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NASA NTRS1995

A conservative staggered-grid Chebyshev multidomain method for compressible flows

We present a new multidomain spectral collocation method that uses staggered grids for the solution of compressible flow problems. The solution unknowns are defined at the nodes of a Gauss quadrature rule. The fluxes are evaluated at the nodes of a Gauss-Lobatto rule. The method is conservative, free-stream preserving, and exponentially accurate. A significant advantage of the method is that subdomain corners are not included in the approximation, making solutions in complex geometries easier to compute.

Kopriva, David A.↗
NASA NTRS1995

A class of stabilizing controllers for flexible multibody systems

The problem of controlling a class of nonlinear multibody flexible space systems consisting of a flexible central body to which a number of articulated appendages are attached is considered. Collocated actuators and sensors are assumed, and global asymptotic stability of such systems is established under a nonlinear dissipative control law. The stability is shown to be robust to unmodeled dynamics and parametric uncertainties. For a special case in which the attitude motion of the central body is small, the system, although still nonlinear, is shown to be stabilized by linear dissipative control laws. Two types of linear controllers are considered: static dissipative (constant gain) and dynamic dissipative. The static dissipative control law is also shown to provide robust stability in the presence of certain classes of actuator and sensor nonlinearities and actuator dynamics. The results obtained for this special case can also be readily applied for controlling single-body linear flexible space structures. For this case, a synthesis technique for the design of a suboptimal dynamic dissipative controller is also presented. The results obtained in this paper are applicable to a broad class of multibody and single-body systems such as flexible multilink manipulators, multipayload space platforms, and space antennas. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems.

Joshi, Suresh M.↗
NASA NTRS1995

Spectral methods on arbitrary grids

Stable and spectrally accurate numerical methods are constructed on arbitrary grids for partial differential equations. These new methods are equivalent to conventional spectral methods but do not rely on specific grid distributions. Specifically, we show how to implement Legendre Galerkin, Legendre collocation, and Laguerre Galerkin methodology on arbitrary grids.

Carpenter, Mark H.↗
NASA NTRS1995

Fuzzy logic techniques for rendezvous and docking of two geostationary satellites

Large assemblings in space require the ability to manage rendezvous and docking operations. In future these techniques will be required for the gradual build up of big telecommunication platforms in the geostationary orbit. The paper discusses the use of fuzzy logic to model and implement a control system for the docking/berthing of two satellites in geostationary orbit. The system mounted in a chaser vehicle determines the actual state of both satellites and generates torques to execute maneuvers to establish the structural latching. The paper describes the proximity operations to collocate the two satellites in the same orbital window, the fuzzy guidance and navigation of the chaser approaching the target and the final Fuzzy berthing. The fuzzy logic system represents a knowledge based controller that realizes the close loop operations autonomously replacing the conventional control algorithms. The goal is to produce smooth control actions in the proximity of the target and during the docking to avoid disturbance torques in the final assembly orbit. The knowledge of the fuzzy controller consists of a data base of rules and the definitions of the fuzzy sets. The knowledge of an experienced spacecraft controller is captured into a set of rules forming the Rules Data Base.

Ortega, Guillermo↗
NASA NTRS1992

Analysis of stresses in finite anisotropic panels with centrally located cutouts

A method for analyzing biaxial- and shear-loaded anisotropic rectangular panels with centrally located circular and elliptical cutouts is presented in the present paper. The method is based on Lekhnitskii's complex variable equations of plane elastostatics combined with a boundary collocation method and a Laurent series approximation. Results are presented for anisotropic panels with elliptical cutouts and subjected to combined shear and compression loading. The effects on the stress field of panel aspect ratio, anisotropy, cutout size, and cutout orientation are addressed. Angle-ply laminates, unidirectional off-axis laminates, and ((+ or - 45/0/90)(sub 3))s, ((+ or - 45/0(sub 2))(sub 3))s, and ((+ or - 45/90(sub 2))(sub 3))s laminates are examined.

