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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

The Effect of Pulse Length and Ejector Radius on Unsteady Ejector Performance

The thrust augmentation of a set of ejectors driven by a shrouded Hartmann-Sprenger tube has been measured at four different frequencies. Each frequency corresponded to a different length to diameter ratio of the pulse of air leaving the driver shroud. Two of the frequencies had length to diameter ratios below the formation number, and two above. The formation number is the value of length to diameter ratio below which the pulse converts to a vortex ring only, and above which the pulse becomes a vortex ring plus a trailing jet. A three level, three parameter Box-Behnken statistical design of experiment scheme was performed at each frequency, measuring the thrust augmentation generated by the appropriate ejectors from the set. The three parameters were ejector length, radius, and inlet radius. The results showed that there is an optimum ejector radius and length at each frequency. Using a polynomial fit to the data, the results were interpolated to different ejector radii and pulse length to diameter ratios. This showed that a peak in thrust augmentation occurs when the pulse length to diameter ratio equals the formation number, and that the optimum ejector radius is 0.87 times the sum of the vortex ring radius and the core radius.

Wilson, Jack↗
DOE OSTI2025

Coupling Approaches with Non-matching Grids for Classical Linear Elasticity and Bond-based Peridynamic Models in 1D

Local-nonlocal coupling approaches provide a means to combine the computational efficiency of local models and the accuracy of nonlocal models. To facilitate the coupling of the two models, non-matching grids are often desirable as nonlocal grids usually require a finer resolution than local grids. In that case, it is often convenient to resort to interpolation operators so that models can exchange information in the overlap regions when nodes from the two grids do not coincide. This paper studies three existing coupling approaches, namely 1) a method that enforces matching displacements in an overlap region, 2) a variant that enforces a constraint on the stresses instead, and 3) a method that considers a variable horizon in the vicinity of the interfaces. Further, the effect of the interpolation order and of the grid ratio on the performance of the three coupling methods with non-matching grids is carefully studied on one-dimensional examples using polynomial manufactured solutions. The numerical results show that the degree of the interpolants should be chosen with care to avoid introducing additional modeling errors, or simply minimize these errors, in the coupling approach.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1981

An analysis of LANDSAT MSS scene-to-scene registration accuracy

Measurements were made for 12 registrations done by ERL for 8 registrations done by SRS. The results indicate that the ERL method is significantly more accurate in five of the eight comparison. The difference between the two methods are not significant in the other three cases. There are two possible reasons for the differences. First, the ERL model is a piecewise linear model and the EDITOR model is a cubic polynomial model. Second, the ERL program resamples using bilinear interpolation while the EDITOR software uses a nearest neighbor resampling. This study did not indicate how much of the difference is attributable to each factor. The average of all merged scene error values for ERL was 31.6 meters and the average for the eight common areas was 32.6 meters. The average of the eight merged scene error values for SRS was 40.1 meters.

Seyfarth, B. R.↗
NASA NTRS1990

Interpolation schemes in the control of systems with unknown dynamics

Time-delay control for systems with unknown dynamics involves estimations. In its present form, these estimations include not only the interpolation of a time-varying function but also its derivative between data points. Presently, the control law is reformulated, taking into account the computation delay. A window-shifting scheme is then devised to view n data points as they are sampled in order to perform the function estimation. At each new sampling time, the window shifts to include the new data point as well as the last n-1 points. Several interpolation methods are considered. These methods use data points from a sampled function to construct a polynomial estimate of the function. The control system performance was experimentally tested using a servosystem. The results show that a Newtonian interpolation provided best results when the computation time was 0.4 times the sampling period.

