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A block-structured grid formulation is presented and discussed. The compressible Euler equations are solved on the decomposed domain with a multigrid method based on Runge-Kutta time stepping and centered spatial differencing. The flexibility of the multiblock approach is demonstrated by computing low speed inviscid flow over two different multielement airfoil configurations.
The program DuctE3D is used for steady or unsteady aerodynamic and aeroelastic analysis of ducted fans. This guide describes the input data required and the output files generated, in using DuctE3D. The analysis solves three dimensional unsteady, compressible Euler equations to obtain the aerodynamic forces. A normal mode structural analysis is used to obtain the aeroelastic equations, which are solved using either the time domain or the frequency domain solution method. Sample input and output files are included in this guide for steady aerodynamic analysis and aeroelastic analysis of an isolated fan row.
A major objective of the Tropical Rainfall Measuring Mission (TRMM) is to produce a multi-year time series of monthly rainfall over 50 latitude by 50 longitude boxes with an uncertainty of 1 mm/day for low rain rates and 10% for high rain rates. Based on some simple assumptions about the error structure, we compute the non-systematic errors of monthly oceanic rainfall over the same space/time domain derived from data taken by the Special Sensor Microwave Imager (SSM/I) on board the Defense Meteorological Satellite Program (DMSP) satellites and TRMM Microwave Imager (TMI). The mean rain rates over a two-year period (1998-1999) are calculated to be 3.0, 2.85, 2.94 mm/day for SSM/I onboard the DMSP F-13, F-14 and TMI, respectively. Assuming that the non-systematic errors for each sensor are independent, the errors are calculated to be 22.2%, 22.4% and 19.7% for F-13, F-14 and for TMI, respectively. The non-systematic error for the TMI is smaller than that for either F-13 or F-14 SSM/I at the low rain rates but is comparable at rain rates higher than about 5 mm/day. The TRMM objective of 1 mm/day for non-systematic error is met by TMI for rain rates up to 5-6 mm/day. For higher rain rates, the nonsystematic error is in the 15% range. The goal of a 10% error for high rain rates may be realized by a combination of sensor measurements from multiple satellites, such as that advocated by the Global Precipitation Mission (GPM).
The Fibonacci grid, proposed by Swinbank and Purser (see companion abstract), provides attractive properties for global numerical atmospheric prediction by offering an optimally homogeneous, geometrically regular, and approximately isotropic discretization, with only the polar regions requiring special numerical treatment. It is a mathematical idealization, applied to the sphere, of the multi-spiral patterns often found in botanical structures, such as in pine cones and sunflower heads. Computationally, it is natural to organize the domain, into zones, in each of which the same pair, or triple, of "Fibonacci spirals" dominate. But the further subdivision of such zones into "tiles" of a shape and size suitable for distribution to the processors of a massively parallel computer requires very careful consideration if the subsequent spatial computations along the respective spirals, especially those computations (such as compact differencing schemes) that involve recursion, can be implemented in an efficient "load-balanced "manner without requiring excessive amounts of inter-processor communications. In this paper we show how certain "number theoretic" properties of the Fibonacci sequence (whose numbers prescribe the multiplicity of successive spirals) may be exploited in the decomposition of grid zones into tidy arrangements of triangular grid tiles, each tile possessing one side approximately parallel to the constant-latitude zone boundary. We also describe how the spatially recursive processes may be decomposed across such a tiling, and the directionality of the recursions reversed on alternate grid lines, to ensure a very high degree of load balancing throughout the execution of the computations required for one time step of a global model.