Britt, Vicki O.↗
NASA NTRS1995

Efficient modeling of interconnects and capacitive discontinuities in high-speed digital circuits

Modeling of interconnects and associated discontinuities with the recent advances high-speed digital circuits has gained a considerable interest over the last decade although the theoretical bases for analyzing these structures were well-established as early as the 1960s. Ongoing research at the present time is focused on devising methods which can be applied to more general geometries than the ones considered in earlier days and, at the same time, improving the computational efficiency and accuracy of these methods. In this thesis, numerically efficient methods to compute the transmission line parameters of a multiconductor system and the equivalent capacitances of various strip discontinuities are presented based on the quasi-static approximation. The presented techniques are applicable to conductors embedded in an arbitrary number of dielectric layers with two possible locations of ground planes at the top and bottom of the dielectric layers. The cross-sections of conductors can be arbitrary as long as they can be described with polygons. An integral equation approach in conjunction with the collocation method is used in the presented methods. A closed-form Green's function is derived based on weighted real images thus avoiding nested infinite summations in the exact Green's function; therefore, this closed-form Green's function is numerically more efficient than the exact Green's function. All elements associated with the moment matrix are computed using the closed-form formulas. Various numerical examples are considered to verify the presented methods, and a comparison of the computed results with other published results showed good agreement.

Oh, K. S.↗
NASA NTRS1995

An efficient numerical procedure for thermohydrodynamic analysis of cavitating bearings

An efficient and accurate numerical procedure to determine the thermo-hydrodynamic performance of cavitating bearings is described. This procedure is based on the earlier development of Elrod for lubricating films, in which the properties across the film thickness are determined at Lobatto points and their distributions are expressed by collocated polynomials. The cavitated regions and their boundaries are rigorously treated. Thermal boundary conditions at the surfaces, including heat dissipation through the metal to the ambient, are incorporated. Numerical examples are presented comparing the predictions using this procedure with earlier theoretical predictions and experimental data. With a few points across the film thickness and across the journal and the bearing in the radial direction, the temperature profile is very well predicted.

Vijayaraghavan, D.↗
NASA NTRS1994

Three-dimensional fully spectral numerical method for mantle convection with depth-dependent properties

A semi-implicit fully spectral collocation method for the simulation of three-dimensional mantle convection with depth-dependent thermo-dynamic and transport properties is presented. The variable property Navier-Stokes equation expressed in terms of the primitive variable velocity and pressure is solved with the mass continuity and temperature equations. The periodic horizontal boundary conditions allow a Fourier expansion for the two horizontal directions. The stress-free, impermeable isothermal boundary conditions along with the depth dependent coefficients are handled with a Chebyshev expansion in the vertical direction. In the limit of an infinite Prandtl number appropriate to mantle convection, the inertial terms in the momentum equation are unimportant. In this case an explicit solution of a Poisson equation for pressure can be avoided; instead a fourth-order equation for vertical velocity can be solved. Simultaneous imposition of both impermeable and continuity boundary conditions during the vertical velocity evaluation is discussed. The pressure distributions on the top and bottom bounding planes were determined by means of an influence matrix technique. The numerical method employed here avoids time-splitting errors and enforces velocity boundary conditions and continuity over the entire domain, including the boundaries, to machine accuracy. Strongly time-dependent three-dimensional solutions up to a surface Rayleigh number of 1 x 10(exp 7) have been obtained. Strong upwellings, pulsating chaotically, are formed by the collective merging of cylindrical plumes.

Balachandar, S.↗
NASA NTRS1994

Separation of lithospheric, external, and core components of the south polar geomagnetic field at satellite altitudes