Youcef-Toumi, K.↗
DOE OSTI2022

Analytic error analysis of cross section interpolation methods in nodal diffusion codes - I : Theory

This paper discusses two cross section interpolation methods commonly found in popular nodal codes; the partial derivatives and multiple tables models. The motivation for choosing a model, and thus a case matrix structure, is a trade off between accuracy and computational cost. Due to decades of experience, there are default structures that are sufficient for current light water reactor analysis. However, this is not necessarily the case for advanced reactor designs. Therefore, it is advantageous to understand the sources of error in cross section interpolation models so that the quality of a case matrix may be improved. A mathematical framework for these models is presented in this work that provides a more rigorous connection between the nuclear engineering field's cross section interpolation methods and the broader mathematical field of function approximation. The two cross section models examined in this paper were found to utilize Lagrange interpolation and are a subset of Lagrange tensor products. Classical results of Lagrange polynomial error analysis were then applied to the partial derivative and multiple tables models to derive expressions for the total point-wise error. The analytical results classify the total error into two parts: the model form error and interpolation error. Finally, based on our observations, a better foundation for improving the quality of a case matrix is proposed. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1985

Minimal norm constrained interpolation

In computational fluid dynamics and in CAD/CAM, a physical boundary is usually known only discreetly and most often must be approximated. An acceptable approximation preserves the salient features of the data such as convexity and concavity. In this dissertation, a smooth interpolant which is locally concave where the data are concave and is locally convex where the data are convex is described. The interpolant is found by posing and solving a minimization problem whose solution is a piecewise cubic polynomial. The problem is solved indirectly by using the Peano Kernal theorem to recast it into an equivalent minimization problem having the second derivative of the interpolant as the solution. This approach leads to the solution of a nonlinear system of equations. It is shown that Newton's method is an exceptionally attractive and efficient method for solving the nonlinear system of equations. Examples of shape-preserving interpolants, as well as convergence results obtained by using Newton's method are also shown. A FORTRAN program to compute these interpolants is listed. The problem of computing the interpolant of minimal norm from a convex cone in a normal dual space is also discussed. An extension of de Boor's work on minimal norm unconstrained interpolation is presented.

Irvine, L. D.↗
DOE OSTI2021

Feasibility of DEIM for retrieving the initial field via dimensionality reduction

When parameter estimation is solved in a high-dimensional space, the dimensionality reduction strategy becomes the primary consideration for alleviating the tremendous computational cost. Here, the discrete empirical interpolation method (DEIM) is explored to retrieve the initial condition (IC) by combining the polynomial chaos (PC) based ensemble Kalman filter (i.e. PC-EnKF), where a non-intrusive PC expansion is considered as a surrogate model in place of the forward model in the prediction step of the ensemble Kalman filter, resulting in fewer forward model integrations but with a comparable accuracy as Monte Carlo-based approaches. The DEIM acts as a hyper-reduction tool to provide the low-dimensional input for the high-dimensional initial field, which can be reconstructed using the information on the sparse interpolation grid points that is adaptively obtained through PC-EnKF data assimilation method. Thus an innovative framework to reconstruct the IC is developed. The detailed procedure at each assimilation iteration includes: the determination of the spatial interpolation points, the estimation of the initial values on the interpolation locations using the optimal observations, and the reconstruction of IC in the full space. The current study uses the reconstruction field of initial conditions of the Navier-Stokes equations as an example to illustrate the efficacy of our method. The experimental results demonstrate the proposed algorithm achieves a satisfactory reconstruction for the initial field. The proposed method helps to extend the applicable area of DEIM in solving inverse problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1987

Analysis of the Continuous Stellar Tracking Attitude Reference (CSTAR) attitude rate processor

The Continuous Stellar Tracking Attitude Reference (CSTAR) system is an in-house project for Space Station to provide high accuracy, drift free attitude and angular rate information for the GN&C system. The outputs of the solid state star trackers are processed to provide attitude information; rate data is then derived from the attitude. Rate derivation is based on discrete time polynomial approximation techniques. This gives simple algorithms which allow for interpolation by other users. Attitude rate is modeled as a constant with low amplitude, low frequency sinusoids superimposed. The rate processor is parameterized to account for the effects of random errors, sample rate, data processing rate and perturbation frequency. The baseline system may be characterized as follows: the three sigma attitude accuracy is 0.01 degrees, the three sigma rate accuracy is 0.0001 degrees per second, the sample rate is 100 Hertz, the sampled signal is bandlimited to 0.5 Hertz, and the data processing rate is 10 Hertz. The above system requires a differentiator of length 127. This will track rate perturbations of frequencies less than 0.01 Hertz with low systematic errors.

