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At least 937 records · Page 52

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NASA NTRS1987

Numerical analysis of discrete fractional integrodifferential structural dampers

This paper develops solution algorithms enabling the handling of the dynamic response of nonlinear structures contained discretely attached dampers modeled by fractional integrodifferential operators of the Grunwald-Liouville-Riemann type. The development consists of two levels of formulation, namely: (1) numerical approximations of fractional operators and, (2) the establishment of global level implicit schemes enabling the solution to nonlinear structural formulations. To generalize the overall results, error estimates are derived for the fractional operator approximation algorithm. These enable an ongoing optimization of solution efficiency for a given error tolerance. To benchmark the scheme, the results of several numerical experiments are presented. These illustrate the numerical characteristics of the overall formulation.

Padovan, Joseph↗

DOE OSTI2021

Error Estimates for the Optimal Control of a Parabolic Fractional PDE

In this work, we consider the integral definition of the fractional Laplacian and analyze a linear-quadratic optimal control problem for the so-called fractional heat equation; control constraints are also considered. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates for the optimal variables. To discretize the state equation we propose a fully discrete scheme that relies on an implicit finite difference discretization in time combined with a piecewise linear finite element discretization in space. We derive stability results and a novel $L^2(0,T;L^2(\Omega))$ a priori error estimate. On the basis of the aforementioned solution technique, we propose a fully discrete scheme for our optimal control problem that discretizes the control variable with piecewise constant functions, and we derive a priori error estimates for it. We illustrate the theory with one- and two-dimensional numerical experiments.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1981

Optimum employment of satellite indirect soundings as numerical model input

The characteristics of satellite-derived temperature soundings that would significantly affect their use as input for numerical weather prediction models were examined. Independent evaluations of satellite soundings were emphasized to better define error characteristics. Results of a Nimbus-6 sounding study reveal an underestimation of the strength of synoptic scale troughs and ridges, and associated gradients in isobaric height and temperature fields. The most significant errors occurred near the Earth's surface and the tropopause. Soundings from the TIROS-N and NOAA-6 satellites were also evaluated. Results again showed an underestimation of upper level trough amplitudes leading to weaker thermal gradient depictions in satellite-only fields. These errors show a definite correlation to the synoptic flow patterns. In a satellite-only analysis used to initialize a numerical model forecast, it was found that these synoptically correlated errors were retained in the forecast sequence.

Horn, L. H.↗

DOE OSTI2024

Behavior and mechanisms of Doppler wind lidar error in complex terrain: stable flow case study at Perdigão

A numerical experiment is carried out investigating the magnitude of biases in ground-based lidar measurements in complex flow conditions. Biases assessed include those arising from flow curvature and from the interaction of turbulence with the wind field reconstruction (WFR) algorithms used by a WindCube lidars and anemometers. RANS-CFD and WRF-LES simulations were performed for the Perdig˜ao Field Experiment site for a range of atmospheric conditions. Virtual anemometer and lidar data were generated for four locations: two near exposed ridge tops and two in low-speed regions in the valley. The LES data at these four locations show that the scalar inflation terms (the relation between scalar and vector averaged wind speed) for virtual lidar and virtual cups agree very well with predictions using perturbation theory. While the lidar errors vary greatly with location and height, the contribution from the flow curvature tends to be larger than the differences arising from scalar inflation. For one lidar/mast pair near the ridge top, comparisons between simulations and measurements are carried out for a resonant mountain wave event on June 14th, 2017, and for the whole duration of the Perdigão campaign for winds perpendicular to the ridges. The lidar error during the mountain wave, a period of strong stability and low inversion height, is significantly larger than the campaign average. The sensitivity of the lidar error to atmospheric stability is confirmed by the RANS simulations, which suggests strong sensitivity of flow curvature error to stability conditions and to the shape of the wind speed profile near the top of the boundary layer.

