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At least 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

The time evolution of spectral discretizations of hyperbolic systems

A Chebyshev collocation spectral method, applied to hyperbolic systems is considered, particularly for those initial boundary value problems which possess only solutions tending to zero at large times. It is shown that the numerical solutions of the system will also vanish at infinity, if and only if, the numerical solution of a scalar equation of the same type does. This result is then generalized for other spectral approximations.

Lustman, L.↗
NASA NTRS1984

Spectral methods for solution of the boundary-layer equations

The basic principles of spectral methods are reviewed, and their application to the two-dimensional incompressible boundary-layer equations is discussed. It is shown that spectral collocation methods provide an accuracy sufficient for engineering applications on extremely coarse grids, and the machine time requirements are small. Although for a given stream-wise discretization, the fully spectral scheme requires more computational effort than the marching scheme, the higher accuracy of the former yields a large net gain in efficiency when considered at equivalent error levels.

Streett, C. L.↗
NASA NTRS1983

Analysis of an internally radially cracked ring segment subject to three-point radial loading

The boundary collocation method was used to generate Mode 1 stress intensity and crack mouth opening displacement coefficients for externally radially cracked ring segments subjected to three point radial loading. Numerical results were obtained for ring segment outer-to-inner radius ratios (R sub o/R sub i) ranging from 1.10 to 2.50 and crack length to segment width ratios (a/W) ranging from 0.1 to 0.8. Stress intensity and crack mouth displacement coefficients were found to depend on the ratios R sub o/R sub i and a/W as well as the included angle between the directions of the reaction forces. Previously announced in STAR as N83-35413

Gross, B.↗
NASA NTRS1983

A comparative study on synthetic aperture radar and optical imagery of ocean waves

The ocean imaging capability of synthetic aperture radar (SAR) is examined in terms of an intercomparison between simultaneous, spatially collocated images of a coastal ocean scene, as recorded by aerial photography and aircraft-borne SAR. Based on a detailed study of these images, this paper examines various local features of oceanographic interest as they are imaged by the two methods. This provides information not available in the usual comparisons of normalized SAR and single point buoy spectra. In addition, aspects of the intensity wavenumber spectra of the two images are examined and discussed. An interesting and surprising conclusion arising from the comparison study is the ability of the SAR to image accurately non-uniform (possibly nonlinear) wave features which are imaged by the aerial photography. This result should have important implications on the development of SAR imaging models and the interpretation of the effect of ocean surface motion on the SAR images.

Banner, M. L.↗
NASA NTRS1984

Stresses around holes in pin-loaded orthotropic plates

The effects of pin elasticity, pin/hole friction, and pin/hole clearance on the stresses around a hole in a pin-loaded orthotropic plate were studied. The problem was modeled as a planar problem, the pin and plate being two elastic bodies interacting through contact. Complex variable elasticity, a collocation scheme to enforce the pin/hole boundary conditions, and an iteration procedure to find the contact, slip, and no-slip regions were used to obtain numerical results. The results indicate that pin elasticity is not as important a variable as friction and clearance are. A rigid pin assumption, as opposed to the popular cosinusoidal radial traction, can be used without much error but clearance and friction should not be ignored.

Hyer, M. W.↗
NASA NTRS1984

A calibration adjustment technique combining ERB parameters from different remote sensing platforms into a long-term data set

Earth-radiation-budget (ERB) experiments on board the Nimbus-6 (ERB 6) and Nimbus-7 (ERB 7) spacecraft have measured wide-field-of-view total (0.2 to 50 micron), shortwave (0.2 to 3.8 micron), and near-infrared (0.7 to 2.8 micron) terrestrial irradiances for a joint lifetime of over 8 years. Though the spectral characteristics of both experiments are nearly identical, instrument degradation and altitude differences introduce discrepancies between the two data sets. ERB parameters from these two observing platforms may be combined into a scientifically meaningful data set only after these discrepancies are eliminated. To facilitate the creation of a long-term ERB data set, comparisons of the ERB 6 experiment irradiances with, and calibration adjustments with respect to, the corresponding ERB 7 irradiances have been performed. Two calibration methods were developed and applied to the irradiance data from 28 pairs of collocated orbits. The differential effects of altitude, illumination, albedo, and scene inhomogeneities were applied. The result is a set of calibration adjustments that adjust the ERB 6 data to match the ERB 7 data.

