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

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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Multigrid properties of upwind-biased data reconstructions

The multigrid properties of two data reconstruction methods used for achieving second-order spatial accuracy when solving the two-dimensional Euler equations are examined. The data reconstruction methods are used with an implicit upwind algorithm which uses linearized backward-Euler time-differencing. The solution of the resulting linear system is performed by an iterative procedure. In the present study only regular quadrilateral grids are considered, so a red-black Gauss-Seidel iteration is used. Although the Jacobian is approximated by first-order upwind extrapolation, two alternative data reconstruction techniques for the flux integral that yield higher-order spatial accuracy at steady state are examined. The first method, probably most popular for structured quadrilateral grids, is based on estimating the cell gradients using one-dimensional reconstruction along curvilinear coordinates. The second method is based on Green's theorem. Analysis and numerical results for the two dimensional Euler equations show that data reconstruction based on Green's theorem has superior multigrid properties as compared to the one-dimensional data reconstruction method.

Warren, Gary P.↗
NASA NTRS2006

Dynamic Theory of Relativistic Electrons Stochastic Heating by Whistler Mode Waves with Application to the Earth Magnetosphere

In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion by group symmetries of the problem were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. It is proved that the upper boundary of particle stochastic heating is conditioned by intrinsic property of the particle chaotic motion. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.

Khazanov, G. V.↗
NASA NTRS2007

Dynamic Theory of Relativistic Electrons Stochastic Heating by Whistler Mode Waves with Application to the Earth Magnetosphere

In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. Calculating the stochastic diffusion of electrons due to a spectrum of whistler modes is presented. The parametric dependence of the diffusion coefficients on the plasma particle density, magnitude of wave field, and the strength of magnetic field is studies. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.

Khazanov, G. V.↗
DOE OSTI2021

An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems

In this paper we consider 2D nonlocal diffusion models with a finite nonlocal horizon parameter δ characterizing the range of nonlocal interactions, and consider the treatment of Neumann-like boundary conditions that have proven challenging for discretizations of nonlocal models. We propose a new generalization of classical local Neumann conditions by converting the local flux to a correction term in the nonlocal model, which provides an estimate for the nonlocal interactions of each point with points outside the domain. While existing 2D nonlocal flux boundary conditions have been shown to exhibit at most first order convergence to the local counter part as δ → 0, the proposed Neumann-type boundary formulation recovers the local case as O(δ 2 ) in the L∞(Ω) norm, which is optimal considering the O(δ 2 ) convergence of the nonlocal equation to its local limit away from the boundary. We analyze the application of this new boundary treatment to the nonlocal diffusion problem, and present conditions under which the solution of the nonlocal boundary value problem converges to the solution of the corresponding local Neumann problem as the horizon is reduced. To demonstrate the applicability of this nonlocal flux boundary condition to more complicated scenarios, we extend the approach to less regular domains, numerically verifying that we preserve second-order convergence for non-convex domains with corners. Finally, based on the new formulation for nonlocal boundary condition, we develop an asymptotically compatible meshfree discretization, obtaining a solution to the nonlocal diffusion equation with mixed boundary conditions that converges with O(δ 2 ) convergence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Structure-preserving neural networks for the regularized entropy-based closure of a linear, kinetic, radiative transport equation

The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural network-based approximation to the entropy-based closure method to accurately compute the solution of the multi-dimensional moment system with a low memory footprint and competitive computational time. We extend methods developed for the standard entropy-based closure to the regularized entropy-based closures. The main idea is to interpret structure-preserving neural network approximations of the regularized entropy-based closure as a two-stage approximation to the original entropy-based closure. We conduct a numerical analysis of this approximation and investigate optimal parameter choices. Our numerical experiments demonstrate that the method has a much lower memory footprint than traditional methods with competitive computation times and simulation accuracy. The code and all trained networks are provided on GitHub.

entropy closure↗
NASA NTRS1991

Sinc-Galerkin estimation of diffusivity in parabolic problems

A fully Sinc-Galerkin method for the numerical recovery of spatially varying diffusion coefficients in linear partial differential equations is presented. Because the parameter recovery problems are inherently ill-posed, an output error criterion in conjunction with Tikhonov regularization is used to formulate them as infinite-dimensional minimization problems. The forward problems are discretized with a sinc basis in both the spatial and temporal domains thus yielding an approximate solution which displays an exponential convergence rate and is valid on the infinite time interval. The minimization problems are then solved via a quasi-Newton/trust region algorithm. The L-curve technique for determining an approximate value of the regularization parameter is briefly discussed, and numerical examples are given which show the applicability of the method both for problems with noise-free data as well as for those whose data contains white noise.

