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NASA NTRS1992

Grid generation and flow solution method for Euler equations on unstructured grids

A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme, which uses Delaunay triangulation, generates the field points for the mesh based on cell aspect ratios and allows clustering of grid points near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss-Seidel procedure that is completely vectorizable. Also, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for an NACA 0012 airfoil as well as a two element configuration. Flow solution results are shown for a two dimensional flow over the NACA 0012 airfoil and for a two element configuration in which the solution was obtained through an adaptation procedure and compared with an exact solution. Preliminary three dimensional results also are shown in which the subsonic flow over a business jet is computed.

Anderson, W. Kyle↗

NASA NTRS1992

Inter- and intra-plate deformation at North American plate boundaries

A geodetic network which spans the region between San Francisco and Lake Tahoe has been measured 5 times completely with triangulation in 1880, 1922, 1929, 1943, 1963. A resurvey with the Global Positioning System (GPS) in 1991 allows the formation of 1 coseismic and 4 interseismic epochs. The data from this network provide a unique opportunity to examine the temporal and spatial evolution of the strain field associated with the 1906 San Francisco earthquake in particular and with the Pacific-North American plate boundary in general. Calculations of strain rate from the network data lead to the following conclusions. (1) There is no resolvable (greater than 0.05 microradians/yr) strain in between Sutter Buttes and the Sierra Nevada. (2) Throughout the time since the 1906 earthquake, a region extending at least as far east as the westernmost Great Valley has been undergoing deformation related to Pac:Nam interaction and the associated earthquake cycle. (3) In the time and space of overlap, our results agree with those from the United States Geological Survey (USGS) trilateration data. Both data sets indicate that strain must be accumulating to the east of Vaca. (4) The San Andreas discrepancy cannot be accommodated in the Great Valley at the 1 sigma level of our results. It is possible to absorb it in that region at the 2 sigma level. (5) Strain rate is elevated in the years following the earthquake and decays slowly with time. It is possible that the rate in the Coast Ranges increases until around 1950 and then decays. With the exception of one epoch, strain rate in the Coast Ranges is consistently fault parallel, shows no sign changes, and is consistent with monotonic strain accumulation.

Beavan, John↗

NASA NTRS1991

Unstructured and adaptive mesh generation for high Reynolds number viscous flows

A method for generating and adaptively refining a highly stretched unstructured mesh suitable for the computation of high-Reynolds-number viscous flows about arbitrary two-dimensional geometries was developed. The method is based on the Delaunay triangulation of a predetermined set of points and employs a local mapping in order to achieve the high stretching rates required in the boundary-layer and wake regions. The initial mesh-point distribution is determined in a geometry-adaptive manner which clusters points in regions of high curvature and sharp corners. Adaptive mesh refinement is achieved by adding new points in regions of large flow gradients, and locally retriangulating; thus, obviating the need for global mesh regeneration. Initial and adapted meshes about complex multi-element airfoil geometries are shown and compressible flow solutions are computed on these meshes.

Mavriplis, D. J.↗

NASA NTRS1992

A composite structured/unstructured-mesh Euler method for complex airfoil shapes

A general two-dimensional Euler zonal method has been developed for computing flows about complex airfoil geometries such as multielement and iced airfoils. The method utilizes a composite structured and unstructured grid generated using conformal mapping and Delaunay triangulation, respectively. The finite-volume Euler method is then modified to couple solutions in the zones with structured and unstructured grids. Solutions about an iced airfoil and a multielement airfoil are given as examples of applications of the scheme.

Hefazi, H.↗

NASA NTRS1993

Expansion-based passive ranging

A new technique of passive ranging which is based on utilizing the image-plane expansion experienced by every object as its distance from the sensor decreases is described. This technique belongs in the feature/object-based family. The motion and shape of a small window, assumed to be fully contained inside the boundaries of some object, is approximated by an affine transformation. The parameters of the transformation matrix are derived by initially comparing successive images, and progressively increasing the image time separation so as to achieve much larger triangulation baseline than currently possible. Depth is directly derived from the expansion part of the transformation. To a first approximation, image-plane expansion is independent of image-plane location with respect to the focus of expansion (FOE) and of platform maneuvers. Thus, an expansion-based method has the potential of providing a reliable range in the difficult image area around the FOE. In areas far from the FOE the shift parameters of the affine transformation can provide more accurate depth information than the expansion alone, and can thus be used similarly to the way they were used in conjunction with the Inertial Navigation Unit (INU) and Kalman filtering. However, the performance of a shift-based algorithm, when the shifts are derived from the affine transformation, would be much improved compared to current algorithms because the shifts - as well as the other parameters - can be obtained between widely separated images. Thus, the main advantage of this new approach is that, allowing the tracked window to expand and rotate, in addition to moving laterally, enables one to correlate images over a very long time span which, in turn, translates into a large spatial baseline - resulting in a proportionately higher depth accuracy.

