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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Exact Integrations of Polynomials and Symmetric Quadrature Formulas over Arbitrary Polyhedral Grids

This paper is concerned with two important elements in the high-order accurate spatial discretization of finite volume equations over arbitrary grids. One element is the integration of basis functions over arbitrary domains, which is used in expressing various spatial integrals in terms of discrete unknowns. The other consists of quadrature approximations to those integrals. Only polynomial basis functions applied to polyhedral and polygonal grids are treated here. Non-triangular polygonal faces are subdivided into a union of planar triangular facets, and the resulting triangulated polyhedron is subdivided into a union of tetrahedra. The straight line segment, triangle, and tetrahedron are thus the fundamental shapes that are the building blocks for all integrations and quadrature approximations. Integrals of products up to the fifth order are derived in a unified manner for the three fundamental shapes in terms of the position vectors of vertices. Results are given both in terms of tensor products and products of Cartesian coordinates. The exact polynomial integrals are used to obtain symmetric quadrature approximations of any degree of precision up to five for arbitrary integrals over the three fundamental domains. Using a coordinate-free formulation, simple and rational procedures are developed to derive virtually all quadrature formulas, including some previously unpublished. Four symmetry groups of quadrature points are introduced to derive Gauss formulas, while their limiting forms are used to derive Lobatto formulas. Representative Gauss and Lobatto formulas are tabulated. The relative efficiency of their application to polyhedral and polygonal grids is detailed. The extension to higher degrees of precision is discussed.

Liu, Yen↗
NASA NTRS1997

The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems

In this paper, we study the Local Discontinuous Galerkin methods for nonlinear, time-dependent convection-diffusion systems. These methods are an extension of the Runge-Kutta Discontinuous Galerkin methods for purely hyperbolic systems to convection-diffusion systems and share with those methods their high parallelizability, their high-order formal accuracy, and their easy handling of complicated geometries, for convection dominated problems. It is proven that for scalar equations, the Local Discontinuous Galerkin methods are L(sup 2)-stable in the nonlinear case. Moreover, in the linear case, it is shown that if polynomials of degree k are used, the methods are k-th order accurate for general triangulations; although this order of convergence is suboptimal, it is sharp for the LDG methods. Preliminary numerical examples displaying the performance of the method are shown.

Cockburn, Bernardo↗
NASA NTRS1997

Conflict Detection and Resolution for Future Air Transportation Management

With a Free Flight policy, the emphasis for air traffic control is shifting from active control to passive air traffic management with a policy of intervention by exception. Aircraft will be allowed to fly user preferred routes, as long as safety Alert Zones are not violated. If there is a potential conflict, two (or more) aircraft must be able to arrive at a solution for conflict resolution without controller intervention. Thus, decision aid tools are needed in Free Flight to detect and resolve conflicts, and several problems must be solved to develop such tools. In this report, we analyze and solve problems of proximity management, conflict detection, and conflict resolution under a Free Flight policy. For proximity management, we establish a system based on Delaunay Triangulations of aircraft at constant flight levels. Such a system provides a means for analyzing the neighbor relationships between aircraft and the nearby free space around air traffic which can be utilized later in conflict resolution. For conflict detection, we perform both 2-dimensional and 3-dimensional analyses based on the penetration of the Protected Airspace Zone. Both deterministic and non-deterministic analyses are performed. We investigate several types of conflict warnings including tactical warnings prior to penetrating the Protected Airspace Zone, methods based on the reachability overlap of both aircraft, and conflict probability maps to establish strategic Alert Zones around aircraft.

Krozel, Jimmy↗
NASA NTRS1997

RIACS

Topics considered include: high-performance computing; cognitive and perceptual prostheses (computational aids designed to leverage human abilities); autonomous systems. Also included: development of a 3D unstructured grid code based on a finite volume formulation and applied to the Navier-stokes equations; Cartesian grid methods for complex geometry; multigrid methods for solving elliptic problems on unstructured grids; algebraic non-overlapping domain decomposition methods for compressible fluid flow problems on unstructured meshes; numerical methods for the compressible navier-stokes equations with application to aerodynamic flows; research in aerodynamic shape optimization; S-HARP: a parallel dynamic spectral partitioner; numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains; application of high-order shock capturing schemes to direct simulation of turbulence; multicast technology; network testbeds; supercomputer consolidation project.