In principle, formal methods offer many advantages for aerospace software development: they can help to achieve ultra-high reliability, and they can be used to provide evidence of the reliability claims which can then be subjected to external scrutiny. However, despite years of research and many advances in the underlying formalisms of specification, semantics, and logic, formal methods are not much used in practice. In our opinion this is related to three major shortcomings. First, the application of formal methods is still expensive because they are labor- and knowledge-intensive. Second, they are difficult to scale up to complex systems because they are based on deep mathematical insights about the behavior of the systems (t.e., they rely on the "heroic proof"). Third, the proofs can be difficult to interpret, and typically stand in isolation from the original code. In this paper, we describe a tool for formally demonstrating safety-relevant aspects of aerospace software, which largely circumvents these problems. We focus on safely properties because it has been observed that safety violations such as out-of-bounds memory accesses or use of uninitialized variables constitute the majority of the errors found in the aerospace domain. In our approach, safety means that the program will not violate a set of rules that can range for the simple memory access rules to high-level flight rules. These different safety properties are formalized as different safety policies in Hoare logic, which are then used by a verification condition generator along with the code and logical annotations in order to derive formal safety conditions; these are then proven using an automated theorem prover. Our certification system is currently integrated into a model-based code generation toolset that generates the annotations together with the code. However, this automated formal certification technology is not exclusively constrained to our code generator and could, in principle, also be integrated with other code generators such as RealTime Workshop or even applied to legacy code. Our approach circumvents the historical problems with formal methods by increasing the degree of automation on all levels. The restriction to safety policies (as opposed to arbitrary functional behavior) results in simpler proof problems that can generally be solved by fully automatic theorem proves. An automated linking mechanism between the safety conditions and the code provides some of the traceability mandated by process standards such as DO-178B. An automated explanation mechanism uses semantic markup added by the verification condition generator to produce natural-language explanations of the safety conditions and thus supports their interpretation in relation to the code. It shows an automatically generated certification browser that lets users inspect the (generated) code along with the safety conditions (including textual explanations), and uses hyperlinks to automate tracing between the two levels. Here, the explanations reflect the logical structure of the safety obligation but the mechanism can in principle be customized using different sets of domain concepts. The interface also provides some limited control over the certification process itself. Our long-term goal is a seamless integration of certification, code generation, and manual coding that results in a "certified pipeline" in which specifications are automatically transformed into executable code, together with the supporting artifacts necessary for achieving and demonstrating the high level of assurance needed in the aerospace domain.
The study of time-dependent solar active region (AR) morphology and its relation to eruptive events requires analysis of imaging data obtained in multiple wavelength domains with differing spatial and time resolution, ideally in combination with 3D physical models. To facilitate this goal, we have undertaken a major enhancement of our IDL-based simulation tool, GX_Simulator, previously developed for modeling microwave and X-ray emission from flaring loops, to allow it to simulate quiescent emission from solar ARs. The framework includes new tools for building the atmospheric model and enhanced routines for calculating emission that include new wavelengths. In this paper, we use our upgraded tool to model and analyze an AR and compare the synthetic emission maps with observations. We conclude that the modeled magneto-thermal structure is a reasonably good approximation of the real one.
The Vredefort Dome is located within and almost central to the Witwatersrand basin in its presently known extent. It exposes a central Archean granite core which is surrounded by a collar of supracrustal rocks. These collar rocks outline a strong polygonal geometry. The Archean core is comprised of two concentric zones, the Outer Granite Gneiss (OGG), and the core central Inlandsee Leucogranofels (ILG). The rocks of the inner core display granulite facies metamorphism, while the OGG is in amphibolite facies. The inner core is believed from recent drill hole information to be underlain by mafic and ultramafic gneisses, the extent of which cannot be assessed at present. A fairly broad zone of charnockites separates the OGG and ILG domains. This zone is characterized by a high concentration of pseudotachylite and ductile shearing. Whereas a number of other domical structures are located within or surrounding the Witwatersrand basin, the Vredefort structure is anomalous, in that it has: a partly polygonal geometry; extensive alkali intrusives in the northwestern sector; granophyre dykes (ring-dykes peripheral to the contact collar-basement and NW-SE or NE-SW trending dykes within the Archean basement); contact metamorphism of the collar supracrustal rocks; the overturning of collar supracrustals in the northern sectors; deformation phenomena widely regarded as representing shock metamorphism (pseudotachylite, (sub)planar microdeformation features in quartz, shatter cones and occurrences of high-P quartz polymorphs); a positive 30 mgal gravity anomaly; and high amplitude magnetic anomalies. Recent geophysical, structural and petrological evidence pertinent for the identification of the processes that led to the formation of the Vredefort structure are summarized.
