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Results for “generalized finite differences”

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 883 records · Page 49
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

Generation of boundary and boundary-layer fitting grids

The details of extended physical processes, such as the gas dynamic flow over an airfoil, the reactive flow through a combustor, or the electric field in a multi-contact transistor, are understood by solving the differential equations of a mathematical model of the process. The accuracy of finite difference methods for the numerical solution of the equations is increased if the underlying mesh fits the region boundaries and is closely spaced in regions where the solution is rapidly varying. Automatic methods for producing a satisfactorily adjusted mesh were developed for one dimensional problems. In one simple, effective scheme of this kind the unknown function and the distribution of mesh modes are found simultaneously, the nodes being placed so that they correspond to points uniformly spaced on the solution curve. In a two dimensional generalization, the nodes correspond to points equally spaced on the solution surface in two directions that are as nearly orthogonal as possible. Examples of such meshes are shown.

Ablow, C. M.↗
NASA NTRS1981

The response of a linear baroclinic equatorial ocean to periodic forcing

An investigation is conducted regarding the periodic response of the linear inviscid shallow water equations in a meridionally unbounded basin to zonal forcings at a single low frequency omega. A general solution in the long wave approximation and on an equatorial beta-plane is obtained by summing the Kelvin mode and the finite sum of Rossby modes whose turning points lie equatorward of the turning latitude at frequency omega. The results of the investigation suggest that even if the low frequency forcing has a simple structure, considerable spatial inhomogeneity in the deep ocean response would have to be expected. On the basis of linear inviscid theory, some conclusions are drawn about the causes of the differences between equatorial thermocline response in the Atlantic and Pacific.

Cane, M. A.↗
NASA NTRS1988

Consistent boundary conditions for Reduced Navier-Stokes (RNS) scheme applied to 3-dimensional internal viscous flows

A consistent and efficient set of boundary conditions is developed for the multi-sweep space-marching pressure-elliptic Reduced Navier-Stokes (RNS) scheme as applied for 3-D internal viscous flow problems. No-slip boundary conditions are directly imposed on the solid walls. There is no iteration procedure required in the cross plane to ensure mass conservation across each marching plane. The finite difference equations forming the coefficient matrix are ordered such that the surface normal velocity is specified on all the solid walls; unlike external flows, a pressure boundary condition in the cross plane is not required. Since continuity is directly satisfied at all points in the flow domain, the first order momentum equations can be solved directly for the pressure without the need for a Poisson pressure correction equation. The procedure developed herein can also be applied with periodic boundary conditions. The analysis is given for general compressible flows. Incompressible flow solutions are obtained, for straight and curved ducts of square cross section, to validate the procedure. These solutions are used to demonstrate the applicability of the RNS scheme, with the improved boundary conditions for internal flows with strong interaction, as would be encountered in ducts and turbomachinery geometries.

Reddy, D. R.↗
DOE OSTI2016

Coupled thermomechanical behavior of graphene using the spring-based finite element approach

The prediction of the thermomechanical behavior of graphene using a new coupled thermomechanical spring-based finite element approach is the aim of this work. Graphene sheets are modeled in nanoscale according to their atomistic structure. Based on molecular theory, the potential energy is defined as a function of temperature, describing the interatomic interactions in different temperature environments. The force field is approached by suitable straight spring finite elements. Springs simulate the interatomic interactions and interconnect nodes located at the atomic positions. Their stiffness matrix is expressed as a function of temperature. By using appropriate boundary conditions, various different graphene configurations are analyzed and their thermo-mechanical response is approached using conventional finite element procedures. A complete parametric study with respect to the geometric characteristics of graphene is performed, and the temperature dependency of the elastic material properties is finally predicted. Comparisons with available published works found in the literature demonstrate the accuracy of the proposed method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

