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NASA NTRS1995

Solutions of the benchmark problems by the dispersion-relation-preserving scheme

The 7-point stencil Dispersion-Relation-Preserving scheme of Tam and Webb is used to solve all the six categories of the CAA benchmark problems. The purpose is to show that the scheme is capable of solving linear, as well as nonlinear aeroacoustics problems accurately. Nonlinearities, inevitably, lead to the generation of spurious short wave length numerical waves. Often, these spurious waves would overwhelm the entire numerical solution. In this work, the spurious waves are removed by the addition of artificial selective damping terms to the discretized equations. Category 3 problems are for testing radiation and outflow boundary conditions. In solving these problems, the radiation and outflow boundary conditions of Tam and Webb are used. These conditions are derived from the asymptotic solutions of the linearized Euler equations. Category 4 problems involved solid walls. Here, the wall boundary conditions for high-order schemes of Tam and Dong are employed. These conditions require the use of one ghost value per boundary point per physical boundary condition. In the second problem of this category, the governing equations, when written in cylindrical coordinates, are singular along the axis of the radial coordinate. The proper boundary conditions at the axis are derived by applying the limiting process of r approaches 0 to the governing equations. The Category 5 problem deals with the numerical noise issue. In the present approach, the time-independent mean flow solution is computed first. Once the residual drops to the machine noise level, the incident sound wave is turned on gradually. The solution is marched in time until a time-periodic state is reached. No exact solution is known for the Category 6 problem. Because of this, the problem is formulated in two totally different ways, first as a scattering problem then as a direct simulation problem. There is good agreement between the two numerical solutions. This offers confidence in the computed results. Both formulations are solved as initial value problems. As such, no Kutta condition is required at the trailing edge of the airfoil.

Tam, Christopher K. W.↗

NASA NTRS1997

Accurate Monotonicity - Preserving Schemes With Runge-Kutta Time Stepping

A new class of high-order monotonicity-preserving schemes for the numerical solution of conservation laws is presented. The interface value in these schemes is obtained by limiting a higher-order polynominal reconstruction. The limiting is designed to preserve accuracy near extrema and to work well with Runge-Kutta time stepping. Computational efficiency is enhanced by a simple test that determines whether the limiting procedure is needed. For linear advection in one dimension, these schemes are shown as well as the Euler equations also confirm their high accuracy, good shock resolution, and computational efficiency.

Suresh, A.↗

NASA NTRS2014

A Technique for Mapping Characteristic Lengths to Preserve Energy Dissipated via Strain Softening in a Multiscale Analysis

It is often advantageous to account for the microstructure of the material directly using multiscale modeling. For computational tractability, an idealized repeating unit cell (RUC) is used to capture all of the pertinent features of the microstructure. Typically, the RUC is dimensionless and depends only on the relative volume fractions of the different phases in the material. This works well for non-linear and inelastic behavior exhibiting a positive-definite constitutive response. Although, once the material exhibits strain softening, or localization, a mesh objective failure theories, such as smeared fracture theories, nodal and element enrichment theories (XFEM), cohesive elements or virtual crack closure technique (VCCT), can be utilized at the microscale, but the dimensions of the RUC must then be defined. One major challenge in multiscale progressive damage modeling is relating the characteristic lengths across the scales in order to preserve the energy that is dissipated via localization at the microscale. If there is no effort to relate the size of the macroscale element to the microscale RUC, then the energy that is dissipated will remain mesh dependent at the macroscale, even if it is regularized at the microscale. Here, a technique for mapping characteristic lengths across the scales is proposed. The RUC will be modeled using the generalized method of cells (GMC) micromechanics theory, and local failure in the matrix constituent subcells will be modeled using the crack band theory. The subcell characteristic lengths used in the crack band calculations will be mapped to the macroscale finite element in order to regularize the local energy in a manner consistent with the global length scale. Examples will be provided with and without the regularization, and they will be compared to a baseline case where the size and shape of the element and RUC are coincident (ensuring energy is preserved across the scales).

softening↗

NASA NTRS1990

Using Strassen's algorithm to accelerate the solution of linear systems

Strassen's algorithm for fast matrix-matrix multiplication has been implemented for matrices of arbitrary shapes on the CRAY-2 and CRAY Y-MP supercomputers. Several techniques have been used to reduce the scratch space requirement for this algorithm while simultaneously preserving a high level of performance. When the resulting Strassen-based matrix multiply routine is combined with some routines from the new LAPACK library, LU decomposition can be performed with rates significantly higher than those achieved by conventional means. We succeeded in factoring a 2048 x 2048 matrix on the CRAY Y-MP at a rate equivalent to 325 MFLOPS.

