lengths in the plasma, the difference between drift and flux surfaces can modify the heating and lead to a symmetric spectrum minority counter-current being driven. In response, a corresponding overall net co-current of comparable size is driven. This beneficial symmetric spectrum current drive in a tokamak is due to the parallel velocity asymmetry in the drift departure from a flux surface. As this new source of driven current is a side effect of minority heating it comes without any additional economic cost to reactor power balance. The symmetric spectrum current driven for near Maxwellian minorities is evaluated by an adjoint method and found to be modest. However, minority heating typically results in strong non-Maxwellian features on minority distributions so it may be possible to drive a significantly larger co-current. A related evaluation is performed for alpha particles in a deuterium minority heated plasma with a tritium majority. The low density of the alphas tends to keep this driven symmetric spectrum current small, but at very high heating levels a significant co-current might be driven. Other mechanisms to drive co-current with a symmetric spectrum are discussed and estimated, including asymmetric electron drag and focusing of the applied minority heating radio frequency fields.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Seismic waves in medium with poroelastic/elastic interfaces: a two-dimensional P-SV finite-difference modelling

SUMMARY We present a new methodology of the finite-difference (FD) modelling of seismic wave propagation in a strongly heterogeneous medium composed of poroelastic (P) and (strictly) elastic (E) parts. The medium can include P/P, P/E and E/E material interfaces of arbitrary shapes. The poroelastic part can be with (i) zero resistive friction, (ii) non-zero constant resistive friction or (iii) JKD model of the frequency-dependent permeability and resistive friction. Our FD scheme is capable of subcell resolution: a material interface can have an arbitrary position in the spatial grid. The scheme keeps computational efficiency of the scheme for a smoothly and weakly heterogeneous medium (medium without material interfaces). Numerical tests against independent analytical, semi-analytical and spectral-element methods prove the efficiency and accuracy of our FD modelling. In numerical examples, we indicate effect of the P/E interfaces for the poroelastic medium with a constant resistive friction and medium with the JKD model of the frequency-dependent permeability and resistive friction. We address the 2-D P-SV problem. The approach can be readily extended to the 3-D problem.

58 GEOSCIENCES↗
DOE OSTI2018

Symmetric spectrum current drive due to finite radial drift effects

The drift surfaces of minority heated ions differ from flux surfaces due to finite poloidal gyroradius effects. As the minority poloidal gyroradius approaches radial scale lengths in the plasma the difference between drift and flux surfaces can modify the heating and lead to a symmetric spectrum minority counter-current being driven. In response, a corresponding overall net co-current of comparable size is driven. This beneficial symmetric spectrum current drive in a tokamak is due to the parallel velocity asymmetry in the drift departure from a flux surface. As this new source of driven current is a side effect of minority heating it comes without any additional economic cost to reactor power balance. The symmetric spectrum current driven for near Maxwellian minorities is evaluated by an adjoint method and found to be modest. However, minority heating typically results in strong non-Maxwellian features on minority distributions so it may be possible to drive significantly larger co-current. A related evaluation is performed for alpha particles in a deuterium minority heated plasma with a tritium majority. The low density of the alphas tends to keep this driven symmetric spectrum current small, but at very high heating levels a significant co-current might be driven. Other mechanisms to drive co-current with a symmetric spectrum are discussed and estimated, including asymmetric electron drag and focusing of the applied minority heating radio frequency fields.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Characterize traction–separation relation and interfacial imperfections by data-driven machine learning models

Abstract Interfacial mechanical properties are important in composite materials and their applications, including vehicle structures, soft robotics, and aerospace. Determination of traction–separation (T–S) relations at interfaces in composites can lead to evaluations of structural reliability, mechanical robustness, and failures criteria. Accurate measurements on T–S relations remain challenging, since the interface interaction generally happens at microscale. With the emergence of machine learning (ML), data-driven model becomes an efficient method to predict the interfacial behaviors of composite materials and establish their mechanical models. Here, we combine ML, finite element analysis (FEA), and empirical experiments to develop data-driven models that characterize interfacial mechanical properties precisely. Specifically, eXtreme Gradient Boosting (XGBoost) multi-output regressions and classifier models are harnessed to investigate T–S relations and identify the imperfection locations at interface, respectively. The ML models are trained by macroscale force–displacement curves, which can be obtained from FEA and standard mechanical tests. The results show accurate predictions of T–S relations ( R 2 = 0.988) and identification of imperfection locations with 81% accuracy. Our models are experimentally validated by 3D printed double cantilever beam specimens from different materials. Furthermore, we provide a code package containing trained ML models, allowing other researchers to establish T–S relations for different material interfaces.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Laser-based ultrasound interrogation of surface and sub-surface features in advanced manufacturing materials

Abstract Structures formed by advanced manufacturing methods increasingly require nondestructive characterization to enable efficient fabrication and to ensure performance targets are met. This is especially important for aerospace, military, and high precision applications. Surface acoustic waves (SAW) generated by laser-based ultrasound can detect surface and sub-surface defects relevant for a broad range of advanced manufacturing processes, including laser powder bed fusion (LPBF). In particular, an all-optical SAW generation and detection configuration can effectively interrogate laser melt lines. Here we report on scattered acoustic energy from melt lines, voids, and surface features. Sub-surface voids are also characterized using X-ray Computed Tomography (CT). High resolution CT results are presented and compared with SAW measurements. Finite difference simulations inform experimental measurements and analysis.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: Comparison with linear subspace techniques