Smith, Ralph C.↗
DOE OSTI2021

Efficient quadrature rules for finite element discretizations of nonlocal equations

Here, in this paper, we design efficient quadrature rules for finite element (FE) discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the prohibitive computational cost and the nontrivial implementation of discretization schemes, especially in three-dimensional settings. In this work, we circumvent both challenges by introducing a parametrized mollifying function that improves the regularity of the integrand, utilizing an adaptive integration technique, and exploiting parallelization. We first show that the “mollified” solution converges to the exact one as the mollifying parameter vanishes, then we illustrate the consistency and accuracy of the proposed method on several two- and three-dimensional test cases. Furthermore, we demonstrate the good scaling properties of the parallel implementation of the adaptive algorithm and we compare the proposed method with recently developed techniques for efficient FE assembly.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1987

Self-pulsing and bichromatic emission in homogeneously broadened bidirectional ring lasers

The effects of saturation-induced Bragg gratings on the mode structure and dynamics of bidirectional homogeneously broadened ring lasers are studied. The grating is viewed as a distributed feedback medium in a ring cavity and modes appropriate to such a structure are used. A Fourier decomposed rate equation model is developed to study the behavior of these modes above threshold. The difference in the properties of these solutions from the modes of an unfilled ring cavity lead to the possibility of bichromatic emission and both regular undamped and irregular damped self-pulsing.

Rabinovich, W. S.↗
NASA NTRS2001

A New Analytical Approach to Predict Spacing Selection in Lamellar and Rod Eutectic Systems

In this paper, we reexamine the Jackson and Hunt (JH) theory and relax the assumption of isothermal solid/liquid interface(SLI) used in their treatment. A modification of the term B. in the expression of the solute concentration profile is also proposed. Based on the predictions of this modified theory the traditional definitions of regular and irregular eutectics are discussed. For regular eutectics the new model identifies a range of spacing within the limits defined by the minimum undercooling of the alpha and beta phase. For the irregular Al-Si eutectic system in particular we identified two different spacing selection mechanisnis: a) for a particular growth rate, a nearly isothermal interface can be achieved at a unique minimum spacing lambda(sub I); b) the average spacing in the microstructure (lambda(sub av) > lambda(sub I)) is essentially dictated by the undercooling of the faceted phase. Based on the modified theoretical model a semi-empirical expression has been developed to account for the influence of the temperature gradient. The theoretical calculations have been found to be in good agreement with the published experimental measurements.

Catalina, Adrian V.↗
DOE OSTI2021

Revisiting matrix-based inversion of scanning mobility particle sizer (SMPS) and humidified tandem differential mobility analyzer (HTDMA) data

Abstract. Tikhonov regularization is a tool for reducing noise amplification during data inversion. This work introduces RegularizationTools.jl, a general-purpose software package for applying Tikhonov regularization to data. The package implements well-established numerical algorithms and is suitable for systems of up to ∼ 1000 equations. Included is an abstraction to systematically categorize specific inversion configurations and their associated hyperparameters. A generic interface translates arbitrary linear forward models defined by a computer function into the corresponding design matrix. This obviates the need to explicitly write out and discretize the Fredholm integral equation, thus facilitating fast prototyping of new regularization schemes associated with measurement techniques. Example applications include the inversion involving data from scanning mobility particle sizers (SMPSs) and humidified tandem differential mobility analyzers (HTDMAs). Inversion of SMPS size distributions reported in this work builds upon the freely available software DifferentialMobilityAnalyzers.jl. The speed of inversion is improved by a factor of ∼ 200, now requiring between 2 and 5 ms per SMPS scan when using 120 size bins. Previously reported occasional failure to converge to a valid solution is reduced by switching from the L-curve method to generalized cross-validation as the metric to search for the optimal regularization parameter. Higher-order inversions resulting in smooth, denoised reconstructions of size distributions are now included in DifferentialMobilityAnalyzers.jl. This work also demonstrates that an SMPS-style matrix-based inversion can be applied to find the growth factor frequency distribution from raw HTDMA data while also accounting for multiply charged particles. The outcome of the aerosol-related inversion methods is showcased by inverting multi-week SMPS and HTDMA datasets from ground-based observations, including SMPS data obtained at Bodega Marine Laboratory during the CalWater 2/ACAPEX campaign and co-located SMPS and HTDMA data collected at the US Department of Energy observatory located at the Southern Great Plains site in Oklahoma, USA. Results show that the proposed approaches are suitable for unsupervised, nonparametric inversion of large-scale datasets as well as inversion in real time during data acquisition on low-cost reduced-instruction-set architectures used in single-board computers. The included software implementation of Tikhonov regularization is freely available, general, and domain-independent and thus can be applied to many other inverse problems arising in atmospheric measurement techniques and beyond.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1991