Bailey, David H.↗

NASA NTRS1994

A high resolution atlas of the galactic plane at 12 microns and 25 microns

High resolution images of the 12 micron and 25 micron IRAS survey data from each HCON crossing the Galactic Plane are being created for those regions that the original IRAS processing labeled as confused. This encompasses the area within 100 deg longitude of the Galactic Center and within 3 deg to 10 deg of the Plane. The procedures used to create the images preserve the spatial resolution inherent in the IRAS instrument. The images are separated into diffuse and point source components and candidate sources are extracted from the point source image after non-linear spatial sharpening. Fluxes are estimated by convolving the candidate sources with the point response function and cross-correlating with the original point source image. A source is considered real if it is seen on at least two HCON's with a rather generous flux match but a stringent position criterion. A number of fields spanning a range of source densities from low to high have been examined. Initial analysis indicates that the imaging and extraction works quite well up to a source density of about 100 sources per square degree or down to roughly 0.8 Janskys.

Price, Stephan D.↗

NASA NTRS1995

Global Stratigraphy of Venus: Analysis of a Random Sample of Thirty-Six Test Areas

The age relations between 36 impact craters with dark paraboloids and other geologic units and structures at these localities have been studied through photogeologic analysis of Magellan SAR images of the surface of Venus. Geologic settings in all 36 sites, about 1000 x 1000 km each, could be characterized using only 10 different terrain units and six types of structures. These units and structures form a major stratigraphic and geologic sequence (from oldest to youngest): (1) tessera terrain; (2) densely fractured terrains associated with coronae and in the form of remnants among plains; (3) fractured and ridged plains and ridge belts; (4) plains with wrinkle ridges; (5) ridges associated with coronae annulae and ridges of arachnoid annulae which are contemporary with wrinkle ridges of the ridged plains; (6) smooth and lobate plains; (7) fractures of coronae annulae, and fractures not related to coronae annulae, which disrupt ridged and smooth plains; (8) rift-associated fractures; and (9) craters with associated dark paraboloids, which represent the youngest 1O% of the Venus impact crater population (Campbell et al.), and are on top of all volcanic and tectonic units except the youngest episodes of rift-associated fracturing and volcanism; surficial streaks and patches are approximately contemporary with dark-paraboloid craters. Mapping of such units and structures in 36 randomly distributed large regions (each approximately 10(exp 6) sq km) shows evidence for a distinctive regional and global stratigraphic and geologic sequence. On the basis of this sequence we have developed a model that illustrates several major themes in the history of Venus. Most of the history of Venus (that of its first 80% or so) is not preserved in the surface geomorphological record. The major deformation associated with tessera formation in the period sometime between 0.5-1.0 b.y. ago (Ivanov and Basilevsky) is the earliest event detected. In the terminal stages of tessera fon-nation, extensive parallel linear graben swarms representing a change in the style of deformation from shortening to extension were formed on the tessera and on some volcanic plains that were emplaced just after, and perhaps also during the latter stages of the major compressional phase of tessera emplacement. Our stratigraphic analyses suggest that following tessera formation, extensive volcanic flooding resurfaced at least 85% of the planet in the form of the presently-ridged and fractured plains. Several lines of evidence favor a high flux in the post-tessera period but we have no independent evidence for the absolute duration of ridged plains emplacement. During this time, the net state of stress in the lithosphere apparently changed from extensional to compressional, first in the form of extensive ridge belt development, followed by the formation of extensive wrinkle ridges on the flow units. Subsequently, there occurred local emplacement of smooth and lobate plains units which are presently essentially undefortned. The major events in the latest 10% of the presently preserved history of Venus (less than 50 m.y. ago) are continued rifting and some associated volcanism, and the redistribution of eolian material largely derived from impact crater deposits.