Uhde-Lacovara, J.↗
NASA NTRS2017

On High-Order Upwind Methods for Advection

In the fourth installment of the celebrated series of five papers entitled "Towards the ultimate conservative difference scheme", Van Leer (1977) introduced five schemes for advection, the first three are piecewise linear, and the last two, piecewise parabolic. Among the five, scheme I, which is the least accurate, extends with relative ease to systems of equations in multiple dimensions. As a result, it became the most popular and is widely known as the MUSCL scheme (monotone upstream-centered schemes for conservation laws). Schemes III and V have the same accuracy, are the most accurate, and are closely related to current high-order methods. Scheme III uses a piecewise linear approximation that is discontinuous across cells, and can be considered as a precursor of the discontinuous Galerkin methods. Scheme V employs a piecewise quadratic approximation that is, as opposed to the case of scheme III, continuous across cells. This method is the basis for the on-going "active flux scheme" developed by Roe and collaborators. Here, schemes III and V are shown to be equivalent in the sense that they yield identical (reconstructed) solutions, provided the initial condition for scheme III is defined from that of scheme V in a manner dependent on the CFL number. This equivalence is counter intuitive since it is generally believed that piecewise linear and piecewise parabolic methods cannot produce the same solutions due to their different degrees of approximation. The finding also shows a key connection between the approaches of discontinuous and continuous polynomial approximations. In addition to the discussed equivalence, a framework using both projection and interpolation that extends schemes III and V into a single family of high-order schemes is introduced. For these high-order extensions, it is demonstrated via Fourier analysis that schemes with the same number of degrees of freedom 𝐾 per cell, in spite of the different piecewise polynomial degrees, share the same sets of eigenvalues and thus, have the same stability and accuracy. Moreover, these schemes are accurate to order 2𝐾−1, which is higher than the expected order of 𝐾.

high-order methods↗
DOE OSTI2013

Sandia Higher Order Elements (SHOE) v 0.5 alpha

SHOE is research code for characterizing and visualizing higher-order finite elements; it contains a framework for defining classes of interpolation techniques and element shapes; methods for interpolating triangular, quadrilateral, tetrahedral, and hexahedral cells using Lagrange and Legendre polynomial bases of arbitrary order; methods to decompose each element into domains of constant gradient flow (using a polynomial solver to identify critical points); and an isocontouring technique that uses this decomposition to guarantee topological correctness. Please note that this is an alpha release of research software and that some time has passed since it was actively developed; build- and run-time issues likely exist.

Thompson, David↗
DOE OSTI2013

Sandia Higher Order Elements (SHOE) v 0.5 alpha

SHOE is research code for characterizing and visualizing higher-order finite elements; it contains a framework for defining classes of interpolation techniques and element shapes; methods for interpolating triangular, quadrilateral, tetrahedral, and hexahedral cells using Lagrange and Legendre polynomial bases of arbitrary order; methods to decompose each element into domains of constant gradient flow (using a polynomial solver to identify critical points); and an isocontouring technique that uses this decomposition to guarantee topological correctness. Please note that this is an alpha release of research software and that some time has passed since it was actively developed; build- and run-time issues likely exist.