High Brightness Room Temperature III-Nitride Based Single Photon Source

Single photon sources (SPS) are quantum light sources where photons are emitted one at a time instead of randomly (e.g. lasers) or in a bunch (e.g. thermal) that can significantly impact quantum information science (computing and secure communications) and quantum metrology. Some highly desirable features of SPS are low second order correlation (g 2 ),controllable emission, electrically injected room temperature operation with high photon rate, high extraction efficiency and controllable directionality. Approaches taken thus far using different material systems have only addressed a subset of these features. III-nitride based approach offers a clear pathway to deterministic, room temperature (R.T.), electrically injected practical SPS as one can potentially also leverage the knowledge and technology from the light emitting diode (LED) world. Here we will describe a hybrid approach wherein a TiO2 based photonic crystal (PC) cavity is fabricated around an InGaN quantum dot (QD) embedded nanoscale post deterministically placed inside a photonic crystal cavity. This project takes the initial steps necessary to achieve a practical, compact SPS. We have used finite difference time domain simulations to optimize the cavity design to achieve high quality factor, mode overlap with QD and high extraction. We have fabricated InGaN quantum dots using a top-down approach involving dry etch and photoelectrochemical etch followed by electron beam lithography based nanofabrication of photonic crystal cavities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Microscopic origin of temperature-dependent magnetism in spin-orbit-coupled transition metal compounds

A few 4 d and 5 d transition metal compounds with various electron fillings were recently found to exhibit magnetic susceptibilities χ and magnetic moments that deviate from the well-established Kotani model. This model has been considered for decades to be the canonical expression for descriing the temperature dependence of magnetism in systems with nonnegligible spin-orbit coupling effects. In this paper, we uncover the origin of such discrepancies and determine the applicability and limitations of the Kotani model by calculating the temperature dependence of the magnetic moments of a series of 4 d (Ru-based) and 5 d (W-based) systems at different electron fillings. For this purpose, we perform exact diagonalization of -derived relativistic multiorbital Hubbard models on finite clusters and compute their magnetic susceptibilities. Comparison with experimentally measured magnetic properties indicates that contributions such as a temperature-independent χ 0 background, crystal field effects, Coulomb and Hund's couplings, and intersite interactions—not included in the Kotani model—are especially crucial for correctly describing the temperature dependence of χ and magnetic moments at various electron fillings in these systems. Based on our results, we propose a generalized approach beyond the Kotani model to accurately describe their magnetism. Published by the American Physical Society 2025

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1998

Exact Solution to Stationary Onset of Convection Due to Surface Tension Variation in a Multicomponent Fluid Layer With Interfacial Deformation

Stationary onset of convection due to surface tension variation in an unbounded multicomponent fluid layer is considered. Surface deformation is included and general flux boundary conditions are imposed on the stratifying agencies (temperature/composition) disturbance equations. Exact solutions are obtained to the general N-component problem for both finite and infinitesimal wavenumbers. Long wavelength instability may coexist with a finite wavelength instability for certain sets of parameter values, often referred to as frontier points. For an impermeable/insulated upper boundary and a permeable/conductive lower boundary, frontier boundaries are computed in the space of Bond number, Bo, versus Crispation number, Cr, over the range 5 x 10(exp -7) less than or equal to Bo less than or equal to 1. The loci of frontier points in (Bo, Cr) space for different values of N, diffusivity ratios, and, Marangoni numbers, collapsed to a single curve in (Bo, D(dimensional variable)Cr) space, where D(dimensional variable) is a Marangoni number weighted diffusivity ratio.

Skarda, J. Raymond Lee↗
DOE OSTI2020

An Initial Assessment of the Design Margins of Different ASME Section III, Division 5 Design Rules

This report develops a method for assessing the design margin of the ASME Section III, Division 5 Class A design rules, focusing on a definition of margin as the ratio between the actual, expected component life and the ASME design life. Full inelastic finite element simulations with a complete damage model capturing the available creep, creep-fatigue, fatigue, and tension test failure data produce the expected component lives, which can then be compared to corresponding ASME design calculations. The focus of this particular work is on Alloy 617 and the ASME creep-fatigue design rules, but the approach is general and could be applied to other design limits and to other materials. A margin assessment of a representative Alloy 617 component shows the ASME creep-fatigue design rules applied to this component have a margin of 10 on design life. The report describes several challenges in completing a more comprehensive margin assessment of the ASME rules, in particular challenges in developing probabilistic assessment methods for high temperature structural components. The report details these challenge and discusses the immediate possibilities of the deterministic margin assessment method developed here.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

