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NASA NTRS1971

Integration methods where force is obtained from the smoothed gravitational field.

Discussion of the possibilities to study the dynamics of collisionless stellar systems by condensing the large number of stars that such systems may contain into a smaller number of superparticles and using numerical or computer models to perform computer experiments simulating Vlasov phenomena by following the simultaneous motion of a large number of superparticles. A computer model for disks of stars and a two-dimensional rod model are considered.

Hohl, F.↗

NASA NTRS1972

Integration methods where force is obtained from the smoothed gravitational field.

Discussion of the application of computer models to collisionless stellar systems. Two more recent computer models - i.e., the two-dimensional rod model, and the model for disks of stars - are described. It is shown that the dynamics of collisionless stellar systems can be studied by representing the system by large numbers of representative stars.

Hohl, F.↗

NASA NTRS2008

Spline-Based Smoothing of Airfoil Curvatures

Constrained fitting for airfoil curvature smoothing (CFACS) is a splinebased method of interpolating airfoil surface coordinates (and, concomitantly, airfoil thicknesses) between specified discrete design points so as to obtain smoothing of surface-curvature profiles in addition to basic smoothing of surfaces. CFACS was developed in recognition of the fact that the performance of a transonic airfoil is directly related to both the curvature profile and the smoothness of the airfoil surface. Older methods of interpolation of airfoil surfaces involve various compromises between smoothing of surfaces and exact fitting of surfaces to specified discrete design points. While some of the older methods take curvature profiles into account, they nevertheless sometimes yield unfavorable results, including curvature oscillations near end points and substantial deviations from desired leading-edge shapes. In CFACS as in most of the older methods, one seeks a compromise between smoothing and exact fitting. Unlike in the older methods, the airfoil surface is modified as little as possible from its original specified form and, instead, is smoothed in such a way that the curvature profile becomes a smooth fit of the curvature profile of the original airfoil specification. CFACS involves a combination of rigorous mathematical modeling and knowledge-based heuristics. Rigorous mathematical formulation provides assurance of removal of undesirable curvature oscillations with minimum modification of the airfoil geometry. Knowledge-based heuristics bridge the gap between theory and designers best practices. In CFACS, one of the measures of the deviation of an airfoil surface from smoothness is the sum of squares of the jumps in the third derivatives of a cubicspline interpolation of the airfoil data. This measure is incorporated into a formulation for minimizing an overall deviation- from-smoothness measure of the airfoil data within a specified fitting error tolerance. CFACS has been extensively tested on a number of supercritical airfoil data sets generated by inverse design and optimization computer programs. All of the smoothing results show that CFACS is able to generate unbiased smooth fits of curvature profiles, trading small modifications of geometry for increasing curvature smoothness by eliminating curvature oscillations and bumps (see figure).

Li, W.↗

DOE OSTI2022

Transfer Learning-Based Independent Component Analysis

Understanding the underlying component structure is crucial for multivariate signal analysis. Among all the techniques that try to learn the latent structure, independent component analysis (ICA) is one of the most important and popular methods, which aims to extract independent components from multivariate signals and enables further analysis. For example, in electroencephalogram (EEG) analysis, artifacts filtering and disease detection are conducted based on the independent components of the signals. One critical challenge in existing ICA approaches is that the component extraction accuracy may degrade when the available data of a unit are limited. To address this issue, this paper proposes a transfer learning-based ICA method by innovatively transferring component distribution from a source domain, so that accurate component extraction results can be achieved even when only limited data are available in the target domain. To the best of our knowledge, this is the first work that leverages transfer learning to improve ICA accuracy with limited available data. In particular, we first extract all the independent components from the source domain by maximizing the log-likelihood function with a Newton-like method on a smooth manifold. Then for the target domain, the component with the largest negentropy is extracted in each round. To effectively leverage the knowledge from the source domain and to prevent the negative transfer, we try to find a component in the source domain that matches the component we are extracting. The probability density function of the matched component will then be used to improve the component extraction accuracy if such matched component can be found; otherwise, no knowledge will be transferred. Finally, numerical simulations and a case study with electrocardiogram (ECG) data are conducted, showing the effectiveness of the proposed method in transferring knowledge and reducing negative transfer.