Ardanuy, P. E.↗
NASA NTRS1984

Fourier-Legendre spectral methods for incompressible channel flow

An iterative collocation technique is described for modeling implicit viscosity in three-dimensional incompressible wall bounded shear flow. The viscosity can vary temporally and in the vertical direction. Channel flow is modeled with a Fourier-Legendre approximation and the mean streamwise advection is treated implicitly. Explicit terms are handled with an Adams-Bashforth method to increase the allowable time-step for calculation of the implicit terms. The algorithm is applied to low amplitude unstable waves in a plane Poiseuille flow at an Re of 7500. Comparisons are made between results using the Legendre method and with Chebyshev polynomials. Comparable accuracy is obtained for the perturbation kinetic energy predicted using both discretizations.

Zang, T. A.↗
NASA NTRS1984

A new aerodynamic integral equation based on an acoustic formula in the time domain

An aerodynamic integral equation for bodies moving at transonic and supersonic speeds is presented. Based on a time-dependent acoustic formula for calculating the noise emanating from the outer portion of a propeller blade travelling at high speed (the Ffowcs Williams-Hawking formulation), the loading terms and a conventional thickness source terms are retained. Two surface and three line integrals are employed to solve an equation for the loading noise. The near-field term is regularized using the collapsing sphere approach to obtain semiconvergence on the blade surface. A singular integral equation is thereby derived for the unknown surface pressure, and is amenable to numerical solutions using Galerkin or collocation methods. The technique is useful for studying the nonuniform inflow to the propeller.

Farassat, F.↗
NASA NTRS1983

Modes of inter-hemispheric wave propagation

Attention is given to observations made in connection with the First GARP (Global Atmospheric Research Program) Global Experiment (FGGE), taking into account the average 200 mb zonal wind for two periods during the First Special Observing Period of FGGE, and the 200 mb velocity potential. The meridional linkages implied in the observations involve sources south of 15 deg N, and the most active extratropical patterns are collocated with regions of tropical easterlies. The possibility is investigated that the theory of reduced Rossby wave propagation through easterlies is not sufficiently general to cover the considered observations, taking into account a shallow water model. It is found that the meridional interactions cannot be associated with Rossby waves because these waves connot be generated in the regions of zero absolute vorticity gradient within which the forcing is embedded.

Paegle, J.↗
NASA NTRS1984

The precise computation of geoid undulation differences with comparison to results obtained from the global positioning system

Ellipsoidal height differences have been determined for 13 station pairs in the central Ohio region using measurements made with the Global Positioning System. This information was used to compute geoid undulation differences based on known orthometric heights. These differences were compared to gravimetrically-computed undulations (using a Stokes integration procedure, and least squares collocation having an internal r.m.s. agreement of plus or minus 1 cm in undulation differences). The two sets of undulation differences have an r.m.s. discrepancy of plus or minus 5 cm while the average station separation is of the order of 14 km. This good agreement suggests that gravimetric data can be used to compute accurate geoid undulation differences that can be used to convert ellipsoidal height differences obtained from GPS to orthometric height differences.

Engelis, T.↗
NASA NTRS1984

Boundary conditions in Chebyshev and Legendre methods

Two different ways of treating non-Dirichlet boundary conditions in Chebyshev and Legendre collocation methods are discussed for second order differential problems. An error analysis is provided. The effect of preconditioning the corresponding spectral operators by finite difference matrices is also investigated.

Canuto, C.↗
NASA NTRS1985

Maser cavity servo-tuning system

Two collocated, weakly coupled probes, one loop and one dipole, detect the magnetic and electric fields inside a maser cavity. Signals from the probes are compared in phase, and the signal output from the phase detector is applied to a varactor, the reactance of which is coupled into the cavity by a microwave coupler. Alternatively, the varactor may be placed inside the cavity. Any deviation of phase from 90 deg as detected by the phase detector will then produce an error signal that will change the reactance coupled into the resonant cavity to change its reactance, and thus correct its resonance frequency. An alternative to using two probes is to use a single disk probe oriented to detect both the magnetic and electric fields, and thus provide the error signal directly.