17 WIND ENERGY↗

NASA NTRS1994

The analysis of star catalogs. 1: An intercomparison among the FK3, the FK4, and the FK5

Progress in the construction of the fundamental catalogs allows one to ask the following questions: 'Now that we have the FK5 with which to measure by, how good was the FK4? The FK3? How realistic were the error estimates they gave for their equatorial coordinates and their proper motions? Have their residual systematic differences continued to decrease in amplitude?' and so forth. Similar questions could be asked of the GC and the N30, and a companion paper will similarly analyze them. Finally, the identical series of questions could be asked of the AGK2, AGK3, AGK3U sequence. In this paper we develop a general method to objectively investigate, post facto, the true quality of star catalog error estimates. We present a complete mathematical formulation of the questions above and delineate the calculations needed to address them. Our initial numerical applications are restricted to a straightforward examination of the mean errors of the coordinates and proper motions in the FK3 (using the FK4 and the FK5 for comparison) and in the FK4 (using the FK5 for comparison). However, we can simply and consistently interpret the results of these computations -- for the FK catalogs fail to follow the predictions of mathematical statistics -- only if the FK3 and the FK4 contain higher angular frequency systematic errors. These errors, at the mean epochs of place of the older catalogs, are larger than the random errors in the FK5 system. We expect that our new ability to discern these features means that we can also prevent them during compilation. Finally, note that the concepts behind our procedures are completely general and can be applied to any set of compiled data -- astrometric, photometric, geodetic, and so forth.

Bucciarelli, B.↗

NASA NTRS1995

An hp-adaptivity and error estimation for hyperbolic conservation laws

This paper presents an hp-adaptive discontinuous Galerkin method for linear hyperbolic conservation laws. A priori and a posteriori error estimates are derived in mesh-dependent norms which reflect the dependence of the approximate solution on the element size (h) and the degree (p) of the local polynomial approximation. The a posteriori error estimate, based on the element residual method, provides bounds on the actual global error in the approximate solution. The adaptive strategy is designed to deliver an approximate solution with the specified level of error in three steps. The a posteriori estimate is used to assess the accuracy of a given approximate solution and the a priori estimate is used to predict the mesh refinements and polynomial enrichment needed to deliver the desired solution. Numerical examples demonstrate the reliability of the a posteriori error estimates and the effectiveness of the hp-adaptive strategy.

Bey, Kim S.↗

DOE OSTI2014

The Role of Moist Processes in the Intrinsic Predictability of Indian Ocean Cyclones

The role of moist processes and the possibility of error cascade from cloud scale processes affecting the intrinsic predictable time scale of a high resolution convection permitting model within the environment of tropical cyclones (TCs) over the Indian region are investigated. Consistent with past studies of extra-tropical cyclones, it is demonstrated that moist processes play a major role in forecast error growth which may ultimately limit the intrinsic predictability of the TCs. Small errors in the initial conditions may grow rapidly and cascades from smaller scales to the larger scales through strong diabatic heating and nonlinearities associated with moist convection. Results from a suite of twin perturbation experiments for four tropical cyclones suggest that the error growth is significantly higher in cloud permitting simulation at 3.3 km resolutions compared to simulations at 3.3 km and 10 km resolution with parameterized convection. Convective parameterizations with prescribed convective time scales typically longer than the model time step allows the effects of microphysical tendencies to average out so convection responds to a smoother dynamical forcing. Without convective parameterizations, the finer-scale instabilities resolved at 3.3 km resolution and stronger vertical motion that results from the cloud microphysical parameterizations removing super-saturation at each model time step can ultimately feed the error growth in convection permitting simulations. This implies that careful considerations and/or improvements in cloud parameterizations are needed if numerical predictions are to be improved through increased model resolution. Rapid upscale error growth from convective scales may ultimately limit the intrinsic mesoscale predictability of the TCs, which further supports the needs for probabilistic forecasts of these events, even at the mesoscales.

cyclones↗

NASA NTRS1980

Distance corrections for single- and dual-color lasers by ray tracing

The physical arc length difference between the red and blue beam of a dual-color laser generates an error term in determining Delta-n as well as n (the refractive index) and D (the line length). Numerical ray trace examples and theoretical approximations show that the resulting relative error Delta-D/D increases as D-squared. Error reduction by a factor of nearly 10 is possible by using the pressure, temperature, and humidity of both endpoints to calculate n. The present study results from a desire to improve the precision of monitoring the local and regional position of the Lunar Laser Ranging Observatory atop Haleakala, Maui, Hawaii; the monitoring of the earth's crustal deformation and strain is a primary concern of the study.