42 ENGINEERING↗

NASA NTRS1992

Simulating hypervelocity impact effects on structures using the smoothed particle hydrodynamics code MAGI

Analysis of interaction occurring between space debris and orbiting structures is of great interest to the planning and survivability of space assets. Computer simulation of the impact events using hydrodynamic codes can provide some understanding of the processes but the problems involved with this fundamental approach are formidable. First, any realistic simulation is necessarily three-dimensional, e.g., the impact and breakup of a satellite. Second, the thickness of important components such as satellite skins or bumper shields are small with respect to the dimension of the structure as a whole, presenting severe zoning problems for codes. Thirdly, the debris cloud produced by the primary impact will yield many secondary impacts which will contribute to the damage and possible breakup of the structure. The problem was approached by choosing a relatively new computational technique that has virtues peculiar to space impacts. The method is called Smoothed Particle Hydrodynamics.

Libersky, Larry↗

NASA NTRS1990

Newton modified barrier method in constrained optimization

In this paper, we develop and investigate the Newton method for solving constrained (non-smooth) optimization problems. This approach is based on the modified barrier functions (MBF) theory and on the global converging step-size version of the Newton method for smooth unconstrained optimization. Due to the excellent properties of the MBF near primal-dual solution, the Newton modified barrier method (NMBM) has a better rate of convergence, better complexity bound, and is much more stable in the final stage of the computational process than the methods which are based on the classical barrier functions (CBF).

Polyak, R.↗

NASA NTRS1993

Spectral solution of the viscous blunt-body problem

The viscous blunt-body problem is solved with a shock-fitted Chebyshev spectral method. No explicit artificial viscosity or filtering is needed to obtain smooth, converged solutions. The method is applied to two problems. First, results for the flow over a right circular cylinder in the Mach number range of 5.5-6.0 are compared with experimental data. Second, a solution for a Mach 25 flow over a hyperbolic cone is compared with a viscous shock-layer calculation.

Kopriva, David A.↗

NASA NTRS2014

Combined Uncertainty and A-Posteriori Error Bound Estimates for General CFD Calculations: Theory and Software Implementation

This workshop presentation discusses the design and implementation of numerical methods for the quantification of statistical uncertainty, including a-posteriori error bounds, for output quantities computed using CFD methods. Hydrodynamic realizations often contain numerical error arising from finite-dimensional approximation (e.g. numerical methods using grids, basis functions, particles) and statistical uncertainty arising from incomplete information and/or statistical characterization of model parameters and random fields. The first task at hand is to derive formal error bounds for statistics given realizations containing finite-dimensional numerical error [1]. The error in computed output statistics contains contributions from both realization error and the error resulting from the calculation of statistics integrals using a numerical method. A second task is to devise computable a-posteriori error bounds by numerically approximating all terms arising in the error bound estimates. For the same reason that CFD calculations including error bounds but omitting uncertainty modeling are only of limited value, CFD calculations including uncertainty modeling but omitting error bounds are only of limited value. To gain maximum value from CFD calculations, a general software package for uncertainty quantification with quantified error bounds has been developed at NASA. The package provides implementations for a suite of numerical methods used in uncertainty quantification: Dense tensorization basis methods [3] and a subscale recovery variant [1] for non-smooth data, Sparse tensorization methods[2] utilizing node-nested hierarchies, Sampling methods[4] for high-dimensional random variable spaces.