A shooting approach to suboptimal control

The shooting method is used to solve the suboptimal control problem where the control history is assumed to be piecewise linear. Suboptimal solutions can be obtained without difficulty and can lead to accurate approximate controls and good starting multipliers for the regular shooting method by increasing the number of nodes. Optimal planar launch trajectories are presented for the advanced launch system.

Hull, David G.↗
DOE OSTI2025

A framework for discrete optimization of stellarator coils

Designing magnets for three-dimensional plasma confinement is a key task for advancing the stellarator as a fusion reactor concept. Stellarator magnets must produce an accurate field while leaving adequate room for other components and being reasonably simple to construct and assemble. In this paper, a framework for coil design and optimization is introduced that enables the attainment of sparse magnet solutions with arbitrary restrictions on where coils may be located. The solution space is formulated as a 'wireframe' consisting of a mesh of interconnected wire segments enclosing the plasma. Two methods are developed for optimizing the current distribution on a wireframe: Regularized Constrained Least Squares, which uses a linear least-squares approach to optimize the currents in each segment, and Greedy Stellarator Coil Optimization, a fully discrete procedure in which loops of current are added to the mesh one by one to achieve the desired magnetic field on the plasma boundary. Examples are presented of solutions obtainable with each method, some of which achieve high field accuracy while obeying spatial constraints that permit easy assembly.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Dirty Word Scanner

SAND2025-09142O Dirty Word Scanner helps prevent the accidental inclusion of sensitive terms by scaning files in repositories to catch "dirty words" before they are committed. While there are existing solutions focused on passwords and API keys, this tool offers additional features tailored to specific security needs. It will function as a standalone tool, incorporating advanced capabilities from similar tools to provide a comprehensive solution. This tool can unpack HDF5 files and examine their contents. It can display image, audio, and visual files to the user and request a manual determination of whether they are safe. It can also detect arbitrary binary files and ask the user to verify that they're safe. The tool enables sophisticated whitelisting of strings and regular expressions for cases where a term is sensitive in certain contexts but not in others. 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.

Gates, Jason [Sandia National Lab. (SNL-CA), Liver↗
NASA NTRS1983

Hybrid perturbation/Bubnov-Galerkin technique for nonlinear thermal analysis

A two step hybrid analysis technique to predict the nonlinear steady state temperature distribution in structures and solids is presented. The technique is based on the regular perturbation expansion and the classical Bubnov-Galerkin approximation. The functions are obtained by using the regular perturbation method. These functions are selected as coordinate functions and the classical Bubnov-Galerkin technique is used to compute their amplitudes. The potential of the proposed hybrid technique for the solution of nonlinear thermal problems is discussed. The effectiveness of this technique is demonstrated by the effects of conduction, convection, and radiation modes of heat transfer. It is indicated that the hybrid technique overcomes the two major drawbacks of the classical techniques: (1) the requirement of using a small parameter in the regular perturbation method; and (2) the arbitrariness in the choice of the coordinate functions in the Bubnov-Galerkin technique. The proposed technique extends the range of applicability of the regular perturbation method and enhances the effectiveness of the Bubnov-Galerkin technique.

Noor, A. K.↗
NASA NTRS1982

ORACLS - A linear-quadratic-Gaussian computer-aided design package

ORACLS, an acronym denoting Optimal Regular Algorithms for the Control of Linear Systems, is a collection of FORTRAN coded subroutines dedicated to the formulation and solution of the Linear-Quadratic-Gaussian (LQG) design problem modeled in both continuous and discrete form. The ORACLS system is under continuous development at the NASA Langley Research Center, Hampton, Virginia, and is widely used by universities and industry within the U.S.A. The current (operational) ORACLS version as well as new software under development is described.