Basilevsky, Alexander T.↗

NASA NTRS1989

Optimal feedback control infinite dimensional parabolic evolution systems: Approximation techniques

A general approximation framework is discussed for computation of optimal feedback controls in linear quadratic regular problems for nonautonomous parabolic distributed parameter systems. This is done in the context of a theoretical framework using general evolution systems in infinite dimensional Hilbert spaces. Conditions are discussed for preservation under approximation of stabilizability and detectability hypotheses on the infinite dimensional system. The special case of periodic systems is also treated.

Banks, H. T.↗

NASA NTRS1989

Optimal feedback control of infinite-dimensional parabolic evolution systems - Approximation techniques

Banks, H. T.↗

NASA NTRS1992

Optimal matrix approximants in structural identification

Problems of model correlation and system identification are central in the design, analysis, and control of large space structures. Of the numerous methods that have been proposed, many are based on finding minimal adjustments to a model matrix sufficient to introduce some desirable quality into that matrix. In this work, several of these methods are reviewed, placed in a modern framework, and linked to other previously known ideas in computational linear algebra and optimization. This new framework provides a point of departure for a number of new methods which are introduced here. Significant among these is a method for stiffness matrix adjustment which preserves the sparsity pattern of an original matrix, requires comparatively modest computational resources, and allows robust handling of noisy modal data. Numerical examples are included to illustrate the methods presented herein.

Beattie, C. A.↗

NASA NTRS2019

Weighted Least-Squares Cell-Average Gradient Construction Methods for the VULCAN-CFD Second-Order Accurate Unstructured-Grid Cell-Centered Finite-Volume Solver

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. The construction of cell-average gradients using a weighted linear least-squares method and the use of these gradients in the construction of the inviscid fluxes is the focus of this paper. A comparison of least-squares stencil construction methodologies is presented and approaches to augment the number of cells participating in the stencil while preserving accuracy are explored. Due to our interest in hypersonic flow, a robust multidimensional cell-average gradient limiter procedure that is consistent with the stencil used to construct the cell-average gradients is described and investigated. Canonical problems are computed to illustrate the challenges and investigate the accuracy, robustness and convergence behavior of the cell-average gradient methods on unstructured cell-centered finite-volume grids. Finally, thermally perfect, chemically frozen, Mach 8 turbulent flow of air around a blunt wedge is computed to demonstrate the robustness and convergence behavior of the new method for constructing stencils of use in a weighted linear least-squares gradient method for a hypersonic flow.

White, Jeffery A.↗

NASA NTRS2011

Policies and Procedures for Accessing Archived NASA Lunar Data via the Web

The National Space Science Data Center (NSSDC) was established by NASA to provide for the preservation and dissemination of scientific data from NASA missions. This paper describes the policies specifically related to lunar science data. NSSDC presently archives 660 lunar data collections. Most of these data (423 units) are stored offline in analog format. The remainder of this collection consists of magnetic tapes and discs containing approximately 1.7 TB of digital lunar data. The active archive for NASA lunar data is the Planetary Data System (PDS). NSSDC has an agreement with the PDS Lunar Data Node to assist in the restoration and preparation of NSSDC-resident lunar data upon request for access and distribution via the PDS archival system. Though much of NSSDC's digital store also resides in PDS, NSSDC has many analog data collections and some digital lunar data sets that are not in PDS. NSSDC stands ready to make these archived lunar data accessible to both the research community and the general public upon request as resources allow. Newly requested offline lunar data are digitized and moved to near-line storage devices called digital linear tape jukeboxes. The data are then packaged and made network-accessible via FTP for the convenience of a growing segment of the user community. This publication will 1) discuss the NSSDC processes and policies that govern how NASA lunar data is preserved, restored, and made accessible via the web and 2) highlight examples of special lunar data requests.