Barniv, Yair↗

NASA NTRS1992

Adaptive remeshing for three-dimensional compressible flow computations

A practical solution algorithm for steady 3D Euler flows is presented. This algorithm employs coupling of a surface triangulator, an automatic tetrahedral mesh generator, an unstructured grid flow solver, and an error estimation procedure. The performance of the method is illustrated using a shock interaction problem in high Mach number flow over a swept circular cylinder.

Peraire, J.↗

NASA NTRS1992

The Ulysses solar X-ray/cosmic gamma-ray burst experiment

The Ulysses X-ray and gamma-ray instrument is described, and its scientific objectives are presented. Some aspects of the history of the Ulysses mission are explained, as well as of the design considerations for this experiment. As this mission will be the most distant one from earth ever to carry a burst detector, the primary cosmic objective will be to localize gamma-burst sources by triangulation.

Hurley, Kevin↗

NASA NTRS1993

Unstructured 3D Delaunay mesh generation applied to planes, trains and automobiles

Technical issues associated with domain-tessellation production, including initial boundary node triangulation and volume mesh refinement, are presented for the 'TGrid' 3D Delaunay unstructured grid generation program. The approach employed is noted to be capable of preserving predefined triangular surface facets in the final tessellation. The capabilities of the approach are demonstrated by generating grids about an entire fighter aircraft configuration, a train, and a wind tunnel model of an automobile.

Blake, Kenneth R.↗

NASA NTRS1991

Error analysis of combined stereo/optical-flow passive ranging

The motion of an imaging sensor causes each imaged point of the scene to correspondingly describe a time trajectory on the image plane. The trajectories of all imaged points are reminiscent of a flow (e.g., 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 depth (or 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 is developed for the combined system under the assumption of an unknown angular bias error common to both cameras of a stereo pair. It is shown that the depth accuracy degradations caused by a bias error is negligible for a combined optical-flow and stereo system as compared to a monocular optical-flow system.

Barniv, Yair↗

NASA NTRS1992

Visual specification of robot motion

The authors describe the use of stereo pairs of images to specify robot motion. The experimental setup includes a SUN workstation, a PUMA 560 robot, and an Imaging 151 vision system. An X-window environment displays stereo images of the work scene. Image processing is performed to extract linear edge segments from the images and the results are displayed on screen. Using a pointing device, the user selects a group of edges from the object relevant to the task. The 3D structure of this group of features is found by stereo triangulation and they can be displayed in 3D from any point of view. A viewpoint orthogonal to the plane defined by these 3D edges is used to specify the robot position relative to object position. The actual robot will then be moved to the specified position.

Shiu, Y. C.↗

NASA NTRS1993

A multi-dimensional kinetic-based upwind solver for the Euler equations

A multidimensional kinetic fluctuation-splitting scheme has been developed for the Euler equations. The scheme is based on an N-scheme discretization of the Boltzmann equation at the kinetic level for triangulated Cartesian meshes with a diagonal-adaptive strategy. The resulting Euler scheme is a cell-vertex fluctuation-splitting scheme where fluctuations in the conserved-variable vector Q are obtained as moments of the fluctuation in the Maxwellian velocity distribution function at the kinetic level. Encouraging preliminary results have been obtained for perfect gases on Cartesian meshes with first-order spatial accuracy. The present approach represents an improvement to the well-established dimensionally-split upwind schemes.

Eppard, W. M.↗

NASA NTRS1992

Automated absolute phase retrieval in across-track interferometry

Discussed is a key element in the processing of topographic radar maps acquired by the NASA/JPL airborne synthetic aperture radar configured as an across-track interferometer (TOPSAR). TOPSAR utilizes a single transmit and two receive antennas; the three-dimensional target location is determined by triangulation based on a known baseline and two measured slant ranges. The slant range difference is determined very accurately from the phase difference between the signals received by the two antennas. This phase is measured modulo 2pi, whereas it is the absolute phase which relates directly to the difference in slant range. It is shown that splitting the range bandwidth into two subbands in the processor and processing each individually allows for the absolute phase. The underlying principles and system errors which must be considered are discussed, together with the implementation and results from processing data acquired during the summer of 1991.