Oliger, Joseph↗
NASA NTRS1998

A Discontinuous Galerkin Finite Element Method for Hamilton-Jacobi Equations

In this paper, we present a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the Runge-Kutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method.

Hu, Changqing↗
NASA NTRS1998

Comments on the Diffusive Behavior of Two Upwind Schemes

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and locally one-dimensional finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2.5 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a speedup of 29 over finite volume.

Wood, William A.↗
NASA NTRS1998

Analyzing Space-Based Interferometric Measurements of Stars and Network Measurements of Gamma-Ray Bursts

Since the announcement of the discovery of sources of bursts of gamma-ray radiation in 1973, hundreds more reports of such bursts have now been published. Numerous artificial satellites have been equipped with gamma-ray detectors including the very successful Compton Gamma Ray Observatory BATSE instrument. Unfortunately, we have made no progress in identifying the source(s) of this high energy radiation. We suspected that this was a consequence of the method used to define gamma-ray burst source "error boxes." An alternative procedure to compute gamma-ray burst source positions, with a purely physical underpinning, was proposed in 1988 by Taff. Since then we have also made significant progress in understanding the analytical nature of the triangulation problem and in computing actual gamma-ray burst positions and their corresponding error boxes. For the former, we can now mathematically illustrate the crucial role of the area occupied by the detectors, while for the latter, the Atteia et al. (1987) catalog has been completely re-reduced. There are very few discrepancies in locations between our results and those of the customary "time difference of arrival" procedure. Thus, we have numerically demonstrated that the end result, for the positions, of these two very different-looking procedures is the same. Finally, for the first time, we provide a sample of realistic "error boxes" whose non-simple shapes vividly portray the difficulty of burst source localization.

Taff, L. G.↗
NASA NTRS1999

Time-Frequency Analysis of the Dispersion of Lamb Modes

Accurate knowledge of the velocity dispersion of Lamb modes is important for ultrasonic nondestructive evaluation methods used in detecting and locating flaws in thin plates and in determining their elastic stiffness coefficients. Lamb mode dispersion is also important in the acoustic emission technique for accurately triangulating the location of emissions in thin plates. In this research, the ability to characterize Lamb mode dispersion through a time-frequency analysis (the pseudo-Wigner-Ville distribution) was demonstrated. A major advantage of time-frequency methods is the ability to analyze acoustic signals containing multiple propagation modes, which overlap and superimpose in the time domain signal. By combining time-frequency analysis with a broadband acoustic excitation source, the dispersion of multiple Lamb modes over a wide frequency range can be determined from as little as a single measurement. In addition, the technique provides a direct measurement of the group velocity dispersion. The technique was first demonstrated in the analysis of a simulated waveform in an aluminum plate in which the Lamb mode dispersion was well known. Portions of the dispersion curves of the AO, A I , So, and S2 Lamb modes were obtained from this one waveform. The technique was also applied for the analysis of experimental waveforms from a unidirectional graphite/epoxy composite plate. Measurements were made both along and perpendicular to the fiber direction. In this case, the signals contained only the lowest order symmetric and antisymmetric modes. A least squares fit of the results from several source to detector distances was used. Theoretical dispersion curves were calculated and are shown to be in good agreement with experimental results.

Prosser, W. H.↗
NASA NTRS1997

Ulysses and WIND simultaneous observations of the radio emission associated with the 6-7 January 1997 coronal mass ejection

The three dimensional source location of interplanetary type 2 radio bursts is intended to be determined from two spacecraft observations, performed by the radio receivers onboard the WIND and Ulysses spacecraft and associated with the interplanetary coronal mass ejection detected by the large advanced spectrometer coronagraph (LASCO) from the SOHO spacecraft. The intensity time profiles recorded by WIND and Ulysses were compared and their directivity is found to vary from one component of radio emission to another. The three dimensional location was obtained by radio triangulation and was deduced from the direction measured at WIND and the difference of the arrival times measured at both spacecraft. The sensitivity of both determination methods to wave scattering and refraction was discussed.