CFD↗

DOE OSTI2023

Insights into the failure mode of the Chelyabinsk meteor from high-fidelity simulation

In 2013, an asteroid with a diameter of approximate 20 m broke up in the atmosphere above the Russian city of Chelyabinsk producing what is known as an airburst event. The event was recorded on video from multiple angles and a 500-kg fragment was recovered from Lake Chebarkul shortly thereafter. These aspects, coupled with the asteroid’s large size, distinguish the Chelyabinsk event as unique. In this study, we use the smoothed particle hydrodynamics method to examine the breakup mode of a Chelyabinsk-sized monolithic asteroid and probe whether a monolithic structure is consistent with observations from the Chelyabinsk event. We model the object as a homogeneous sphere with properties consistent with Chelyabinsk meteorites. We use planar-2D simulations to test the sensitivity of results to variations in the material model and to qualitatively inspect the cause of crack nucleation and fragmentation. We then compare results from a 3D simulation to observations from the event. Our 3D simulation predicts a burst height within 3 km of the observed peak luminosity suggesting the responsible asteroid may have been monolithic.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Simulations of Tidal Disruption Events

Numerical simulations have historically played a major role in understanding the hydrodynamics of the tidal disruption process. Given the complexity of the geometry of the system, the challenges posed by the problem have indeed stimulated much work on the numerical side. Smoothed Particles Hydrodynamics methods, for example, have seen their very first applications in the context of tidal disruption and still play a major role to this day. Likewise, initial attempts at simulating the evolution of the disrupted star with the so-called affine method have been historically very useful. Here, we provide an overview of the numerical techniques used in the field and of their limitations, and summarize the work that has been done to simulate numerically the tidal disruption process.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Growth of ultra-flat ultra-thin alkali antimonide photocathode films

Ultra-flat, ultra-thin alkali antimonide photocathodes with high crystallinity can exhibit high quantum efficiency and low mean transverse energy of outgoing electrons, which are essential requirements for a variety of applications for photocathode materials. Here, we investigate the growth of Cs 3 Sb on graphene-coated 4H–SiC (Gr/4H–SiC), 3C–SiC, and Si 3 N 4 substrates. Sb is deposited using pulsed laser deposition, while Cs is deposited thermally and simultaneously. We demonstrate, employing x-ray analysis and quantum efficiency measurements, that this growth method yields atomically smooth Cs 3 Sb photocathodes with a high quantum efficiency (>10%), even in the ultra-thin limit (<30 nm). For the Si 3 N 4 substrate, film growth is shown to be polycrystalline, while films grown on Gr/4H–SiC show a high degree of ordering with signs of epitaxy.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Recent Hydrodynamic Modeling Enhancements in OpenFAST

To improve the hydrodynamic modeling capabilities of the offshore wind design and modeling tool OpenFAST, a restructuring of the HydroDyn hydrodynamics module was undertaken with several new features implemented. The generation of the wave field is now separated from HydroDyn into a new module called SeaState. Unlike previous versions of HydroDyn, which precomputed the wave kinematics at the undisplaced positions of the hydrodynamic nodes, the new SeaState module computes the complete time history of the wave field at the vertices of a user-defined wave grid. During the simulation, the wave kinematics at any point within the grid can be efficiently interpolated, allowing the strip-theory wave loads to be evaluated based on the wave kinematics at the displaced structure position. A phase correction was also implemented for the potential-flow wave-exciting loads to account for large structure displacements. Several wave-stretching methods were implemented for the strip-theory solution along with a wave-load redistribution method that ensures smooth variation of the nodal loads as the nodes of a discrete hydrodynamic mesh enter and exit the water. The load smoothing is included to avoid the excitation of unphysical high-frequency structural vibration during hydroelastic simulations. The MacCamy-Fuchs diffraction correction for the strip-theory solution and the capability to insert a constrained NewWave into extreme stochastic sea states with directional spreading were also added. The present article documents the formulations of the new improvements to HydroDyn with example applications and numerical results.

