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At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Higher order methods for convection-diffusion problems

This paper applies C1 cubic Hermite polynomials embedded in an orthogonal collocation scheme to the spatial discretization of the unsteady nonlinear Burgers equation as a model of the equations of fluid mechanics. The temporal discretization is carried out by means of either a noniterative finite difference or an iterative finite difference procedure. Results of this method are compared with those of a second-order finite difference scheme and a splined-cubic Taylor's series scheme. Stability limits are derived and the matrix structure of the several schemes are compared.

Murphy, J. D.↗
NASA NTRS1985

Recent applications of spectral methods in fluid dynamics

Origins of spectral methods, especially their relation to the method of weighted residuals, are surveyed. Basic Fourier and Chebyshev spectral concepts are reviewed and demonstrated through application to simple model problems. Both collocation and tau methods are considered. These techniques are then applied to a number of difficult, nonlinear problems of hyperbolic, parabolic, elliptic and mixzed type. Fluid dynamical applications are emphasized.

Zang, T. A.↗
NASA NTRS1986

Adjustable Work Station for Video Displays and Keyboards

Work station for video displays and keyboards adaptable to operational and anthropometric requirements of individual operators. Visual displays placed beyond keyboard and in line with inclination of keyboard to minimize operator's head movement. In addition, station arranged so operator's eyes and hands focus onto three primary control and display areas. Quickens operating response and decreases chance of error, since input devices and feedback to operator are collocated.

Roe, F.↗
NASA NTRS1986

Stability analysis of spectral methods for hyperbolic initial-boundary value systems

A constant coefficient hyperbolic system in one space variable, with zero initial data is discussed. Dissipative boundary conditions are imposed at the two points x = + or - 1. This problem is discretized by a spectral approximation in space. Sufficient conditions under which the spectral numerical solution is stable are demonstrated - moreover, these conditions have to be checked only for scalar equations. The stability theorems take the form of explicit bounds for the norm of the solution in terms of the boundary data. The dependence of these bounds on N, the number of points in the domain (or equivalently the degree of the polynomials involved), is investigated for a class of standard spectral methods, including Chebyshev and Legendre collocations.

Gottlieb, D.↗
NASA NTRS1986

Spectral methods in fluid dynamics

Fundamental aspects of spectral methods are introduced. Recent developments in spectral methods are reviewed with an emphasis on collocation techniques. Their applications to both compressible and incompressible flows, to viscous as well as inviscid flows, and also to chemically reacting flows are surveyed. The key role that these methods play in the simulation of stability, transition, and turbulence is brought out. A perspective is provided on some of the obstacles that prohibit a wider use of these methods, and how these obstacles are being overcome.

Hussaini, M. Y.↗
NASA NTRS1986

A spectral multidomain method for the solution of hyperbolic systems

A multidomain Chebyshev spectral collocation method for solving hyperbolic partial differential equations were developed. Though spectral methods are global methods, an attractive idea is to break a computational domain into several domains, and a way to handle the interfaces is described. The multidomain approach offers advantages over the use of a single Chebyshev grid. It allows complex geometries to be covered, and local refinement can be used to resolve important features. For steady state problems it reduces the stiffness associated with the use of explicit time integration as a relaxation scheme. Furthermore, the proposed method remains spectrally accurate. Results showing performance of the method on one dimensional linear models and one and two dimensional nonlinear gas dynamics problems are presented.

Kopriva, D.↗
NASA NTRS1985

Controller design and parameter identifiability studies for a large space antenna

The problem of control systems synthesis and parameter identifiability are considered for a large, space-based antenna. Two methods are considered for control system synthesis, the first of which uses torque actuators and collocated attitude and rate sensors, and the second method is based on the linear-quadratic-Gaussian (LQG) control theory. The predicted performance obtained by computing variances of pointing, surface and feed misalignment errors in the presence of sensor noise indicates that the LQG-based controller yields superior results. Since controller design requires the knowledge of the system parameters, the identifiability of the structural parameters is investigated by obtaining Cramer-Rao lower bounds. The modal frequencies are found to have the best identifiability, followed by damping ratios, and mode-slopes.