Sydnor, R. L.↗
NASA NTRS1985

Statistical magnetic anomalies from satellite measurements for geologic analysis

The errors of numerically averaging satellite magnetic anomaly data for geologic analysis are investigated using orbital anomaly simulations of crustal magnetic sources by Gauss-Legendre quadrature integration. These simulations suggest that numerical averaging errors constitute small and relatively minor contributions to the total error-budget of higher orbital estimates (approx. 400 km), whereas for lower orbital estimates the error of averaging may increase substantially. Least-squares collocation is also investigated as an alternative to numerical averaging and found to produce substantially more accurate anomaly estimates as the elevation of prediction is decreased towards the crustal sources.

Goyal, H. K.↗
NASA NTRS1985

The stress distribution in pin-loaded orthotropic plates

The performance of mechanically fastened composite joints was studied. Specially, a single-bolt connector was modeled as a pin-loaded, infinite plate. The model that was developed used two dimensional, complex variable, elasticity techniques combined with a boundary collocation procedure to produce solutions for the problem. Through iteration, the boundary conditions were satisfied and the stresses in the plate were calculated. Several graphite epoxy laminates were studied. In addition, parameters such as the pin modulus, coefficient of friction, and pin-plate clearance were varied. Conclusions drawn from this study indicate: (1) the material properties (i.e., laminate configuration) of the plate alter the stress state and, for highly orthotropic materials, the contact stress deviates greatly from the cosinusoidal distribution often assumed; (2) friction plays a major role in the distribution of stresses in the plate; (3) reversing the load direction also greatly effects the stress distribution in the plate; (4) clearance (or interference) fits change the contact angle and thus the location of the peak hoop stress; and (5) a rigid pin appears to be a good assumption for typical material systems.

Klang, E. C.↗
NASA NTRS1984

A review of spectral methods

An outline for spectral methods for partial differential equations is presented. The basic spectral algorithm is defined, collocation are emphasized and the main advantage of the method, the infinite order of accuracy in problems with smooth solutions are discussed. Examples of theoretical numerical analysis of spectral calculations are presented. An application of spectral methods to transonic flow is presented. The full potential transonic equation is among the best understood among nonlinear equations.

Lustman, L.↗
NASA NTRS1985

Spectral methods for the Euler equations. I - Fourier methods and shock capturing

Spectral methods for compressible flows are introduced in relation to finite difference and finite element techniques within the framework of the method of weighted residuals. Current spectral collociation methods are put into historical context. The basic concepts of Fourier spectral collocation methods are provided. Filtering strategies for shock-capturing approaches are also presented. Fourier shock-capturing techniques are evaluated using a one-dimensional, periodic astrophysical 'nozzle' problem.

Hussaini, M. Y.↗
NASA NTRS1985

Spectral methods for the Euler equations. II - Chebyshev methods and shock fitting

The Chebyshev spectral collocation method for the Euler gasdynamic equations is described. It is used with shock fitting to compute several two-dimensional gasdynamic flows. Examples include a shock/acoustic wave interaction, a shock/vortex interaction, and the classical blunt-body problem. With shock fitting, the spectral method has a clear advantage over second-order finite differences in that equivalent accuracy can be obtained with far fewer grid points.

Hussaini, M. Y.↗
NASA NTRS1985

Robustness of velocity feedback controllers for flexible spacecraft

The robustness properties of collocated velocity feedback controllers used for damping enhancement in large, flexible space structures are investigated. It is proved that the closed-loop system using such controllers is asymptotically stable in the large when: (1) unmodeled linear time-invariant dynamics (such as sensors/actuators) are present, provided that the phase angle of such dynamics is between -90 deg and 90 deg; (2) time-varying or invariant nonlinearities lying in the first and the third quadrant (i.e., belonging to the /0, infinity/ sector) are present; or (3) sector-type nonlinearities following first-order stable dynamics are present in the feedback loop.

Joshi, S. M.↗