We present a new approach to producing scalar Magsat magnetic anomaly maps based on correlation coefficient filtering and the use of almost all of the available orbits. Our method differs from earlier techniques with respect to the following: (1) Passes are selected based on their variance properties rather than planetary indices such as Kp. (2) The core field model is least squares fit to individual passes and subsequently removed instead of substracting the model directly. This technique replaces band pass filtering or polynomial trend removal methods. (3) Each selected pass is sorted geographically and by local time, placed into one of four different altitude bands, and correlation coefficient filtered with the two adjacent passes. The filtering is the second step toward isolating the static lithospheric signal from the more dynamic external field signals. (4) Least squares collocation is used to grid the correlated passes; subsequently, the dawn and dusk maps are also correlation filtered providing another step toward removal of external fields. (5) The four resultant total field maps are continued to a common altitude and again correlation filtered for the static lithospheric anomalies. (6) The filtered results are then averaged together to provide a new total field map of the lithosphere south of 40 deg S latitude. Our total field map differs from previous efforts over the crustal blocks of West Antarctica. We obtained a positive anomaly over Edward VII Peninsula, extending into the Byrd subglacial basin and obtained a negative anomaly over the Ellsworth Mountains and parts of the Byrd subglacial basin. Also, a positive anomaly extending from the Ross Sea to offshore Wilkes Land is present in our map; however, this feature is absent in other maps. Positive anomalies marking the Weddell Sea in previous efforts are not present in our map. Prominent external field anomalies in the quadrant offshore of Wilkes Land are present in all previous efforts; however, these signatures are reduced in our total field map. This map significantly advances efforts for the identification and interpretation of magnetic anomalies of the south polar lithosphere.

Alsdorf, Douglas E.↗
NASA NTRS1994

Validation of a technique for estimating outgoing longwave radiation from HIRS radiance observations

Simultaneous observations by the Earth Radiation Budget Experiment (ERBE) scanning radiometer and the High-Resolution Infrared Sounder (HIRS) on board the NOAA-9 spacecraft have been used to validate a multispectral technique for estimating the outgoing longwave radiation (OLR) from the earth-atmosphere system. Results from approximately 100 000 collocated observations show that the HIRS technique provides instantaneous OLR estimates that agree with the ERBE observations just as well as different ERBE scanners agree with each other--about 5 W m(exp -2) rms. Although there are differences between the HIRS and ERBE estimates that depend upon the scene type and time of day, the HIRS technique explained more than 99% of the variance of the ERBE observations for both day and night observations. The results suggest that the HIRS OLR technique is a suitable replacement for the Advanced Very High Resolution Radiometer technique now used by the National Oceanic and Atmospheric Administration for operational estimates of the OLR.

Ellingson, Robert G.↗
NASA NTRS1994

Feasibility of sea ice typing with synthetic aperture radar (SAR): Merging of Landsat thematic mapper and ERS 1 SAR satellite imagery

Earth Remote-Sensing Satellite (ERS) 1 synthetic aperture radar (SAR) and Landsat thematic mapper (TM) images were acquired for the same area in the Beaufort Sea, April 16 and 18, 1992. The two image pairs were colocated to the same grid (25-m resolution), and a supervised ice type classification was performed on the TM images in order to classify ice free, nilas, gray ice, gray-white ice, thin first-year ice, medium and thick first-year ice, and old ice. Comparison of the collocated SAR pixels showed that ice-free areas can only be classified under calm wind conditions (less than 3 m/s) and for surface winds greater than 10 m/s based on the backscattering coefficient alone. This is true for pack ice regions during the cold months of the year where ice-free areas are spatially limited and where the capillary waves that cause SAR backscatter are dampened by entrained ice crystals. For nilas, two distinct backscatter classes were found at -17 dB and at -10 dB. The higher backscattering coefficient is attributed to the presence of frost flowers on light nilas. Gray and gray-white ice have a backscatter signature similar to first-year ice and therefore cannot be distinguished by SAR alone. First-year and old ice can be clearly separated based on their backscattering coefficient. The performance of the Geophysical Processor System ice classifier was tested against the Landsat derived ice products. It was found that smooth first-year ice and rough first-year ice were not significantly different in the backscatter domain. Ice concentration estimates based on ERS 1 C band SAR showed an error range of 5 to 8% for high ice concentration regions, mainly due to misclassified ice-free and smooth first-year ice areas. This error is expected to increase for areas of lower ice concentration. The combination of C band SAR and TM channels 2, 4, and 6 resulted in ice typing performance with an estimated accuracy of 90% for all seven ice classes.