James, Nathan L.↗

NASA NTRSDate not supplied

Developing Urban Air Mobility Vehicle Models to Support Air Traffic Management Concept Development

To support Urban Air Mobility (UAM) research efforts at NASA, the Airspace Target Generator (ATG) software used in the FutureFlight Central (FFC) air traffic control tower simulator is undergoing updates to support physics-based UAM vehicle models. A process was developed to integrate UAM vertical takeoff and landing (VTOL) aircraft into the fixed-wing ATG modeling environment without significant change to the underlying equations of motion and vehicle model database. The VTOL aircraft models were converted from a six degrees-of-freedom (6-DOF) representation into a four degrees-of-freedom (4-DOF) representation for integration within ATG. Three vehicle designs from the NASA Revolutionary Vertical-Lift Technologies (RVLT) project were selected: a lift-plus-cruise (LPC) aircraft model and quadrotor, electric-powered (QEP) 1-seater and 6-seater models. With the LPC model comprised of a nonlinear force and moment build-up, and the QEP models comprised of linearized stability derivatives, two separate processes were developed to convert the lift, drag, and propulsion characteristics of each model into the ATG model database. Key aircraft performance characteristics including climb, cruise, and descent performance were preserved during the conversion process. Because ATG simulates fixed-wing aircraft through ground taxi and takeoff to approach and landing, acceleration command algorithms were developed to model the vertical takeoff and vertical landing phase of UAM operations. A strategy was then developed to transition the aircraft model to- and from- the new control mode.

urban air mobility↗

NASA NTRS1978

Autonomous satellite orbital navigation and attitude determination

A known linear landmark navigation system is described. It involves the use of an electro-optical sensor to provide sightings to linear earth features such as highways and coast lines. The sensor concept and the navigation system mechanization are described. Performance analysis results show that landmark sightings provide accurate navigation update and that this accuracy can be preserved using radar altimeter measurements. Description of a stellar inertial attitude determination system is also presented. Attitude reference performance consistent with the requirement of the navigation system is shown to be achievable by this method.

Kau, S. P.↗

NASA NTRS1984

A compact finite element method for elastic bodies

A nonconforming finite method is described for treating linear equilibrium problems, and a convergence proof showing second order accuracy is given. The close relationship to a related compact finite difference scheme due to Phillips and Rose is examined. A condensation technique is shown to preserve the compactness property and suggests an approach to a certain type of homogenization.

Rose, M. E.↗

NASA NTRS2001

A Linear Bicharacteristic FDTD Method

The linear bicharacteristic scheme (LBS) was originally developed to improve unsteady solutions in computational acoustics and aeroacoustics [1]-[7]. It is a classical leapfrog algorithm, but is combined with upwind bias in the spatial derivatives. This approach preserves the time-reversibility of the leapfrog algorithm, which results in no dissipation, and it permits more flexibility by the ability to adopt a characteristic based method. The use of characteristic variables allows the LBS to treat the outer computational boundaries naturally using the exact compatibility equations. The LBS offers a central storage approach with lower dispersion than the Yee algorithm, plus it generalizes much easier to nonuniform grids. It has previously been applied to two and three-dimensional freespace electromagnetic propagation and scattering problems [3], [6], [7]. This paper extends the LBS to model lossy dielectric and magnetic materials. Results are presented for several one-dimensional model problems, and the FDTD algorithm is chosen as a convenient reference for comparison.

Beggs, John H.↗

NASA NTRS2008

ISIS Topside-Sounder Plasma-Wave Investigations as Guides to Desired Virtual Wave Observatory (VWO) Data Search Capabilities

Many plasma-wave phenomena, observed by space-borne radio sounders, cannot be properly explained in terms of wave propagation in a cold plasma consisting of mobile electrons and infinitely massive positive ions. These phenomena include signals known as plasma resonances. The principal resonances at the harmonics of the electron cyclotron frequency, the plasma frequency, and the upper-hybrid frequency are well explained by the warm-plasma propagation of sounder-generated electrostatic waves, Other resonances have been attributed to sounder-stimulated plasma instability and non-linear effects, eigenmodes of cylindrical electromagnetic plasma oscillations, and plasma memory processes. Data from the topside sounders of the International Satellites for Ionospheric Studies (ISIS) program played a major role in these interpretations. A data transformation and preservation effort at the Goddard Space Flight Center has produced digital ISIS topside ionograms and a metadata search program that has enabled some recent discoveries pertaining to the physics of these plasma resonances. For example, data records were obtained that enabled the long-standing question (several decades) of the origin of the plasma resonance at the fundamental electron cyclotron frequency to be explained [Muldrew, Radio Sci., 2006]. These data-search capabilities, and the science enabled by them, will be presented as a guide to desired data search capabilities to be included in the Virtual Wave Observatory (VWO).