Hoang, S.↗
NASA NTRS1998

The Ulysses Supplement to the BATSE 3B Catalog of Cosmic Gamma-Ray Bursts

We present Interplanetary Network Localization information for 219 gamma-ray burst of the 3rd BATSE catalog, obtained by analyzing the arrival times of these bursts at the Ulysses and Compton Gamma Ray Observatory (CGRO) spacecraft. For any given burst observed by these two spacecraft, arrival time analysis (triangulation) results in an annulus of possible arrival directions whose width varies between 7 arcseconds and 32 arcminutes, depending on the intensity and time history of the burst, and the distance of the Ulysses spacecraft from Earth. This annulus generally intersects the BATSE error circle, resulting in an average reduction of the error box area by a factor of 30.

Hurley, K.↗
NASA NTRS1998

The Ulysses Supplement to the BATSE 4B Catalog of Cosmic Gamma-Ray Bursts

We present Interplanetary Network Localization information for 150 gamma-ray bursts observed by the Burst and Transient Source Experiment(BATSE) between the end of the 3rd BATSE catalog and the end of the 4th BATSE catalog obtained by analyzing the arrival times of these bursts at the Ulysses and Compton Gamma Ray Observatory (CGRO) spacecraft. For any given burst observed by these two spacecraft, arrival time analysis (triangulation) results in an annulus of possible arrival directions whose width varies between 7 arcseconds and 2.3 degrees, depending on the intensity and time history of the burst, and the distance of the Ulysses spacecraft from Earth. This annulus generally intersects the BATSE error circle, resulting in an average reduction of the error box area by a factor of 25.

Hurley, K.↗
NASA NTRS1998

SGR 1900+14

SGR 1900+14 soft gamma-ray repeater has entered an extraordinary new phase of activity with a previously unobserved frequency and intensity of bursts. Activity began on May 26 and has continued at least through May 30. Triangulation with Ulysses and BATSE gives a preliminary annulus whose center is at R.A. = 2lh58ml8s, Decl. = -11ol8'.4 (equinox 2000.0), and whose radius is 47.269 +/- 0.019 deg. This annulus includes the network synthesis error box (Hurley et al. 1994, Ap.J. 431, L31), the ROSAT source proposed as a possible quiescent x-ray counterpart to the soft repeater, and the peculiar double M star system coincident with the ROSAT source. As all these locations are mutually consistent, we conclude that the ROSAT source and M star system are indeed the counterparts to the soft gamma-ray repeater, and urge that observations at other wavelengths be undertaken immediately, while the source remains active. An image may be found at http://ssl.berkeley.edu/ipn3/sgrl9OO+l4/. On May 30, BATSE triggered on an extremely intense outburst from this source that comprised at least 38 bursts of varying intensity and duration; the series of bursts started at May 30.37759 UT and lasted for about 350 s. The peak flux of each of the three major bursts in the series is 1.1 x lOE-4 erg cmE-2 sE-1 (between 25 and 300 keV, integrated for 128 ms). Assuming a distance of about 12 kpc for SGR 1900+14, this corresponds to a luminosity of about 2 X 10(exp 42) ergs / second for each burst. This bunching of emission is very similar to the behavior of SGR 1806-20 as detected with the Rossi X-ray Timing explorer in 1996. Overall, between May 26 and June 1, we have detected over 50 bursts from SGR 1900+4. The frequency and intensity of emissions are unlike any previously seen behavior from this source. Follow-up observations at infrared and radio wavelengths, while the source is still active are encouraged.

Hurley, K.↗
NASA NTRS1999

A Search for Simultaneous Optical Counterparts of Gamma-Ray Bursts (LOTIS: Livermore Optical Transient Imaging System)

Under this grant the UC Berkeley PI, K. Hurley, joined the LOTIS collaboration. His task was to provide precise localization data on cosmic gamma-ray bursts, so that the LOTIS automated camera data could be searched more efficiently for evidence of optical emission from gamma-ray burst sources. This was accomplished. A program is now in place which automatically sends Interplanetary Network data on bursts via e-mail to H.S. Park, for every burst detected by the GRB experiment aboard the Ulysses spacecraft (for which K. Hurley is the P.I.). The data consist either of triangulation annuli (obtained when just two spacecraft observe the burst) or error boxes (when three widely separated spacecraft observe it). These define a locus of possible burst positions. The annuli intersect the large error circles of the CGRO-BATSE experiment, and reduce their areas by a factor of approximately 25 or more. The error boxes reduce the areas by factors of several hundred. This in turn reduces the area which must be searched for an optical counterpart. No such counterparts have been observed to date by the LOTIS experiment, but several interesting upper limits have been obtained.