Madsen, Soren N.↗

NASA NTRS1993

The cartography of Venus with Magellan data

Maps of Venus based on Magellan data are being compiled at 1:50,000,000, 1:5,000,000 and 1:1,500,000 scales. Topographic contour lines based on radar altimetry data are overprinted on the image maps, along with feature nomenclature. Map controls are based on existing knowledge of the spacecraft orbit; photogrammetric triangulation, a traditional basis for geodetic control for bodies where framing cameras were used, is not feasible with the radar images of Venus. Preliminary synthetic aperture radar (SAR) image maps have some data gaps and cosmetic inconsistencies, which will be corrected on final compilations. Eventual revision of geodetic controls and of the adopted Venusian spin-axis location will result in geometric adjustments, particularly on large-scale maps.

Kirk, R. L.↗

NASA NTRS1993

Do it yourself remote sensing: Generating an inexpensive, high tech, real science lake mapping project for the classroom

The utilization of modest equipment and software revealed bottom contours and water column conditions of a dynamic water body. Classroom discussions of field techniques and equipment capabilities followed by exercises with the data sets in cause-and-effect analysis all contributed to participatory education in the process of science. This project is presented as a case study of the value of engaging secondary and collegiate level students in planning, executing and appraising a real world investigation which they can directly relate to. A 1 km wide bay, experiencing marsh inflow, along an 8 km long lake situated 120 km north of Ottawa, Canada, on the glaciated Canadian Precambrian Shield was mapped in midsummer for submerged topography, bottom composition, temperature profile, turbudity, dissolved oxygen and biota distribution. Low level aerial photographs scanned into image processing software are permitting spatial classification of bottom variations in biology and geology. Instrumentation consisted of a portable sport fishing SONAR depth finder, an electronic lead line multiprobe with photocell, thermistor and dissolved oxygen sensors, a selective depth water sampler, portable pH meter, an underwater camera mounted on a home-made platform with a bottom-contact trigger and a disposable underwater camera for shallow survey work. Sampling transects were referenced using a Brunton hand transit triangulating several shore markers.

Metzger, Stephen M.↗

NASA NTRS1993

Topographic slope from the SAR interferometric phase gradient

A new algorithm for the direct calculation of topographic slope maps from synthetic aperture radar (SAR) interferograms is presented. The algorithm derives slope maps without first requiring the creation of a digital elevational model (DEM) from the interferogram, thus obviating the need for high SNR in the interferogram and altitude calibration points for the scene. SAR data useful for interferometry has been collected by the Active Microwave Imager on board the ERS-1 satellite, when it was in a short period repeat orbit. Two passes of the radar sensor form a cross-track interferometric baseline. For a point target at some position (x,y,h), the interferometric phase difference phi is proportional to the difference in path lengths for the two sensor positions to the scatterer. Given the phase difference as measured in the complex interferogram and an accurate baseline geometry, the position of the scatterer, most significantly the height h, can be determined through triangulation. The interferometric phase measurement however is known only modulo 2-pi, and hence it is necessary to determine the correct multiple of 2-pi to add to the phase at each point to obtain an estimate of the actual phase with respect to an absolute datum. This phase unwrapping process is required for creating DEM's, and is difficult or impossible for regions of low SNR or SAR image layover. The new algorithm described here derives slope maps without requiring phase unwrapping.

Werner, Charles L.↗

NASA NTRS1993

Unstructured surface grid generation

Viewgraphs on unstructured surface grid generation are presented. Topics covered include: requirements for curves, surfaces, solids, and text; surface approximation; triangulation; advancing; projection; mapping; and parametric curves.

Jamshid Samareh-Abolhassani↗

NASA NTRS1993

Computational geometry issues

Presented in viewgraph format are some of the benefits of computational geometry for grid generation, including benefits to grid quality and algorithm efficiency. Many efficient algorithms are available, but it is concluded that high aspect ratio triangulations are not among them.

Mary-Anne Posenau↗

NASA NTRS1993

Surface acquisition through virtual milling

Surface acquisition deals with the reconstruction of three dimensional objects from a set of data points. The most straightforward techniques require human intervention, a time consuming proposition. It is desirable to develop a fully automated alternative. Such a method is proposed in this paper. It makes use of surface measurements obtained from a 3-D laser digitizer - an instrument which provides the (x,y,z) coordinates of surface data points from various viewpoints. These points are assembled into several partial surfaces using a visibility constraint and a 2-D triangulation technique. Reconstruction of the final object requires merging these partial surfaces. This is accomplished through a procedure that emulates milling, a standard machining operation. From a geometrical standpoint the problem reduces to constructing the intersection of two or more non-convex polyhedra.

Marshal L Merriam↗