Natural convection in porous media is a highly nonlinear multiphysical problem relevant to many engineering applications (e.g., the process of CO 2 sequestration). Here, we extend and present a non-intrusive reduced order model of natural convection in porous media employing deep convolutional autoencoders for the compression and reconstruction and either radial basis function (RBF) interpolation or artificial neural networks (ANNs) for mapping parameters of partial differential equations (PDEs) on the corresponding nonlinear manifolds. To benchmark our approach, we also describe linear compression and reconstruction processes relying on proper orthogonal decomposition (POD) and ANNs. Further, we present comprehensive comparisons among different models through three benchmark problems. The reduced order models, linear and nonlinear approaches, are much faster than the finite element model, obtaining a maximum speed-up of 7 × 10 6 because our framework is not bound by the Courant–Friedrichs–Lewy condition; hence, it could deliver quantities of interest at any given time contrary to the finite element model. Our model’s accuracy still lies within a relative error of 7% in the worst-case scenario. We illustrate that, in specific settings, the nonlinear approach outperforms its linear counterpart and vice versa. We hypothesize that a visual comparison between principal component analysis (PCA) and t-Distributed Stochastic Neighbor Embedding (t-SNE) could indicate which method will perform better prior to employing any specific compression strategy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A tight-binding molecular dynamics study of the noble metals Cu, Ag and Au

Here we have used the Naval Research Lab (NRL) tight-binding (TB) method to study the electronic and mechanical properties of the noble metals. In order to perform molecular dynamics simulations, we used new TB parameters that work well at smaller interatomic distances. The TB parameters were fitted to the fcc, bcc and sc periodic structures and were demonstrated to be transferable and robust for calculating additional dynamical properties which they had not been fitted to. We calculated the phonon frequencies and density of states at finite temperature and we also performed simulations to determine the temperature dependence of the coefficient of thermal expansion and the mean squared displacement. The energy for vacancy formation as well as energy for fcc-based, bcc-based clusters and icosahedral clusters of different sizes were also calculated. The results compared very well with experimental observations and independent (non-fitted) first-principles density functional calculations.

36 MATERIALS SCIENCE↗
DOE OSTI2022

The Schwarz alternating method for transient solid dynamics

Abstract In our earlier work, we formulated the Schwarz alternating method as a means for concurrent multiscale coupling in finite deformation solid mechanics for quasi‐static problems. Herein, we advance this method for the study of transient dynamic multiscale solid mechanics problems where information is exchanged back and forth between small and large scales. The extension to dynamics relies on the notion of a global time stepper. Within each global time step, the subdomains are coupled by the standard Schwarz iterative process. Remarkably, each subdomain can use its own time step or even its own time integrator to advance its solution in time, provided that they synchronize at each global time step. We study the performance of the Schwarz method on several examples designed for this purpose. Our numerical experiments demonstrate that the method is capable of coupling regions with different mesh resolutions, different element types, and different time integration schemes (e.g., implicit and explicit), all without introducing any artifacts that afflict other coupling methods for transient dynamics. Finally, we apply the dynamic Schwarz alternating method to the simulation of a bolted joint subjected to dynamic loading, as a demonstration of the performance of the method in a realistic scenario.

Mota, Alejandro↗
DOE OSTI2021

Variational Self-Consistent Theory for Beam-Loaded Cavities

A new variational theory is presented for beam loading in microwave cavities. The beam{field interaction is formulated as a dynamical interaction whose stationarity according to Hamilton’s principle will naturally lead to steady-state solutions that indicate how a cavity’s resonant frequency, Q and optimal coupling coefficient will detune as a result of the beam loading. A driven cavity Lagrangian is derived from first principles, including the effects of cavity wall losses, input power and beam interaction. The general formulation is applied to a typical klystron input cavity to predict the appropriate detuning parameters required to maximize the gain (or modulation depth) in the average Lorentz factor boost, (Δ γ). Numerical examples are presented, showing agreement with the general detuning trends previously observed in the literature. The developed formulation carries several advantages for beam-loaded cavity structures. It provides a self-consistent model for the dynamical (nonlinear) beam{field interaction, a procedure for maximizing gain under beam-loading conditions, and a useful set of parameters to guide cavity-shape optimization during the design of beam-loaded systems. Enhanced clarity of the physical picture underlying the problem seems to be gained using this approach, allowing straightforward inclusion or exclusion of different field configurations in the calculation and expressing the final results in terms of measurable quantities. Two field configurations are discussed for the klystron input cavity, using finite magnetic confinement or no confinement at all. Formulating the problem in a language that is directly accessible to the powerful techniques found in Hamiltonian dynamics and canonical transformations may potentially carry an additional advantage in terms of analytical computational gains, under suitable conditions

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

A Novel Honeycomb-DD Multi Coil Design for Wireless Power Transfer Systems

Wireless power transfer (WPT) technology has received significant attention recently as an alternative charging method for batteries in a wide range of power levels. In the literature, many types of coil structures have been well-studied. Honeycomb coil arrays, which have been used mostly for low-power applications, have not been well-studied for high-power-level applications. In this paper, a novel honeycomb-DD coil design is proposed for high-power wireless battery charging systems. The proposed coil design with step by step design process is given and Finite Element Analysis (FEA) was performed to observe the full performance characteristics of the system for a 100 kW system. In addition, the misalignment tolerance of the proposed system was observed by shifting the secondary side charging pad at different misalignment positions, and the electromagnetic compatibility to the standards was investigated. The core and strand losses were obtained. The results show that the honeycomb coil array provides high coupling coefficient and better misalignment tolerance, making it a potential coil topology for WPT applications.

Aydin, Emrullah↗