constrained wave↗

DOE OSTI2022

Anti-Icing Coatings using Ionomer Film Layer Structuring

This research effort examined the application of Nafion polymers in alcohol solvents as an anti-ice surface coating, as a mixture with hydrophilic polymers and freezing point depressant salt systems. Co-soluble systems of Nafion, polymer and salt were applied using dip coating methods to create smooth films for frost observation over a Peltier plate thermal system in ambient laboratory conditions. Cryo-DSC was applied to examine freezing events of the Nafion-surfactant mixtures, but the sensitivity of the measurement was insufficient to determine frost behavior. Collaborations with the Fog Chamber at Sandia-Albuquerque, and in environmental SAXS measurements with CINT-LANL were requested but were not able to be performed under the research duration. Since experimental characterization of these factors is difficult to achieve directly, computational modeling was used to guide the scientific basis for property improvement. Computational modeling was performed to improve understanding of the dynamic association between ionomer side groups and added molecules and deicing salts. The polyacrylic acid in water system was identified at the start of the project as a relevant system for exploring the effect of varying counterions on the properties of fully deprotonated polyacrylic acid (PAA) in the presence of water. Simulations were modeled with four different counterions, two monovalent counterions (K+ and Na+) and two divalent counterions (Ca2+ and Mg2+). The wt% of PAA in these systems was varied from ~10 to 80 wt% PAA for temperatures from 250K to 400K. In the second set of simulations, the interpenetration of water into a dry PAA film was studied for Na+ or Ca2+ counterions for temperatures between 300K and 400K. The result of this project is a sprayable Nafion film composite which resists ice nucleation at -20 °C for periods of greater than three hours. It is composed of Nafion polymer, hydrophilic polyethylene oxide polymer and CaCl2 anti-ice crosslinker. Durability and field performance properties remain to be determined.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1975

The use of local basis functions in unsteady aerodynamics

This paper reports a successful demonstration of using local basis functions to solve Kussner's integral equation for unsteady airloads. Pressure basis functions are defined over relatively small subsets of the aerodynamic surface and are zero elsewhere. This formulation combines the accuracy and smoothness of distribution methods with the simplicity and versatility of panel methods. Application is made to subsonic compressible flow about oscillating planar surfaces with controls. Numerical results are presented. Convergence with respect to panel size, extensions to more general classes of solutions, and areas needing additional investigation are discussed.

Fromme, J.↗

NASA NTRS1981

Accelerated finite-volume calculation of transonic potential flows

A fully conservative finite-volume algorithm is used to calculate transonic potential flows past isolated airfoils and through two-dimensional channels. The difference equations are solved by a multigrid technique which uses an alternating direction implicit method as a smoothing algorithm. The finite-volume formulation provides a framework within which to treat flows past complicated geometries, while the multigrid/alternating direction scheme provides rapid convergence of the solution to very small residuals.

Jameson, A.↗

NASA NTRS1982

The passage of a star by a massive black hole

The gridless, smoothed particle hydrodynamic method of Lucy (1977) and Gingold and Monaghan (1977, 1980, a, b, 1981) is used to solve the three-dimensional problem posed by the effects on a 1.0 solar mass star of a 10,000 solar mass black hole's passage, in an initially parabolic orbit with a variety of pericenter distances. It is found that the tidal forces induce rotation and radial and nonradial pulsations in the star, and that the loss of orbital energy to these internal motions leads to the star's capture by the black hole. While the outer layers of the star are disrupted at small pericenter distances, the entire star is destroyed at even smaller distances. These results are applicable to X-ray sources, active galactic nuclei, and quasars

Nolthenius, R. A.↗

NASA NTRS1983

Variational global analysis of satellite temperature soundings

A variational spherical harmonic analysis is developed for the production of global geopotential height and geostropic wind fields from the TIROS-N spacecraft's temperature sounding profiles. This scheme is based on Tykhonov's (1964) regularization method, and the smoothing parameter is determined by cross validation. The scheme is noted to be stable and computationally efficient, and it does not depend on a priori information. Its applications to three-dimensional temperature retrievals and to four-dimensional spectral analyses are illustrated.

Halem, M.↗

NASA NTRS1987

NASA/MSFC prediction techniques

The NASA/MSFC method of forecasting is more formal than NOAA's. The data is smoothed by the Lagrangian method and linear regression prediction techniques are used. The solar activity period is fixed at 11 years--the mean period of all previous cycles. Interestingly, the present prediction for the time of the next solar minimum is February or March of 1987, which, within the uncertainties of two methods, can be taken to be the same as the NOAA result.

Smith, Robert E.↗