Steffen, Konrad↗
NASA NTRS1993

An improved gravity model for Mars: Goddard Mars Model 1

Doppler tracking data of three orbiting spacecraft have been reanalyzed to develop a new gravitational field model for the planet Mars, Goddard Mars Model 1 (GMM-1). This model employs nearly all available data, consisting of approximately 1100 days of S band tracking data collected by NASA's Deep Space Network from the Mariner 9 and Viking 1 and Viking 2 spacecraft, in seven different orbits, between 1971 and 1979. GMM-1 is complete to spherical harmonic degree and order 50, which corresponds to a half-wavelength spatial resolution of 200-300 km where the data permit. GMM-1 represents satellite orbits with considerably better accuracy than previous Mars gravity models and shows greater resolution of identifiable geological structures. The notable improvement in GMM-1 over previous models is a consequence of several factors: improved computational capabilities, the use of otpimum weighting and least squares collocation solution techniques which stabilized the behavior of the solution at high degree and order, and the use of longer satellite arcs than employed in previous solutions that were made possible by improved force and measurement models. The inclusion of X band tracking data from the 379-km altitude, nnear-polar orbiting Mars Observer spacecraft should provide a significant improvement over GMM-1, particularly at high latitudes where current data poorly resolve the gravitational signature of the planet.

Smith, D. E.↗
NASA NTRS1993

Trajectory optimization based on differential inclusion

A method for generating finite-dimensional approximations to the solutions of optimal control problems is introduced. By employing a description of the dynamical system in terms of its attainable sets in favor of using differential equations, the controls are completely eliminated from the system model. Besides reducing the dimensionality of the discretized problem compared to state-of-the-art collocation methods, this approach also alleviates the search for initial guesses from where standard gradient search methods are able to converge. The mechanics of the new method are illustrated on a simple double integrator problem. The performance of the new algorithm is demonstrated on a 1-D rocket ascent problem (`Goddard Problem') in presence of a dynamic pressure constraint.

Seywald, Hans↗
NASA NTRS1994

Stratospheric aerosol acidity, density, and refractive index deduced from SAGE 2 and NMC temperature data

Water vapor concentrations obtained by the Stratospheric Aerosol and Gas Experiment 2 (SAGE 2) and collocated temperatures provided by the National Meteorological Center (NMC) from 1986 to 1990 are used to deduce seasonally and zonally averaged acidity, density, and refractive index of stratospheric aerosols. It is found that the weight percentage of sulfuric acid in the aerosols increases from about 60 just above the tropopause to about 86 at 35 km. The density increases from about 1.55 to 1.85 g/cu cm between the same altitude limits. Some seasonal variations of composition and density are evident at high latitudes. The refractive indices at 1.02, 0.694, and 0.532 micrometers increase, respectively, from about 1.425, 1.430, and 1.435 just above the tropopause to about 1.445, 1.455, and 1.458 at altitudes above 27 km, depending on the season and latitude. The aerosol properties presented can be used in models to study the effectiveness of heterogeneous chemistry, the mass loading of stratospheric aerosols, and the extinction and backscatter of aerosols at different wavelengths. Computed aerosol surface areas, rate coefficients for the heterogeneous reaction ClONO2 + H2O yields HOCl + HNO3 and aerosol mass concentrations before and after the Pinatubo eruption in June 1991 are shown as sample applications.

Yue, G. K.↗
NASA NTRS1995

Simultaneous prenoon and postnoon observations of three field-aligned current systems from Viking and DMSP-F7

The spatial structure of dayside large-scale field-aligned current (FAC) systems is examined by using Viking and Defense Meteorological Satellite Program-F7 (DMSP-F7) data. We focus on four events in which the satellites simultaneously observed postnoon and prenoon three FAC systems: the region 2, the region 1, and the mantle (referred to as midday region O) systems, from equatorward to poleward. These events provide the most solid evidence to date that the midday region O system is a separate and unique FAC system, and is not an extension of the region 1 system from other local times. The events are examined comprehensively by making use of a mulit-instrumental data set, which includes magnetic field, particle flux, electric field, auroral UV image data from the satellites, and the Sondrestrom convection data. The results are summarized as follows: (1) Region 2 currents flow mostly in the central plasma sheet (CPS) precipitation region, often overlapping with the boundary plasma sheet (BPD) at their poleward edge. (2) The region 1 system is located in the core part of the auroral oval and is confined in a relatively narrow range in latitude which includes the convection reversal. The low-latitude boundary layer, possibly including the outer part of the plasma sheet, and the external cusp are the major source regions of dayside region 1 currents. (2) Midday region O currents flow on open field lines and are collocated with the shear of antisunward convection flows with velocites decreasing poleward. On the basis of these results we support the view that both prenoon and postnoon current systems consist of the three-sheet structure when the disctortion ofthe convection pattern associated with interplanetary magnetic field (IMF) B(sub Y) is small and both morningside and eveningside convection cells are crescent-shaped. We also propose that the midday region O and a part of the region 1 systems are closely coupled to the same source.