Joshi, S. M.↗
NASA NTRS1985

Analysis of an externally radially crack ring segment subject to three-point radial loading

The boundary collocation method was used to generate Mode I stress intensity and crack mouth opening displacement coefficients for externally radially (through-the-thickness) cracked ring segments subjected to three-point radial loading. Numerical results were obtained for ring segment outer-to-inner radius ratios (Ro/Ri) 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 Ro/Ri and a/W as well as the included angle between the directions of the reaction forces.

Gross, B.↗
NASA NTRS1985

The Dugdale model for compact specimen

Plastic zone size and crack tip opening displacement (CTOD) equations were developed. Boundary collocation analyses were used to analyze the compact specimen subjected to various loading conditions (pin loads, concentrated forces, and uniform pressure acting on the crack surface). Stress intensity factor and crack surface displacement equations for some of these loadings were developed and used to obtain the Dugdale model. The results from the equations for plastic zone size and CTOD agreed well with numerical values calculated by Terada for crack length to width ratios greater than 0.4.

Mall, S.↗
NASA NTRS1986

New algorithms for microwave measurements of ocean winds Applications to Seasat and the special sensor microwave imager

Improved second generation wind algorithms are used to process the three month Seasat SMMR and SASS data sets. The new algorithms are derived without using in situ anemometer measurements. All known biases in the sensors prime measurements are removed, and the algorithms prime model functions are internally self-consistent. The computed SMMR and SASS winds are collocated and compared on a 10 km cell-by-cell basis, giving a total of 115444 wind comparisons. The comparisons are done using three different sets of SMMR channels. When the 6.6H SMMR channel is used for wind retrieval, the SMMR and SASS winds agree to within 1.3 m/s over the SASS primary swath. At nadir where the radar cross section is less sensitive to wind, the agreement degrades to 1.9 m/s. The agreement is very good for winds from 0 to 15 m/s. Above 15 m/s, the off-nadir SASS winds are consistently lower than the SMMR winds, while at nadir the high SASS winds are greater than SMMR's. When 10.7H is used for the SMMR wind channel, the SMMR/SASS wind comparisons are not quite as good. When the frequency of the wind channel is increased to 18 GHz, the SMMR/SASS agreement substantially degrades to about 5 m/S.

Wentz, F. J.↗
NASA NTRS1986

Attitude control system synthesis for the Hoop/Column antenna using the LQG/LTR method

This paper investigates the application of the linear-quadratic-Gaussian (LQG)/loop transfer recovery (LTR) method to the problem of synthesizing a fine-pointing control system for a large flexible space anenna. The study is based on an antenna, which consists of three rigid-body rotational modes and the first ten elastic modes. A robust compensator design for achieving the required pointing performance in the presence of modeling uncertainties is obtained using the LQG/LTR method. For the Hoop/Column antenna, a satisfactory controller design meeting a desired bandwidth of .1 rad/sec and ensuring stability with unmodelled high frequency modes is obtained using only a collocated pair of 3-axis attitude sensors and torque actuators. This study also indicates that to achieve the desired performance bandwidth of 0.1 rad/sec. and to ensure stability in the presence of higher frequency elastic modes, the design model should include at least the first three flexible modes together with the rigid body modes.

Sundararajan, N.↗
NASA NTRS1986

Thermohydrodynamic analysis for laminar lubricating films

A Galerkin-type analysis to include thermal effects in laminar lubricating films was performed. The lubricant properties were assumed constant except for a temperature-dependent Newtonian viscosity. The cross-film temperature profile is established by collocation at the film boundaries and two interior Lobatto points. The interior temperatures are determined by requiring that the zeroth and first moment of the energy equation be satisfied across the film. The fluidity is forced to conform to a third--degree polynomial appropriate to the Lobatto-point temperatures. Preliminary indications are that the use of just two such sampling points enables satisfactory prediction of bearing performance even in the presence of substantial viscosity variation.