Source record↗
DOE OSTI2012

Atmospheric PSF Interpolation for Weak Lensing in Short Exposure Imaging Data

A main science goal for the Large Synoptic Survey Telescope (LSST) is to measure the cosmic shear signal from weak lensing to extreme accuracy. One difficulty, however, is that with the short exposure time ({approx_equal}15 seconds) proposed, the spatial variation of the Point Spread Function (PSF) shapes may be dominated by the atmosphere, in addition to optics errors. While optics errors mainly cause the PSF to vary on angular scales similar or larger than a single CCD sensor, the atmosphere generates stochastic structures on a wide range of angular scales. It thus becomes a challenge to infer the multi-scale, complex atmospheric PSF patterns by interpolating the sparsely sampled stars in the field. In this paper we present a new method, psfent, for interpolating the PSF shape parameters, based on reconstructing underlying shape parameter maps with a multi-scale maximum entropy algorithm. We demonstrate, using images from the LSST Photon Simulator, the performance of our approach relative to a 5th-order polynomial fit (representing the current standard) and a simple boxcar smoothing technique. Quantitatively, psfent predicts more accurate PSF models in all scenarios and the residual PSF errors are spatially less correlated. This improvement in PSF interpolation leads to a factor of 3.5 lower systematic errors in the shear power spectrum on scales smaller than {approx} 13, compared to polynomial fitting. We estimate that with psfent and for stellar densities greater than {approx_equal}1/arcmin{sup 2}, the spurious shear correlation from PSF interpolation, after combining a complete 10-year dataset from LSST, is lower than the corresponding statistical uncertainties on the cosmic shear power spectrum, even under a conservative scenario.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Few-electron atomic ions in non-relativistic QED: The ground state

Following detailed analysis of relativistic, QED and mass corrections for helium-like and lithium-like ions with static nuclei for Z≤20 the domain of applicability of Non-Relativistic QED (NRQED) is localized for ground state energy. It is demonstrated that for both helium-like and lithium-like ions with Z≤20 the finite nuclear mass effects do not change 4–5 significant digits (s.d.), and the leading relativistic and QED effects leave unchanged 3–4 s.d. in the ground state energy. It is shown that the non-relativistic ground state energy can be interpolated with accuracy not less than 13 s.d. for Z≤12, and not less than 12 s.d. for Z≤50 for helium-like as well as for Z≤20 for lithium-like ions by a compact meromorphic function in variable λ=√(Z−Z{sub B}) (here Z{sub B} is the 2nd critical charge (Turbiner et al., 2016)), P{sub 9}(λ)∕Q{sub 5}(λ). It is found that both the Majorana formula – a second degree polynomial in Z with two free parameters – and a fourth degree polynomial in λ (a generalization of the Majorana formula) reproduce the ground state energy of the helium-like and lithium-like ions for Z≤20 in the domain of applicability of NRQED, thus, at least, 3 s.d. It is noted that ≳99.9% of the ground state energy is given by the variational energy for properly optimized trial function of the form of (anti)-symmetrized product of three (six) screened Coulomb orbitals for two-(three) electron system with 3 (7) free parameters for Z≤20, respectively. It may imply that these trial functions are, in fact, exact wavefunctions in non-relativistic QED, thus, the NRQED effective potential can be derived. It is shown that the sum of relativistic and QED effects in leading approximation - 3 s.d. - for both 2 and 3 electron systems is interpolated by 4th degree polynomial in Z for Z≤20.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2012