Armstrong, E. S.↗
NASA NTRS1986

Hopf bifurcation with dihedral group symmetry - Coupled nonlinear oscillators

The theory of Hopf bifurcation with symmetry developed by Golubitsky and Stewart (1985) is applied to systems of ODEs having the symmetries of a regular polygon, that is, whose symmetry group is dihedral. The existence and stability of symmetry-breaking branches of periodic solutions are considered. In particular, these results are applied to a general system of n nonlinear oscillators coupled symmetrically in a ring, and the generic oscillation patterns are described. It is found that the symmetry can force some oscillators to have twice the frequency of others. The case of four oscillators has exceptional features.

Golubitsky, Martin↗
NASA NTRS2000

Magnetic Field Suppression of Flow in Semiconductor Melt

One of the most promising approaches for the reduction of convection during the crystal growth of conductive melts (semiconductor crystals) is the application of magnetic fields. Current technology allows the experimentation with very intense static fields (up to 80 KGauss) for which nearly convection free results are expected from simple scaling analysis in stabilized systems (vertical Bridgman method with axial magnetic field). However, controversial experimental results were obtained. The computational methods are, therefore, a fundamental tool in the understanding of the phenomena accounting during the solidification of semiconductor materials. Moreover, effects like the bending of the isomagnetic lines, different aspect ratios and misalignments between the direction of the gravity and magnetic field vectors can not be analyzed with analytical methods. The earliest numerical results showed controversial conclusions and are not able to explain the experimental results. Although the generated flows are extremely low, the computational task is a complicated because of the thin boundary layers. That is one of the reasons for the discrepancy in the results that numerical studies reported. Modeling of these magnetically damped crystal growth experiments requires advanced numerical methods. We used, for comparison, three different approaches to obtain the solution of the problem of thermal convection flows: (1) Spectral method in spectral superelement implementation, (2) Finite element method with regularization for boundary layers, (3) Multiquadric method, a novel method with global radial basis functions, that is proven to have exponential convergence. The results obtained by these three methods are presented for a wide region of Rayleigh and Hartman numbers. Comparison and discussion of accuracy, efficiency, reliability and agreement with experimental results will be presented as well.

Fedoseyev, A. I.↗
NASA NTRS2010

Separation of Lift-Generated Vortex Wakes Into Two Diverging Parts

As part of an ongoing study of the spreading rate of lift-generated vortex wakes, the present investigation considers possible reasons as to why segments of lift-generated wakes sometimes depart from the main part of the wake to move rapidly in either an upward or downward direction. It is assumed that deficiencies or enhancements of the lift carry over across the fuselage-shrouded wing are the driving mechanism for departures of wake-segments. The computations presented first indicate that upwardly departing wake segments that were observed and photographed could have been produced by a deficiency in lift carryover across the fuselage-shrouded part of the wing. Computations made of idealized vortex wakes indicate that upward departure of a wake segment requires a centerline reduction in the span loading of 70% or more, whether the engines are at idle or robust thrust. Similarly, it was found that downward departure of wake segments is produced when the lift over the center part of the wing is enhanced. However, it was also found that downward departures do not occur without the presence of robust engine-exhaust streams (i.e., engines must NOT be at idle). In those cases, downward departures of a wake segment occurs when the centerline value of the loading is enhanced by any amount between about 10% to 100%. Observations of condensation trails indicate that downward departure of wake segments is rare. Upward departures of wake segments appears to be more common but still rare. A study to determine the part of the aircraft that causes wake departures has not been carried out. However, even though departures of wake segments rarely occur, some aircraft do regularly shed these wake structures. If aircraft safety is to be assured to a high degree of reliability, and a solution for eliminating them is not implemented, existing guidelines for the avoidance of vortex wakes [1,3] may need to be broadened to include possible increases in wake sizes caused by vertical departures of wake segments. Further study may indicate that it is not possible to modify existing aircraft enough to prevent wake departures. Wake-avoidance guidelines must then be adjusted to provide the desired degree of safety. It appears that steps to avoid upwardly moving wake segments have already been incorporated into the avoidance procedures used for aircraft on approach to runways at the Frankfurt Airport [6,7]. The uncertainty in the prospects for compromises in flight safety caused by rapidly upwardly or downwardly moving wake segments suggest that it be specified that aircraft do not fly above or below each other during operations in the airport vicinity where aircraft are likely to be closely spaced [20].

Rossow, Vernon J.↗