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NASA NTRS1992

SkICAT: A cataloging and analysis tool for wide field imaging surveys

We describe an integrated system, SkICAT (Sky Image Cataloging and Analysis Tool), for the automated reduction and analysis of the Palomar Observatory-ST ScI Digitized Sky Survey. The Survey will consist of the complete digitization of the photographic Second Palomar Observatory Sky Survey (POSS-II) in three bands, comprising nearly three Terabytes of pixel data. SkICAT applies a combination of existing packages, including FOCAS for basic image detection and measurement and SAS for database management, as well as custom software, to the task of managing this wealth of data. One of the most novel aspects of the system is its method of object classification. Using state-of-theart machine learning classification techniques (GID3* and O-BTree), we have developed a powerful method for automatically distinguishing point sources from non-point sources and artifacts, achieving comparably accurate discrimination a full magnitude fainter than in previous Schmidt plate surveys. The learning algorithms produce decision trees for classification by examining instances of objects classified by eye on both plate and higher quality CCD data. The same techniques will be applied to perform higher-level object classification (e.g., of galaxy morphology) in the near future. Another key feature of the system is the facility to integrate the catalogs from multiple plates (and portions thereof) to construct a single catalog of uniform calibration and quality down to the faintest limits of the survey. SkICAT also provides a variety of data analysis and exploration tools for the scientific utilization of the resulting catalogs. We include initial results of applying this system to measure the counts and distribution of galaxies in two bands down to Bj is approximately 21 mag over an approximate 70 square degree multi-plate field from POSS-II. SkICAT is constructed in a modular and general fashion and should be readily adaptable to other large-scale imaging surveys.

Weir, N.↗

NASA NTRS1993

Application of symbolic and algebraic manipulation software in solving applied mechanics problems

As its name implies, symbolic and algebraic manipulation is an operational tool which not only can retain symbols throughout computations but also can express results in terms of symbols. This report starts with a history of symbolic and algebraic manipulators and a review of the literatures. With the help of selected examples, the capabilities of symbolic and algebraic manipulators are demonstrated. These applications to problems of applied mechanics are then presented. They are the application of automatic formulation to applied mechanics problems, application to a materially nonlinear problem (rigid-plastic ring compression) by finite element method (FEM) and application to plate problems by FEM. The advantages and difficulties, contributions, education, and perspectives of symbolic and algebraic manipulation are discussed. It is well known that there exist some fundamental difficulties in symbolic and algebraic manipulation, such as internal swelling and mathematical limitation. A remedy for these difficulties is proposed, and the three applications mentioned are solved successfully. For example, the closed from solution of stiffness matrix of four-node isoparametrical quadrilateral element for 2-D elasticity problem was not available before. Due to the work presented, the automatic construction of it becomes feasible. In addition, a new advantage of the application of symbolic and algebraic manipulation found is believed to be crucial in improving the efficiency of program execution in the future. This will substantially shorten the response time of a system. It is very significant for certain systems, such as missile and high speed aircraft systems, in which time plays an important role.

Tsai, Wen-Lang↗

DOE OSTI2025

Computational Modeling of a 3D Printed Recuperator and Subsequent Experimental Loop for Supercritical Carbon Dioxide Cycles

Oak Ridge National Laboratory (ORNL), in collaboration with mechanical-thermal energy storage (mTES) provider EarthEn, a US Department of Energy (DOE) Lab-Embedded Entrepreneurship Program (LEEP) recipient at ORNL’s Innovation Crossroads 2023, is utilizing a state-of-the-art patented 3D printing technique to design an additively manufactured (AM) supercritical CO2 (sCO2) recuperator (REC) for EarthEn’s charge/discharge cycle. The AM REC will be printed at ORNL’s Manufacturing Demonstration Facility using Inconel Alloy 718 and tested on a closed-loop, ∼100 kW scale experimental facility that is under construction. The testing will compare the printed design against a commercial-off-the-shelf Printed Circuit Heat Exchanger (PCHE) REC. The design of the sCO2 facility is guided by a Modelica-based system model which is primarily dependent on the open-source TRANSFORM library developed at ORNL and uses the open-source CoolProp library for thermophysical properties of sCO2 via the External Media library. It is envisioned that an iterative process will be followed between the physical loop and the system model wherein the initial experimental data will be used to tune the model, which in turn will be used to guide future loop operation. Simultaneously, the AM REC is being designed using computer-aided design models, and it is also being analyzed for hydraulic and thermomechanical response using commercial computational fluid dynamics software, Simcenter STAR-CCM+, on highperformance computing resources.1

See, Nate [ORNL] (ORCID:0000000178581202)↗

NASA NTRS2011

Engineering and Scientific Applications: Using MatLab(Registered Trademark) for Data Processing and Visualization

MatLab(TradeMark)(MATrix LABoratory) is a numerical computation and simulation tool that is used by thousands Scientists and Engineers in many countries. MatLab does purely numerical calculations, which can be used as a glorified calculator or interpreter programming language; its real strength is in matrix manipulations. Computer algebra functionalities are achieved within the MatLab environment using "symbolic" toolbox. This feature is similar to computer algebra programs, provided by Maple or Mathematica to calculate with mathematical equations using symbolic operations. MatLab in its interpreter programming language form (command interface) is similar with well known programming languages such as C/C++, support data structures and cell arrays to define classes in object oriented programming. As such, MatLab is equipped with most of the essential constructs of a higher programming language. MatLab is packaged with an editor and debugging functionality useful to perform analysis of large MatLab programs and find errors. We believe there are many ways to approach real-world problems; prescribed methods to ensure foregoing solutions are incorporated in design and analysis of data processing and visualization can benefit engineers and scientist in gaining wider insight in actual implementation of their perspective experiments. This presentation will focus on data processing and visualizations aspects of engineering and scientific applications. Specifically, it will discuss methods and techniques to perform intermediate-level data processing covering engineering and scientific problems. MatLab programming techniques including reading various data files formats to produce customized publication-quality graphics, importing engineering and/or scientific data, organizing data in tabular format, exporting data to be used by other software programs such as Microsoft Excel, data presentation and visualization will be discussed.