Ohtani, S.↗
NASA NTRS1995

Four large-scale field-aligned current systmes in the dayside high-latitude region

A system of four current sheets of large-scale field-aligned currents (FACs) was discovered in the data set of simultaneous Viking and Defense Meteorological Satellire Program-F7 (DMSP-F7) crossing of the dayside high-latitude region. This paper reports four examples of this system that were observed in the prenoon sector. The flow polarities of FACs are upward, downward, upward, and downward, from equatorward to poleward. The lowest-latitude upward current is flowing mostly in the central plasma sheet (CPS) precipitation region, often overlapping with the boundary plasma sheet (BPS) at its poleward edge, andis interpreted as a region 2 current. The pair of downward and upward FACs in the middle of te structure are collocated with structured electron precipitation. The precipitation of high-energy (greater than 1 keV) electrons is more intense in the lower-latitude downward current sheet. The highest-latitude downward flowing current sheet is located in a weak, low-energy particle precipitation region, suggesting that this current is flowing on open field lines. Simulaneous observations in the postnoon local time sector reveal the standard three-sheet structure of FACs, sometimes described as region 2, region 1, and mantle (referred to the midday region O) currents. A high correlation was found between the occurrence of the four FAC sheet structure and negative interplanetary magnetic field (IMF) B(sub Y). We discuss the FAC structurein terms of three types of convection cells: the merging, viscous, andlobe cells. During strongly negative IMF B(sub Y), two convection reversals exist in the prenoon sector; one is inside the viscous cell, and the other is between the viscous cell and the lobe cell. This structure of convection flow is supported by the Viking electric field and auroral UV image data. Based on the convection pattern, the four FAC sheet structure is interpreted as the latitude overlap of midday and morning FAC systems. We suggest that the for-current sheet structure is common in a certain prenoon localtime sector during strongly negative IMF B(sub Y).

Ohtani, S.↗
NASA NTRS1995

On a generating mechanism for Yanai waves and the 25-day oscillation

A spectral Chebyshev-collocation method applied to the linear, 1.5 layer reduced-gravity ocean model equations is used to study the dynamics of Yanai (or mixed Rossby-gravity) wave packets. These are of interest because of the observations of equatorial instability waves (which have the characteristics of Yanai waves) and their role in the momentum and heat budgets in the tropics. A series of experiments is performed to investigate the generation of the waves by simple cross-equatorial wind stress forcings in various configurations and the influence of a western boundary on the waves. They may be generated in the interior ocean as well as from a western boundary. The observations from all the oceans indicate that the waves have a preferential period and wavelength of around 25 days and 1000 km respectively. These properties are also seen in the model results and a plausible explanation is provided as being due to the dispersive properties of Yanai waves.

Kelly, Brian G.↗
NASA NTRS1992

Fourier/Chebyshev methods for the incompressible Navier-Stokes equations in finite domains

A fully spectral numerical scheme for the incompressible Navier-Stokes equations in domains which are infinite or semi-infinite in one dimension. The domain is not mapped, and standard Fourier or Chebyshev expansions can be used. The handling of the infinite domain does not introduce any significant overhead. The scheme assumes that the vorticity in the flow is essentially concentrated in a finite region, which is represented numerically by standard spectral collocation methods. To accomodate the slow exponential decay of the velocities at infinity, extra expansion functions are introduced, which are handled analytically. A detailed error analysis is presented, and two applications to Direct Numerical Simulation of turbulent flows are discussed in relation with the numerical performance of the scheme.

Corral, Roque↗