Computational simulations using overset grids typically involve multiple steps and a variety of software modules. A graphical interface called OVERGRID has been specially designed for such purposes. Data required and created by the different steps include geometry, grids, domain connectivity information and flow solver input parameters. The interface provides a unified environment for the visualization, processing, generation and diagnosis of such data. General modules are available for the manipulation of structured grids and unstructured surface triangulations. Modules more specific for the overset approach include surface curve generators, hyperbolic and algebraic surface grid generators, a hyperbolic volume grid generator, Cartesian box grid generators, and domain connectivity: pre-processing tools. An interface provides automatic selection and viewing of flow solver boundary conditions, and various other flow solver inputs. For problems involving multiple components in relative motion, a module is available to build the component/grid relationships and to prescribe and animate the dynamics of the different components.
The North American Carbon Program (NACP) was formed to further the scientific understanding of sources, sinks, and stocks of carbon in Earth's environment. Carbon cycle science integrates multidisciplinary research, providing decision-support information for managing climate and carbon-related change across multiple sectors of society. This investigation uses the conceptual framework of com-munities of practice (CoP) to explore the role that the NACP has played in connecting researchers into a carbon cycle knowledge network, and in enabling them to conduct physical science that includes ideas from social science. A CoP describes the communities formed when people consistently engage in shared communication and activities toward a common passion or learning goal. We apply the CoP model by using keyword analysis of abstracts from scientific publications to analyze the research outputs of the NACP in terms of its knowledge domain. We also construct a co-authorship network from the publications of core NACP members, describe the structure and social pathways within the community. Results of the content analysis indicate that the NACP community of practice has substantially expanded its research on human and social impacts on the carbon cycle, contributing to a better understanding of how human and physical processes interact with one another. Results of the co-authorship social network analysis demonstrate that the NACP has formed a tightly connected community with many social pathways through which knowledge may flow, and that it has also expanded its network of institutions involved in carbon cycle research over the past seven years.
In an accepted method of measuring D region electron density with a rocket-borne dc-mode Langmuir probe, the resulting fine-structure signal is modified by a high-pass filter. While this form of data has been successfully used for power spectral analysis, it fails to reveal important spatial domain features without further processing. It is demonstrated that the broadband signal can be recovered by use of a digital filter that corrects for the on-board high-pass filter effects. The D-region broadband structure so recovered for a daytime equatorial flight shows variations in electron density consistent with a model of Kelvin-Helmholtz billows, and not consistent with inertial range turbulence. The isolated regions of irregularity are about 100 m thick near an altitude of 75 km, imbedded in a region with a staircase-structure electron density profile with about 200-m steps. Suggestive similarities to a numerical model of KHI are to undersea observations of KHI-caused microstructure are shown.
A statistically generated weighting function for a second-order polynomial curve fit of residual functions has been developed. The residual flexibility test method, from which a residual function is generated, is a procedure for modal testing large structures in an external constraint-free environment to measure the effects of higher order modes and interface stiffness. This test method is applicable to structures with distinct degree-of-freedom interfaces to other system components. A theoretical residual function in the displacement/force domain has the characteristics of a relatively flat line in the lower frequencies and a slight upward curvature in the higher frequency range. In the test residual function, the above-mentioned characteristics can be seen in the data, but due to the present limitations in the modal parameter evaluation (natural frequencies and mode shapes) of test data, the residual function has regions of ragged data. A second order polynomial curve fit is required to obtain the residual flexibility term. A weighting function of the data is generated by examining the variances between neighboring data points. From a weighted second-order polynomial curve fit, an accurate residual flexibility value can be obtained. The residual flexibility value and free-free modes from testing are used to improve a mathematical model of the structure. The residual flexibility modal test method is applied to a straight beam with a trunnion appendage and a space shuttle payload pallet simulator.