Berg, E.↗

DOE OSTI2018

A Galerkin method with two-dimensional Haar basis functions for the computation of the Karhunen–Loève expansion

We study the numerical approximation of a homogeneous Fredholm integral equation of second kind associated with the Karhunen–Loève expansion of Gaussian random fields. We develop, validate, and discuss an algorithm based on the Galerkin method with two-dimensional Haar wavelets as basis functions. The shape functions are constructed from the orthogonal decomposition of tensor-product spaces of one-dimensional Haar functions, and a recursive algorithm is employed to compute the matrix of the discrete eigenvalue system without the explicit calculation of integrals, allowing the implementation of a fast and efficient algorithm that provides considerable reduction in CPU time, when compared with classical Galerkin methods. Numerical experiments confirm the convergence rate of the method and assess the approximation error and the sparsity of the eigenvalue system when the wavelet expansion is truncated. We illustrate the numerical solution of a diffusion problem with random input data with the present method. In this problem, accuracy was retained after dropping the coefficients below a threshold value that was numerically determined. A similar method with scaling functions rather than wavelet functions does not need a discrete wavelet transform and leads to eigenvalue systems with better conditioning but lower sparsity.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1977

Guidance and trajectory considerations in lunar mass transportation

Flight-mechanics problems associated with large-scale transport of lunar mass to a space colony or manufacturing facility are discussed. The proposed transport method involves launch of payloads from a mass-driver on the lunar surface, onto ballistic trajectories to a passive mass-catcher located near the L2 libration point, with the caught mass subsequently being transported to the colony. Arrival velocities at L2, sensitivities in arrival dispersion due to launch errors, and effects of launch site location are treated, via numerically integrated orbits in the restricted three-body problem. From any launch site it is possible to define a target point reached with zero dispersion due to errors in a selected component of launch velocity. Effects of lunar geometrical librations and of obliquity, as well as the conditions for biasing a trajectory away from L2 so as to reduce stationkeeping costs, are dealt with along with transfer orbits from L2 to the colony. The theory of capture and the theory of resonance lead to a colony orbit, with period approximately two weeks, reached from L2 with velocity increment as low as 9.02 m/sec.

Heppenheimer, T. A.↗

NASA NTRS1961

ON THE ACCURACY OF MEASUREMENTS MADE UPON FILMS PHOTOGRAPHED BY BAKER-NUNN SATELLITE TRACKING CAMERAS

The photographs taken by the Baker-Nunn cameras of the Smithsonian Astrophysical Observatory were formerly measured with Van Biesbroeck goniometers, but are now measured exclusively with Mann two-screw comparators. Instead of measuring point images, we usually have to measure oblong images, either trails or breaks (the latter produced by interruption of the exposure). We can therefore expect that the accuracy of the determination of their positions is more influenced by the personal errors than it is in conventional astrometry. Approximately 800 measurements were made on 34 images of different length, and, from these, the frequency distribution of settings was determined. Then the relationship between this distribution and the length of the image (trail or break) was examined, and the relationship between the "magnitude error" and the length of image was determined. Measurements were made at different angles formed by the trails and the reticle lines, and it was found that the accuracy was not affected by the angle of the setting. Position determinations have been made using reference stars at different distances. On the basis of these results, we can conclude that the accuracy is neither influenced by the distortion of the emulsion nor by the optical distortion within an area of a diameter of S cm (5°.8). We believe that we are justified in using the linear plate constant method, at least within this area. From numerous double and multiple measurements, the following standard errors were determined for a single position.

ASTROMETRY↗

DOE OSTI2022

Machine Straightness Error Measurement Based on Optical Fiber Fabry–Pérot Interferometer Monitoring Technique

Abstract In this research, we propose an Error Separation Technique (EST) based on optical fiber sensors for on-machine straightness error measurement. Two fiber optic Fabry–Pérot interferometers have been developed serving as two displacement sensors. The displacement distance is computed according to the reflected spectrum from interferometers, which can achieve a sub-micrometer resolution. The two-point method has been employed to separate the straightness error of the slides and the profile error of a fine-polished standard block. The spacing distance between two interferometers is determined by the diameter of optical fibers so that the EST's resolution has the potential to reach the sub-millimeter scale. In the experiment, the straightness error has been measured on a commercially available computer numerical control machine tool, and the measurement has been conducted on its x-axis. The spacing distance between two optical fiber sensors is 1.5 mm which equals the EST's resolution along the machine tool's x-axis. The separated profile error of the measured standard block is around 30 µm which has been verified by a high precision Coordinate Measurement Machine (CMM). The magnitude of the separated straightness error is around 40 µm. This technique is flexible and simple to be conducted, which can contribute to the micro-machine tool calibration and other straightness error applications.