Park, H.-S.↗
NASA NTRS1992

Error Analysis of Combined Optical-Flow and Stereo Passive Ranging

The motion of an imaging sensor causes each imaged point of the seem to describe a time trajectory on the image plane. The trajectories of all imaged points are reminiscent of a flow (eg, of liquid) which is the source of the term "optical flow". Optical-flow ranging is a method by which the stream of two-dimensional images obtained from a forward-looking forward-moving passive sensor is used to compute range to points in the field of view. Another well-known ranging method consists of triangulation based on stereo images obtained from at least two stationary sensors. In this paper we analyze the potential accuracies of a combined optical flow and stereo passive-ranging system in the context of helicopter nap-of-the-earth obstacle avoidance. The Cramer-Rao lower bound (CRLB) is developed for the combined system under the assumption of a random angular misalignment common to both cameras of a stereo pair. It is shown that the range accuracy degradations caused by misalignment is negligible for a combined optical-flow and stereo system as compared with a monocular optical-flow system.

Barniv, Yair↗
NASA NTRS1999

Ames Optimized TCA Configuration

Configuration design at Ames was carried out with the SYN87-SB (single block) Euler code using a 193 x 49 x 65 C-H grid. The Euler solver is coupled to the constrained (NPSOL) and the unconstrained (QNMDIF) optimization packages. Since the single block grid is able to model only wing-body configurations, the nacelle/diverter effects were included in the optimization process by SYN87's option to superimpose the nacelle/diverter interference pressures on the wing. These interference pressures were calculated using the AIRPLANE code. AIRPLANE is an Euler solver that uses a unstructured tetrahedral mesh and is capable of computations about arbitrary complete configurations. In addition, the buoyancy effects of the nacelle/diverters were also included in the design process by imposing the pressure field obtained during the design process onto the triangulated surfaces of the nacelle/diverter mesh generated by AIRPLANE. The interference pressures and nacelle buoyancy effects are added to the final forces after each flow field calculation. Full details of the (recently enhanced) ghost nacelle capability are given in a related talk. The pseudo nacelle corrections were greatly improved during this design cycle. During the Ref H and Cycle 1 design activities, the nacelles were only translated and pitched. In the cycle 2 design effort the nacelles can translate vertically, and pitch to accommodate the changes in the lower surface geometry. The diverter heights (between their leading and trailing edges) were modified during design as the shape of the lower wing changed, with the drag of the diverter changing accordingly. Both adjoint and finite difference gradients were used during optimization. The adjoint-based gradients were found to give good direction in the design space for configurations near the starting point, but as the design approached a minimum, the finite difference gradients were found to be more accurate. Use of finite difference gradients was limited by the CPU time limit available on the Cray machines. A typical optimization run using finite difference gradients can use only 30 to 40 design variables and one optimization iteration within the 8 hour queue limit for the chosen grid size and convergence level. The efficiency afforded by the adjoint method allowed for 50-120 design variables and 5-10 optimization iterations in the 8 hour queue. Geometric perturbations to the wing and fuselage were made using the Hicks/Henne (HH) shape functions. The HH functions were distributed uniformly along the chords of the wing defining sections and lofted linearly. During single-surface design, constraints on thickness and volume at selected wing stations were imposed. Both fuselage camber and cross-sectional area distributions were permitted to change during design. The major disadvantage to the use of these functions is the inherent surface waviness produced by repeated use of such functions. Many smoothing operations were required following optimization runs to produce a configuration with reasonable smoothness. Wagner functions were also used on the wing sections but were never used on the fuselage. The Wagner functions are a family of increasingly oscillatory functions that have also been used extensively in airfoil design. The leading and trailing edge regions of the wing were designed by use of polynomial and monomial functions respectively. Twist was attempted but was abandoned because of little performance improvement available from changing the baseline twist.