Method for Pre-Conditioning a Measured Surface Height Map for Model Validation

This software allows one to up-sample or down-sample a measured surface map for model validation, not only without introducing any re-sampling errors, but also eliminating the existing measurement noise and measurement errors. Because the re-sampling of a surface map is accomplished based on the analytical expressions of Zernike-polynomials and a power spectral density model, such re-sampling does not introduce any aliasing and interpolation errors as is done by the conventional interpolation and FFT-based (fast-Fourier-transform-based) spatial-filtering method. Also, this new method automatically eliminates the measurement noise and other measurement errors such as artificial discontinuity. The developmental cycle of an optical system, such as a space telescope, includes, but is not limited to, the following two steps: (1) deriving requirements or specs on the optical quality of individual optics before they are fabricated through optical modeling and simulations, and (2) validating the optical model using the measured surface height maps after all optics are fabricated. There are a number of computational issues related to model validation, one of which is the "pre-conditioning" or pre-processing of the measured surface maps before using them in a model validation software tool. This software addresses the following issues: (1) up- or down-sampling a measured surface map to match it with the gridded data format of a model validation tool, and (2) eliminating the surface measurement noise or measurement errors such that the resulted surface height map is continuous or smoothly-varying. So far, the preferred method used for re-sampling a surface map is two-dimensional interpolation. The main problem of this method is that the same pixel can take different values when the method of interpolation is changed among the different methods such as the "nearest," "linear," "cubic," and "spline" fitting in Matlab. The conventional, FFT-based spatial filtering method used to eliminate the surface measurement noise or measurement errors can also suffer from aliasing effects. During re-sampling of a surface map, this software preserves the low spatial-frequency characteristic of a given surface map through the use of Zernike-polynomial fit coefficients, and maintains mid- and high-spatial-frequency characteristics of the given surface map by the use of a PSD model derived from the two-dimensional PSD data of the mid- and high-spatial-frequency components of the original surface map. Because this new method creates the new surface map in the desired sampling format from analytical expressions only, it does not encounter any aliasing effects and does not cause any discontinuity in the resultant surface map.

Sidick, Erkin↗
NASA NTRS2005

High Accuracy, Absolute, Cryogenic Refractive Index Measurements of Infrared Lens Materials for JWST NIRCam using CHARMS

The current refractive optical design of the James Webb Space Telescope (JWST) Near Infrared Camera (NIRCam) uses three infrared materials in its lenses: LiF, BaF2, and ZnSe. In order to provide the instrument s optical designers with accurate, heretofore unavailable data for absolute refractive index based on actual cryogenic measurements, two prismatic samples of each material were measured using the cryogenic, high accuracy, refraction measuring system (CHARMS) at NASA GSFC, densely covering the temperature range from 15 to 320 K and wavelength range from 0.4 to 5.6 microns. Measurement methods are discussed and graphical and tabulated data for absolute refractive index, dispersion, and thermo-optic coefficient for these three materials are presented along with estimates of uncertainty. Coefficients for second order polynomial fits of measured index to temperature are provided for many wavelengths to allow accurate interpolation of index to other wavelengths and temperatures.

Leviton, Douglas↗
NASA NTRS2020

Recommendations for Using Noise Monitors to Estimate Noise Exposure During X-59 Community Tests

A low fidelity simulation approach is used to explore how to place and use noise monitors during X-59 QueSST community tests, where people’s annoyance to the noise produced by the X-59 aircraft will be gathered. Several recommendations are provided including: 1) the desired number of sparsely spaced noise monitor sites within the survey area, 2) whether to group and average measurements across multiple noise monitors located at a site, 3) what spacing should be used if grouped noise monitors are used, 4) an approach to mitigate ambient noise contamination at the measurement sites, 5) a method to combine empirical and predicted dose estimates to provide a single dose estimate for respondents, and 6) assessing how changes in turbulence intensity and array configuration affect dose uncertainty. To make these recommendations, the error that is expected when fitting contrived, smoothly varying sonic boom “reference exposure surfaces” is studied when a spatially sparse and scattered set of samples is used as responses for the fit. The reference exposure surfaces mimic the sonic boom exposure at ground level that might be expected in the X-59 survey area in the absence of atmospheric turbulence, ambient noise, and other localized effects. The spatial extent of these surfaces varies and is representative of the different survey area sizes that might be expected during future X-59 community overflight tests. These contrived reference surfaces are sampled, and those reference samples are then perturbed to mimic atmospheric turbulence, ambient noise and other localized effects that might affect noise monitor measurements within overflown communities. Two different surface fitting methods are investigated when fitting these perturbed samples to approximate the reference surface. The first method uses interpolation between the perturbed data at the scattered sites to compute the fit. The second method fits a polynomial surface model to the perturbed data using ordinary least squares regression analysis. For both fitting methods, the root mean square fit error is computed from the pointwise difference between the fit surface and the reference surface as the count and configuration of the sites is varied while also averaging the error across many different realizations of both the smooth variation of the reference exposure surface and the random, localized perturbations at the sample sites. Different site configurations are compared using this error statistic to make the recommendations noted above. Additionally, the two fitting approaches (interpolation vs linear regression) are compared based on the fit error observed in these simulations. These analyses, comparisons, and recommendations should inform future decisions on the noise monitor placement and the methods used to analyze the noise monitor data that is collected during X-59 community overflights.