Benson, Robert F.↗

NASA NTRS2014

Structure and Evolution of the Lunar Procellarum Region as Revealed by GRAIL Gravity Data

The Procellarum region is a broad area on the nearside of the Moon that is characterized by low elevations, thin crust, and high surface concentrations of the heat-producing elements uranium, thorium, and potassium. The Procellarum region has been interpreted as an ancient impact basin approximately 3200 km in diameter, though supporting evidence at the surface would have been largely obscured as a result of the great antiquity and poor preservation of any diagnostic features. Here we use data from the Gravity Recovery and Interior Laboratory (GRAIL) mission to examine the subsurface structure of Procellarum. The Bouguer gravity anomalies and gravity gradients reveal a pattern of narrow linear anomalies that border the Procellarum region and are interpreted to be the frozen remnants of lava-filled rifts and the underlying feeder dikes that served as the magma plumbing system for much of the nearside mare volcanism. The discontinuous surface structures that were earlier interpreted as remnants of an impact basin rim are shown in GRAIL data to be a part of this continuous set of quasi-rectangular border structures with angular intersections, contrary to the expected circular or elliptical shape of an impact basin. The spatial pattern of magmatic-tectonic structures bounding Procellarum is consistent with their formation in response to thermal stresses produced by the differential cooling of the province relative to its surroundings, coupled with magmatic activity driven by the elevated heat flux in the region.

Procellarum↗

NASA NTRS2012

Method for Pre-Conditioning a Measured Surface Height Map for Model Validation

This software allows one to up-sample or down-sample a measured surface map for model validation, not only without introducing any re-sampling errors, but also eliminating the existing measurement noise and measurement errors. Because the re-sampling of a surface map is accomplished based on the analytical expressions of Zernike-polynomials and a power spectral density model, such re-sampling does not introduce any aliasing and interpolation errors as is done by the conventional interpolation and FFT-based (fast-Fourier-transform-based) spatial-filtering method. Also, this new method automatically eliminates the measurement noise and other measurement errors such as artificial discontinuity. The developmental cycle of an optical system, such as a space telescope, includes, but is not limited to, the following two steps: (1) deriving requirements or specs on the optical quality of individual optics before they are fabricated through optical modeling and simulations, and (2) validating the optical model using the measured surface height maps after all optics are fabricated. There are a number of computational issues related to model validation, one of which is the "pre-conditioning" or pre-processing of the measured surface maps before using them in a model validation software tool. This software addresses the following issues: (1) up- or down-sampling a measured surface map to match it with the gridded data format of a model validation tool, and (2) eliminating the surface measurement noise or measurement errors such that the resulted surface height map is continuous or smoothly-varying. So far, the preferred method used for re-sampling a surface map is two-dimensional interpolation. The main problem of this method is that the same pixel can take different values when the method of interpolation is changed among the different methods such as the "nearest," "linear," "cubic," and "spline" fitting in Matlab. The conventional, FFT-based spatial filtering method used to eliminate the surface measurement noise or measurement errors can also suffer from aliasing effects. During re-sampling of a surface map, this software preserves the low spatial-frequency characteristic of a given surface map through the use of Zernike-polynomial fit coefficients, and maintains mid- and high-spatial-frequency characteristics of the given surface map by the use of a PSD model derived from the two-dimensional PSD data of the mid- and high-spatial-frequency components of the original surface map. Because this new method creates the new surface map in the desired sampling format from analytical expressions only, it does not encounter any aliasing effects and does not cause any discontinuity in the resultant surface map.

Sidick, Erkin↗