Elrod, H. G.↗
NASA NTRS1986

Finite length effects in Taylor-Couette flow

Axisymmetric numerical solutions of the unsteady Navier-Stokes equations for flow between concentric rotating cyclinders of finite length are obtained by a spectral collocation method. These representative results pertain to two-cell/one-cell exchange process, and are compared with recent experiments.

Streett, C. L.↗
NASA NTRS1987

Improving the geological interpretation of magnetic and gravity satellite anomalies

Quantitative analysis of the geologic component of observed satellite magnetic and gravity fields requires accurate isolation of the geologic component of the observations, theoretically sound and viable inversion techniques, and integration of collateral, constraining geologic and geophysical data. A number of significant contributions were made which make quantitative analysis more accurate. These include procedures for: screening and processing orbital data for lithospheric signals based on signal repeatability and wavelength analysis; producing accurate gridded anomaly values at constant elevations from the orbital data by three-dimensional least squares collocation; increasing the stability of equivalent point source inversion and criteria for the selection of the optimum damping parameter; enhancing inversion techniques through an iterative procedure based on the superposition theorem of potential fields; and modeling efficiently regional-scale lithospheric sources of satellite magnetic anomalies. In addition, these techniques were utilized to investigate regional anomaly sources of North and South America and India and to provide constraints to continental reconstruction. Since the inception of this research study, eleven papers were presented with associated published abstracts, three theses were completed, four papers were published or accepted for publication, and an additional manuscript was submitted for publication.

Hinze, William J.↗
NASA NTRS1986

Generalized INF-SUP condition for Chebyshev approximation of the Navier-Stokes equations

An abstract mixed problem and its approximation are studied; both are well-posed if and only if several inf-sup conditions are satisfied. These results are applied to a spectral Galerkin method for the Stokes problem in a square, when it is formulated in Chebyshev weighted Sobolev spaces. Finally, a collocation method for the Navier-Stokes equations at Chebyshev nodes is analyzed.

Bernardi, Christine↗
NASA NTRS1986

A practical assessment of spectral accuracy for hyperbolic problems with discontinuities

Physical and transform space filtering has been applied to the Fourier spectral collocation solution of the constant coefficient scalar wave equation with a discontinuous initial condition. High order accuracy can be extracted from the unfiltered solution. Smooth, high order Fourier space filtering gives expected polynomial order solutions away from the discontinuity. Spectral accuracy is observed with the physical space filter of Gottlieb and Tadmor.

Kopriva, David A.↗
NASA NTRS1987

Toward the large-eddy simulations of compressible turbulent flows

New subgrid-scale models for the large-eddy simulation of compressible turbulent flows are developed based on the Favre-filtered equations of motion for an ideal gas. A compressible generalization of the linear combination of the Smagorinsky model and scale-similarity model (in terms of Favre-filtered fields) is obtained for the subgrid-scale stress tensor. An analogous thermal linear combination model is also developed for the subgrid-scale heat flux vector. The three dimensionless constants associated with these subgrid-scale models are obtained by correlating with the results of direct numerical simulations of compressible isotropic turbulence performed on a 96 to the third power grid using Fourier collocation methods. Extensive comparisons between the direct and modeled subgrid-scale fields are provided in order to validate the models. Future applications of these compressible subgrid-scale models to the large-eddy simulation of supersonic aerodynamic flows are discussed briefly.

Erlebacher, G.↗
NASA NTRS1987

A new approach for vibration control in large space structures

An approach for augmenting vibration damping characteristics in space structures with large panels is presented. It is based on generation of bending moments rather than forces. The moments are generated using bimetallic strips, suitably mounted at selected stations on both sides of the large panels, under the influence of differential solar heating, giving rise to thermal gradients and stresses. The collocated angular velocity sensors are utilized in conjunction with mini-servos to regulate the control moments by flipping the bimetallic strips. A simple computation of the rate of dissipation of vibrational energy is undertaken to assess the effectiveness of the proposed approach.

Kumar, K.↗