sonic boom↗
DOE OSTI2014

A one-time truncate and encode multiresolution stochastic framework

In this work a novel adaptive strategy for stochastic problems, inspired from the classical Harten's framework, is presented. The proposed algorithm allows building, in a very general manner, stochastic numerical schemes starting from a whatever type of deterministic schemes and handling a large class of problems, from unsteady to discontinuous solutions. Its formulations permits to recover the same results concerning the interpolation theory of the classical multiresolution approach, but with an extension to uncertainty quantification problems. The present strategy permits to build numerical scheme with a higher accuracy with respect to other classical uncertainty quantification techniques, but with a strong reduction of the numerical cost and memory requirements. Moreover, the flexibility of the proposed approach allows to employ any kind of probability density function, even discontinuous and time varying, without introducing further complications in the algorithm. The advantages of the present strategy are demonstrated by performing several numerical problems where different forms of uncertainty distributions are taken into account, such as discontinuous and unsteady custom-defined probability density functions. In addition to algebraic and ordinary differential equations, numerical results for the challenging 1D Kraichnan–Orszag are reported in terms of accuracy and convergence. Finally, a two degree-of-freedom aeroelastic model for a subsonic case is presented. Though quite simple, the model allows recovering some physical key aspect, on the fluid/structure interaction, thanks to the quasi-steady aerodynamic approximation employed. The injection of an uncertainty is chosen in order to obtain a complete parameterization of the mass matrix. All the numerical results are compared with respect to classical Monte Carlo solution and with a non-intrusive Polynomial Chaos method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Hermite WENO limiting for multi-moment finite-volume methods using the ADER-DT time discretization for 1-D systems of conservation laws

New Hermite Weighted Essentially Non-Oscillatory (HWENO) interpolants are developed and investigated within the Multi-Moment Finite-Volume (MMFV) formulation using the ADER-DT time discretization. Whereas traditional WENO methods interpolate pointwise, function-based WENO methods explicitly form a non-oscillatory, high-order polynomial over the cell in question. This study chooses a function-based approach and details how fast convergence to optimal weights for smooth flow is ensured. Methods of sixth-, eighth-, and tenth-order accuracy are developed. We compare these against traditional single-moment WENO methods of fifth-, seventh-, ninth-, and eleventh-order accuracy to compare against more familiar methods from literature. The new HWENO methods improve upon existing HWENO methods (1) by giving a better resolution of unreinforced contact discontinuities and (2) by only needing a single HWENO polynomial to update both the cell mean value and cell mean derivative. Test cases to validate and assess these methods include 1-D linear transport, the 1-D inviscid Burger's equation, and the 1-D inviscid Euler equations. Smooth and non-smooth flows are used for evaluation. These HWENO methods performed better than comparable literature-standard WENO methods for all regimes of discontinuity and smoothness in all tests herein. They exhibit improved optimal accuracy due to the use of derivatives, and they collapse to solutions similar to typical WENO methods when limiting is required. The study concludes that the new HWENO methods are robust and effective when used in the ADER-DT MMFV framework. Finally, these results are intended to demonstrate capability rather than exhaust all possible implementations.

97 MATHEMATICS AND COMPUTING↗