Modeling of Stick-Slip Behavior in Sheared Granular Fault Gouge Using the Combined Finite-Discrete Element Method

Sheared granular layers undergoing stick-slip behavior are broadly employed to study the physics and dynamics of earthquakes. In this paper, a two-dimensional implementation of the combined finite-discrete element method (FDEM), which merges the finite element method (FEM) and the discrete element method (DEM), is used to explicitly simulate a sheared granular fault system including both gouge and plate, and to investigate the influence of different normal loads on seismic moment, macroscopic friction coefficient, kinetic energy, gouge layer thickness, and recurrence time between slips. In the FDEM model, the deformation of plates and particles is simulated using the FEM formulation while particle-particle and particle-plate interactions are modeled using DEM-derived techniques. The simulated seismic moment distributions are generally consistent with those obtained from the laboratory experiments. In addition, the simulation results demonstrate that with increasing normal load, (i) the kinetic energy of the granular fault system increases; (ii) the gouge layer thickness shows a decreasing trend; and (iii) the macroscopic friction coefficient does not experience much change. Analyses of the slip events reveal that, as the normal load increases, more slip events with large kinetic energy release and longer recurrence time occur, and the magnitude of gouge layer thickness decrease also tends to be larger; while the macroscopic friction coefficient drop decreases. Finally, the simulations not only reveal the influence of normal loads on the dynamics of sheared granular fault gouge, but also demonstrate the capabilities of FDEM for studying stick-slip dynamic behavior of granular fault systems.

58 GEOSCIENCES↗
DOE OSTI2016

First-principles calculated decomposition pathways for LiBH 4 nanoclusters

Here, we analyze thermodynamic stability and decomposition pathways of LiBH 4 nanoclusters using grand-canonical free-energy minimization based on total energies and vibrational frequencies obtained from density-functional theory (DFT) calculations. We consider (LiBH 4 ) n nanoclusters with n = 2 to 12 as reactants, while the possible products include (Li) n , (B) n , (LiB) n , (LiH) n , and Li 2 B n H n ; off-stoichiometric LinBnHm (m ≤ 4n) clusters were considered for n = 2, 3, and 6. Cluster ground-state configurations have been predicted using prototype electrostatic ground-state (PEGS) and genetic algorithm (GA) based structural optimizations. Free-energy calculations show hydrogen release pathways markedly differ from those in bulk LiBH 4 . While experiments have found that the bulk material decomposes into LiH and B, with Li 2 B 12 H 12 as a kinetically inhibited intermediate phase, (LiBH 4 ) n nanoclusters with n ≤ 12 are predicted to decompose into mixed Li n B n clusters via a series of intermediate clusters of Li n B n H m (m ≤ 4n). The calculated pressure-composition isotherms and temperature-pressure isobars exhibit sloping plateaus due to finite size effects on reaction thermodynamics. Generally, decomposition temperatures of free-standing clusters are found to increase with decreasing cluster size due to thermodynamic destabilization of reaction products.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Real-space solution to the electronic structure problem for nearly a million electrons

We report a Kohn–Sham density functional theory calculation of a system with more than 200 000 atoms and 800 000 electrons using a real-space high-order finite-difference method to investigate the electronic structure of large spherical silicon nanoclusters. Our system of choice was a 20 nm large spherical nanocluster with 202 617 silicon atoms and 13 836 hydrogen atoms used to passivate the dangling surface bonds. To speed up the convergence of the eigenspace, we utilized Chebyshev-filtered subspace iteration, and for sparse matrix–vector multiplications, we used blockwise Hilbert space-filling curves, implemented in the PARSEC code. For this calculation, we also replaced our orthonormalization + Rayleigh–Ritz step with a generalized eigenvalue problem step. We utilized all of the 8192 nodes (458 752 processors) on the Frontera machine at the Texas Advanced Computing Center. We achieved two Chebyshev-filtered subspace iterations, yielding a good approximation of the electronic density of states. Our work pushes the limits on the capabilities of the current electronic structure solvers to nearly 106 electrons and demonstrates the potential of the real-space approach to efficiently parallelize large calculations on modern high-performance computing platforms.