Engineering↗

NASA NTRS1997

Computations of Complex Three-Dimensional Turbulent Free Jets

Three-dimensional, incompressible turbulent jets with rectangular and elliptical cross-sections are simulated with a finite-difference numerical method. The full Navier- Stokes equations are solved at low Reynolds numbers, whereas at high Reynolds numbers filtered forms of the equations are solved along with a sub-grid scale model to approximate the effects of the unresolved scales. A 2-N storage, third-order Runge-Kutta scheme is used for temporary discretization and a fourth-order compact scheme is used for spatial discretization. Although such methods are widely used in the simulation of compressible flows, the lack of an evolution equation for pressure or density presents particular difficulty in incompressible flows. The pressure-velocity coupling must be established indirectly. It is achieved, in this study, through a Poisson equation which is solved by a compact scheme of the same order of accuracy. The numerical formulation is validated and the dispersion and dissipation errors are documented by the solution of a wide range of benchmark problems. Three-dimensional computations are performed for different inlet conditions which model the naturally developing and forced jets. The experimentally observed phenomenon of axis-switching is captured in the numerical simulation, and it is confirmed through flow visualization that this is based on self-induction of the vorticity field. Statistical quantities such as mean velocity, mean pressure, two-point velocity spatial correlations and Reynolds stresses are presented. Detailed budgets of the mean momentum and Reynolds stresses are presented. Detailed budgets of the mean momentum and Reynolds stress equations are presented to aid in the turbulence modeling of complex jets. Simulations of circular jets are used to quantify the effect of the non-uniform curvature of the non-circular jets.

Wilson, Robert V.↗

NASA NTRS1989

Control of the errors of discretization and idealization in finite element analysis

Understanding of the basic principles which control errors of discretization in finite element analysis has increased very substantially since 1980. The main milestones were: (1) development of the theoretical basis of p-extensions (1981); (2) understanding of the proper interplay between mesh design and assignment of polynomial degree to elements. Practical realization of exponential convergence rates, independently of the smoothness of the exact solution (1984); and (3) industrial experience with the new finite element technology known as the p- or hp-version of the finite element method: General Dynamics reported thirty- to forty-fold savings in terms of human time and large savings in computer time (1986). Lockheed reported favorably on their evaluation of error estimation and quality control capabilities of the p-version in industrial settings (1987). The gains in our understanding of how to control the errors of discretization represent only half of the control necessary to ensure that a numerical model is in fact an accurate representation of the corresponding physical system. Control of the errors of idealization is equally important. A brief overview of the main ideas of how to ensure the quality and reliability of mathematical models of structural systems is presented.

Szabo, Barna A.↗

DOE OSTI2012

INCORPORATING AMBIPOLAR AND OHMIC DIFFUSION IN THE AMR MHD CODE RAMSES

We have implemented non-ideal magnetohydrodynamics (MHD) effects in the adaptive mesh refinement code RAMSES, namely, ambipolar diffusion and Ohmic dissipation, as additional source terms in the ideal MHD equations. We describe in details how we have discretized these terms using the adaptive Cartesian mesh, and how the time step is diminished with respect to the ideal case, in order to perform a stable time integration. We have performed a large suite of test runs, featuring the Barenblatt diffusion test, the Ohmic diffusion test, the C-shock test, and the Alfven wave test. For the latter, we have performed a careful truncation error analysis to estimate the magnitude of the numerical diffusion induced by our Godunov scheme, allowing us to estimate the spatial resolution that is required to address non-ideal MHD effects reliably. We show that our scheme is second-order accurate, and is therefore ideally suited to study non-ideal MHD effects in the context of star formation and molecular cloud dynamics.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1978