Cliff, Susan E.↗
NASA NTRS2000

SIM Configuration Evolution

The Space Interferometry Mission (SIM) is a space-based 10 m baseline Michelson interferometer. Planned for launch in 2005 aboard a Delta III launch vehicle, or equivalent, its primary objective is to measure the positions of stars and other celestial objects with an unprecedented accuracy of 4 micro arc seconds. With such an instrument, tremendous advancement can be expected in our understanding of stellar and galactic dynamics. Using triangulation from opposite sides of the orbit around the sun (i.e. by using parallax) one can measure the distance to any observable object in our galaxy. By directly measuring the orbital wobble of nearby stars, the mass and orbit of planets can be determined over a wide range of parameters. The distribution of velocity within nearby galaxies will be measurable. Observations of these and other objects will improve the calibration of distance estimators by more than an order of magnitude. This will permit a much better determination of the Hubble Constant as well as improving our overall understanding of the evolution of the universe. SIM has undergone several transformations, especially over the past year and a half since the start of Phase A. During this phase of a project, it is desirable to perform system-level trade studies, so the substantial evolution of the design that has occurred is quite appropriate. Part of the trade-off process has addressed two major underlying architectures: SIM Classic; and Son of SIM. The difference between these two architectures is related to the overall arrangement of the optical elements and the associated metrology system. Several different configurations have been developed for each architecture. Each configuration is the result of design choices that are influenced by many competing considerations. Some of the more important aspects will be discussed. The Space Interferometry Mission has some extremely challenging goals: millikelvin thermal stability, nanometer stabilization of optics, picometer measurement of wavefront, and others. In order to meet these goals, a significant amount of technological development is required. Although there has been a program operating for about a decade developing technologies specifically to address the challenges of space-based interferometry, there still remains a tremendous effort to achieve the incredible accuracy required of SIM. The projected viability of some of these areas has influenced design choices during the evolution of the many configurations that have been developed. For instance, the perceived complexity of the IR laser metrology system used to measure and control the positions of key optical elements was the strongest discriminator between the two architectures, and led to a decision to select SOS rather than Classic in early 1998. More recently, an appreciation of the sensitivity to beam-walk within the SOS architecture is forcing a reconsideration of that decision. At the time of submission of this abstract, there is some hope that a full-aperture metrology system may alleviate this issue. In addition to describing the current configuration of SIM, the influence of a few selected areas on the evolution of the configuration will be discussed.

Aaron, Kim M.↗
NASA NTRS2000

Preliminary Study of a Model Rotor in Descent

Within a program designed to develop experimental techniques for measuring the trajectory and structure of vortices trailing from the tips of rotor blades, the present preliminary study focuses on a method for quantifying the trajectory of the trailing vortex during descent flight conditions. This study also presents rotor loads and blade surface pressures for a range of tip-path plane angles and Mach numbers. Blade pressures near the leading edge and along the outer radius are compared with data obtained on the same model rotor, but in open jet facilities. A triangulation procedure based on two directable laser-light sheets, each containing an embedded reference, proved effective in defining the spatial coordinates of the trailing vortex. When interrogating a cross section of the flow that contains several trailing vortices, the greatest clarity was found to result when the flow is uniformly seeded. Surface pressure responses during blade-vortex interactions appeared equally sensitive near the leading edge and along the outer portion of the blade, but diminished rapidly as the distance along the blade chord increased. The pressure response was virtually independent of whether the tip-path plane angle was obtained through shaft tilt or cyclic pitch. Although the shape and frequency of the pressure perturbations on the advancing blade during blade-vortex interaction are similar to those obtained in open-jet facilities, the angle of the tip-path plane may need to be lower than the range covered in this study.

McAlister, K. W.↗
NASA NTRS2001

Using Minimum-Surface Bodies for Iteration Space Partitioning

A number of known techniques for improving cache performance in scientific computations involve the reordering of the iteration space. Some of these reorderings can be considered as coverings of the iteration space with the sets having good surface-to-volume ratio. Use of such sets reduces the number of cache misses in computations of local operators having the iteration space as a domain. We study coverings of iteration spaces represented by structured and unstructured grids. For structured grids we introduce a covering based on successive minima tiles of the interference lattice of the grid. We show that the covering has good surface-to-volume ratio and present a computer experiment showing actual reduction of the cache misses achieved by using these tiles. For unstructured grids no cache efficient covering can be guaranteed. We present a triangulation of a 3-dimensional cube such that any local operator on the corresponding grid has significantly larger number of cache misses than a similar operator on a structured grid.

Frumlin, Michael↗