Chemistry↗
DOE OSTI2019

A Multilevel in Space and Energy Solver for 3-D Multigroup Diffusion and Coarse-Mesh Finite Difference Eigenvalue Problems

The Multilevel in Space and Energy Diffusion (MSED) method accelerates the iterative convergence of multigroup diffusion eigenvalue problems by performing work on lower-order equations with only one group and/or coarser spatial grids. It consists of two primary components: (1) a grey (one-group) diffusion eigenvalue problem that is solved via Wielandt-shifted power iteration (PI) and (2) a multigrid-in-space linear solver. In previous work, the efficiency of MSED was verified using Fourier analysis and numerical results from a one-dimensional multigroup diffusion code. Since that work, MSED has been implemented as a solver for the coarse-mesh finite difference (CMFD) system in the three-dimensional Michigan Parallel Characteristics Transport (MPACT) code. In this paper, the results from the implementation of MSED in MPACT are introduced, and the changes needed to make MSED more suitable for MPACT are described. For problems without feedback, the conclusions in this paper show that MSED can reduce the CMFD run time by an order of magnitude and the overall run time by a factor of 2 to 3 compared to the default CMFD solver in MPACT [PI with the generalized minimal residual (GMRES) method]. For problems with feedback, the convergence of the outer Picard iteration scheme is worsened by the well-converged CMFD solutions produced by the standard MSED method. To overcome this unintuitive deficiency, MSED may be run with looser convergence criteria (a modified version of the MSED method called MSED-L) to circumvent the issue until the multiphysics iteration in MPACT is improved. Results show that MSED-L can reduce the CMFD run time in MPACT by an order of magnitude, without negatively impacting the outer Picard iteration scheme.

3-D↗
DOE OSTI2018

Quasilocal charges and the generalized Gibbs ensemble in the Lieb-Liniger model

Here, we consider the construction of a generalized Gibbs ensemble composed of complete bases of conserved charges in the repulsive Lieb-Liniger model. We will show that it is possible to construct these bases with varying locality as well as demonstrating that such constructions are always possible provided one has in hand at least one complete basis set of charges. This procedure enables the construction of bases of charges that possess well-defined, finite expectation values given an arbitrary initial state. We demonstrate the use of these charges in the context of two different quantum quenches: a quench where the strength of the interactions in a one-dimensional gas is switched suddenly from zero to some finite value and the release of a one-dimensional cold atomic gas from a confining parabolic trap. While we focus on the Lieb-Liniger model in this paper, the principle of the construction of these charges applies to all integrable models, both in continuum and lattice form.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1972

Convection in the tanks of a rotating spacecraft

A general study of convection and mixing of a stratified fluid in a rotating container is described, with application to the special problem of fluid heating and convection in a spacecraft tank. The analysis was based on a set of approximate equations for the Navier-Stokes description of fluid convection with small density variations in a rotating system, including effects of body forces due to temperature stratification (caused by a heater) and arbitrary time-dependent rotation of the tank about a noncentral axis. An efficient numerical finite difference scheme and computational method are described for the convection of vorticity and energy in a two-dimensional tank. Special procedures were developed for analysis of the thermodynamic states resulting from the approximate flow equations derived for small density variations. Results of the numerical simulation are presented for studying the effectiveness of rotation maneuvers in mixing stratified oxygen in the tanks of an Apollo spacecraft. Significant effects of the rotation maneuvers are discussed, including the reduction of the potential for pressure collapse.

Source record↗
NASA NTRS1993

Positivity-preserving numerical schemes for multidimensional advection

This report describes the construction of an explicit, single time-step, conservative, finite-volume method for multidimensional advective flow, based on a uniformly third-order polynomial interpolation algorithm (UTOPIA). Particular attention is paid to the problem of flow-to-grid angle-dependent, anisotropic distortion typical of one-dimensional schemes used component-wise. The third-order multidimensional scheme automatically includes certain cross-difference terms that guarantee good isotropy (and stability). However, above first-order, polynomial-based advection schemes do not preserve positivity (the multidimensional analogue of monotonicity). For this reason, a multidimensional generalization of the first author's universal flux-limiter is sought. This is a very challenging problem. A simple flux-limiter can be found; but this introduces strong anisotropic distortion. A more sophisticated technique, limiting part of the flux and then restoring the isotropy-maintaining cross-terms afterwards, gives more satisfactory results. Test cases are confined to two dimensions; three-dimensional extensions are briefly discussed.