Error analysis of an aircraft-mounted backscatter ultraviolet experiment

An experiment has been proposed to measure the zenith sky intensity and directly transmitted solar flux density at several wavelengths in the near ultraviolet from an aircraft platform located at about 15 km. From these measurements, the vertical distribution of ozone above the platform is to be inferred, by inversion of the equation of radiative transfer. The present study is an analysis of the errors to be expected in a real experiment, due to atmospheric fluctuations, numerical procedures, and ignorance of various parameters necessary for the calculation of the intensities and fluxes to be expected. These errors are found to vary from 17% at the shorter wavelengths to about 3% at the longer wavelengths used. It is shown elsewhere (Twomey et al., 1977) that unacceptable levels of instability and non-uniqueness of results will be found if the error levels in the measurements upon which we wish to invert exceed 3%. On the basis of this, it is concluded that with the present instrumentation and the present knowledge of necessary ancillary parameters, this experiment will not be feasible.

Rabinoff, R.↗

NASA NTRS1985

The error associated with use of various forms of the divergence equation to diagnose geopotential and temperature

An experimental study was made of errors arising from diagnosing the geopotential and temperature for numerical weather prediction models by means of an inviscid divergence equation (DE). The experiment consisted of a simulation of a snow storm which occurred in 1979, with observational data being input for every point of the model grid and for the geopotential boundary condition, thereby eliminating errors in the horizontal and vertical analysis. The DE terms were recorded at each grid point, and were found to include synoptic-scale geopotential height errors up to 23 m and rms temperature errors exceeding 26 C in the PBL. The errors were minimal above 800 mb. The various unsuccessful attempts to reduce or eliminate the errors are described.

Modica, G. M.↗

DOE OSTI2023

A reduced-order modeling of a tubular solar reactor for long duration thermochemical energy storage

The storage of solar energy in a solid form, referred to as a “solar fuel”, can be achieved through a process known as endothermic solar thermochemistry. This process transforms the absorbed solar energy into a stable and retrievable form that can be stored for extended periods of time. This paper presents a low–order heat transfer model of a counter–current tubular falling bed reactor designed to produce thermally reduced magnesium manganese oxide pellets for long duration thermochemical energy storage. The energy required for the endothermic reduction was supplied by concentrated solar energy or renewable electricity via indirect heating of the gas and solid reactants flowing in a ceramic tube. The counter-current gas flow enhances the mixing of the solid particles with the heat recuperation zone, allowing the gas and particles to enter and exit the tubular reactor close to room temperature. Further, the reactor was vertically oriented and was heated circumferentially by an adjustable level heat flux along a finite segment of its length. The temperature distribution of the reactor in response to transient changes along the tube was modeled by considering conduction, convection, and radiation heat transfer. Governing equations for the heat transfer model were solved by discretizing the reactor tube into a finite number of control volumes and using an energy balance for the heat exchange between the reactor wall, gas, and particles within the control volume. The energy absorbed during this endothermic reaction was modeled numerically by fitting the data of the chemical conversion rate with the corresponding temperature of particles in the heating zone. The numerical model has been experimentally validated using a reactor prototype made of a 121.92 cm alumina tube heated by a 7kW electric tube–furnace. The alumina tube receives magnesium manganese oxide pellets of 3.66±0.516 mm in diameter from the top, and a counter–current gas flow from the bottom. The reactor wall temperature was monitored by six thermocouples installed along the reactor tube length. The experimental procedure was numerically simulated, and the temperature variation along the reactor tube was compared with a matrix of experimental runs for a range of particles mass flowrates (0.75–1.25g/s) and corresponding gas flowrates (36–65 SLPM). The reactor system was heated gradually from room temperature to a steady state temperature of 1673K, and then cooled down to room temperature. The heating and cooling processes were simulated, and the numerical and experimental results were compared throughout processes. The numerical model showed similar trends to the experimental results, with an error of 0.69 to 7.9% for the particle inlet and 0.7 to 7.9% for the gas inlet during steady-state operation. The proposed numerical model can be implemented as a simplified physical model to design a feedback control system to regulate reactor temperature.

14 SOLAR ENERGY↗