Accurate mathematical models are clearly an important part of the design, modification, control, and damage assessment of large space structures. A critical part of model determination of any type of structure is the use of system identification (SI), a process for using measured excitation and response data to improve the form of a mathematical model or the values of the parameters in it. The reasons for using SI are manifold, but most of them involve uncertainties in either the form of or the parameters in the mathematical model. Some of the more common uncertainties are the following: the nature of the damping, the characteristics of sloppy or sticky joints, inelastic material properties, and parameters in a reduced Degree-of-Freedom (DOF) model. This paper contains a description of the SI algorithm followed by two illustrations: one in which all parameters in a shear building model are determined using pull back and quick release data, and another in which an equivalent reduced DOF model is obtained for a two story frame.
In this paper it is argued that the time-frequency analysis of structural impulse responses may be used to reveal the wave types carrying significant energy through a structure. Since each wave type is characterized by its own dispersion relation, each wave type may be associated with particular features appearing in the time-frequency domain representation of an impulse response. Here the Wigner Distribution is introduced as a means for obtaining appropriate time-frequency representations of impulse responses. Practical aspects of the calculation of the Wigner Distribution are discussed and examples of its application to the analysis of structural impulse responses are given. These examples will show that the Wigner Distribution may be conveniently used to distinguish between the contributions of various waves types to a total structural response.
Results of Monte Carlo numerical simulations conducted to study the close-mode performance of the Ibrahim Time-Domain (ITD) modal identification algorithm are presented. The ITD technique is a matrix eigensolution method for obtaining structural modal parameters directly from free-response test data without using the FFT. Thus, the well-known resolution and leakage limitations of the FFT procedure, that are particularly significant with short records, are avoided. As an example, one of several experimental data analyses where close modes have been accurately identified using very short records is shown. Although the identification scatter is found to increase as the square of reductions in frequency separation at small separations, the ability to differentiate modes spaced at fractions of the FFT resolution is substantiated.
The Eigensystem Realization Algorithm (ERA) is a multiinput/multioutput time-domain algorithm for minimum-order system realization and modal parameter identification. It has been used for structural dynamics data analysis at the Langley Research Center for several years. Some of the practical experiences encountered in these projects are discussed in this paper. Three examples are used: the Galileo spacecraft, the Solar Array Flight Experiment, and a laboratory space-truss model. Several techniques for assessing identification accuracy are illustrated.
The problem of designing fine-pointing controllers is considered for large, flexible space structures using modern multivariable synthesis methods. The first method is an iterative procedure which utilizes frequency-domain singular-value techniques, and is found to yield satisfactory performance and robustness. For the second method, which is based on coprime factorizations, a particular bicoprime is obtained, and the steps in the design process are described. This method is still under development.
Geophysical models of the first 600 Ma ofthe earth's history following accretion and core formation point to a period of great environmental disequilibrium. In such an environment, the passage of energy from the earth's interior and from the sun through gas-liquid-solid domains and their boundaries with each other generated a dynamically interacting, complex hierarchy of self-organized structures ranging from bubbles at the sea-air interface to tectonic plates. The ability of a planet to produce such a hierarchy is speculated to be a prerequisite to the origin and sustenance of life. The application of this criterion to Mars argues against the origin of Martian life.
A collection of computer programs for aircraft system identification is described and demonstrated. The programs, collectively called System IDentification Programs for AirCraft, or SIDPAC, were developed in MATLAB as m-file functions. SIDPAC has been used successfully at NASA Langley Research Center with data from many different flight test programs and wind tunnel experiments. SIDPAC includes routines for experiment design, data conditioning, data compatibility analysis, model structure determination, equation-error and output-error parameter estimation in both the time and frequency domains, real-time and recursive parameter estimation, low order equivalent system identification, estimated parameter error calculation, linear and nonlinear simulation, plotting, and 3-D visualization. An overview of SIDPAC capabilities is provided, along with a demonstration of the use of SIDPAC with real flight test data from the NASA Glenn Twin Otter aircraft. The SIDPAC software is available without charge to U.S. citizens by request to the author, contingent on the requestor completing a NASA software usage agreement.