Leonard, B. P.↗
NASA NTRS1996

Artificial Boundary Conditions for Computation of Oscillating External Flows

In this paper, we propose a new technique for the numerical treatment of external flow problems with oscillatory behavior of the solution in time. Specifically, we consider the case of unbounded compressible viscous plane flow past a finite body (airfoil). Oscillations of the flow in time may be caused by the time-periodic injection of fluid into the boundary layer, which in accordance with experimental data, may essentially increase the performance of the airfoil. To conduct the actual computations, we have to somehow restrict the original unbounded domain, that is, to introduce an artificial (external) boundary and to further consider only a finite computational domain. Consequently, we will need to formulate some artificial boundary conditions (ABC's) at the introduced external boundary. The ABC's we are aiming to obtain must meet a fundamental requirement. One should be able to uniquely complement the solution calculated inside the finite computational domain to its infinite exterior so that the original problem is solved within the desired accuracy. Our construction of such ABC's for oscillating flows is based on an essential assumption: the Navier-Stokes equations can be linearized in the far field against the free-stream back- ground. To actually compute the ABC's, we represent the far-field solution as a Fourier series in time and then apply the Difference Potentials Method (DPM) of V. S. Ryaben'kii. This paper contains a general theoretical description of the algorithm for setting the DPM-based ABC's for time-periodic external flows. Based on our experience in implementing analogous ABC's for steady-state problems (a simpler case), we expect that these boundary conditions will become an effective tool for constructing robust numerical methods to calculate oscillatory flows.

Tsynkov, S. V.↗
NASA NTRS2007

Revisiting and Extending Interface Penalties for Multi-Domain Summation-by-Parts Operators

General interface coupling conditions are presented for multi-domain collocation methods, which satisfy the summation-by-parts (SBP) spatial discretization convention. The combined interior/interface operators are proven to be L2 stable, pointwise stable, and conservative, while maintaining the underlying accuracy of the interior SBP operator. The new interface conditions resemble (and were motivated by) those used in the discontinuous Galerkin finite element community, and maintain many of the same properties. Extensive validation studies are presented using two classes of high-order SBP operators: 1) central finite difference, and 2) Legendre spectral collocation.

Carpenter, Mark H.↗
DOE OSTI2017

A practical approach to the sensitivity analysis for kinetic Monte Carlo simulation of heterogeneous catalysis

Lattice kinetic Monte Carlo simulations have become a vital tool for predictive quality atomistic understanding of complex surface chemical reaction kinetics over a wide range of reaction conditions. In order to expand their practical value in terms of giving guidelines for atomic level design of catalytic systems, it is very desirable to readily evaluate a sensitivity analysis for a given model. The result of such a sensitivity analysis quantitatively expresses the dependency of the turnover frequency, being the main output variable, on the rate constants entering the model. In the past the application of sensitivity analysis, such as Degree of Rate Control, has been hampered by its exuberant computational effort required to accurately sample numerical derivatives of a property that is obtained from a stochastic simulation method. Here in this study we present an efficient and robust three stage approach that is capable of reliably evaluating the sensitivity measures for stiff microkinetic models as we demonstrate using CO oxidation on RuO 2 (110) as a prototypical reaction. In a first step, we utilize the Fisher Information Matrix for filtering out elementary processes which only yield negligible sensitivity. Then we employ an estimator based on linear response theory for calculating the sensitivity measure for non-critical conditions which covers the majority of cases. Finally we adopt a method for sampling coupled finite differences for evaluating the sensitivity measure of lattice based models. This allows efficient evaluation even in critical regions near a second order phase transition that are hitherto difficult to control. The combined approach leads to significant computational savings over straightforward numerical derivatives and should aid in accelerating the nano scale design of heterogeneous catalysts.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