Sen, Syamal K.↗

DOE OSTI2024

First considerations on the supporting structures of FCC-ee booster and collider in the arc regions

In 2022, the FCC Feasibility Study management mandated a working group to analyse the best configuration of the FCC-ee tunnel in the arc regions, in view of the construction of a mock-up of the arc half-cell. One of the main and most challenging goals of the study, named FCC-ee Arc Half-Cell Mock-up Project, was to perform a preliminary investigation on the principles of supporting the Short-Straight Sections and dipoles of the half-cells, both for the booster and for the collider machines. This is an important input needed for the choice of the best configuration of the relative placement of the booster with respect to the collider. The structural stiffness, mass and stability of the supporting structures must be optimized to minimize the vibrations transmitted/transferred to the magnetic system of the accelerators by elements such as pumps, water cooling system, beam thermomechanical stresses, powering elements, etc. To perform the study, tools such as CAD software, FEM and analytical techniques were employed. This paper summarizes the preliminary design concepts and the results of the simulations performed.

Accelerator Subsystems and Technologies↗

NASA NTRS2008

Space Telecommunications Radio Systems (STRS) Hardware Architecture Standard: Release 1.0 Hardware Section

This report defines a hardware architecture approach for software-defined radios to enable commonality among NASA space missions. The architecture accommodates a range of reconfigurable processing technologies including general-purpose processors, digital signal processors, field programmable gate arrays, and application-specific integrated circuits (ASICs) in addition to flexible and tunable radiofrequency front ends to satisfy varying mission requirements. The hardware architecture consists of modules, radio functions, and interfaces. The modules are a logical division of common radio functions that compose a typical communication radio. This report describes the architecture details, the module definitions, the typical functions on each module, and the module interfaces. Tradeoffs between component-based, custom architecture and a functional-based, open architecture are described. The architecture does not specify a physical implementation internally on each module, nor does the architecture mandate the standards or ratings of the hardware used to construct the radios.

Reinhart, Richard C.↗

DOE OSTI2015

The effect of urban design parameters on the local microclimate

Two-dimensional steady-state simulations have been performed using the standard k-e turbulence model coupled with the heat transfer models available in the CFD software FLUENT 6.1, in order to examine the impact of radiation on the Urban Heat Island phenomenon. Specifically, the impact of radiation in three typical urban areas of Cyprus during the summer period is examined. The first geometry considered represents a typical suburban area and is termed as the reference geometry. The second geometry represents an area at the centre of a town with higher buildings and relatively narrower roads. The third geometry, on the other hand, describes a suburban area with wider roads and larger houses than the reference model. Computed values for air temperature in the urban street canyon have indicated that the increase in temperature associated with radiative heat transfer can be reduced by optimising the canyon geometry and, ultimately, help to mitigate the human thermal discomfort. The present study has also revealed that the selection of construction materials can be optimised to offer further reductions in the air temperature of the urban environment. It can be concluded that the combined effect of these remedies can lead to reductions in the energy consumption for building air-conditioning over the summer period.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1993

Optimal design of composite hip implants using NASA technology

Using an adaptation of NASA software, we have investigated the use of numerical optimization techniques for the shape and material optimization of fiber composite hip implants. The original NASA inhouse codes, were originally developed for the optimization of aerospace structures. The adapted code, which was called OPORIM, couples numerical optimization algorithms with finite element analysis and composite laminate theory to perform design optimization using both shape and material design variables. The external and internal geometry of the implant and the surrounding bone is described with quintic spline curves. This geometric representation is then used to create an equivalent 2-D finite element model of the structure. Using laminate theory and the 3-D geometric information, equivalent stiffnesses are generated for each element of the 2-D finite element model, so that the 3-D stiffness of the structure can be approximated. The geometric information to construct the model of the femur was obtained from a CT scan. A variety of test cases were examined, incorporating several implant constructions and design variable sets. Typically the code was able to produce optimized shape and/or material parameters which substantially reduced stress concentrations in the bone adjacent of the implant. The results indicate that this technology can provide meaningful insight into the design of fiber composite hip implants.

Blake, T. A.↗

DOE OSTI2021

Controlled dehumidification to extract clean water from a multicomponent gaseous mixture of organic contaminants

Rapid expansion of the unconventional oil and gas extraction has increased American energy independence, but also led to increased production of large amounts of contaminated water. Wastewater from the oil and gas industry contains a wide range of contaminants. Injecting such contaminated water into disposal wells or discharging it to the environment jeopardizes freshwater resources. Conventional and membrane-based wastewater treatment techniques are often not effective choices to treat highly contaminated wastewater; however, a suitable way to remove contaminants from wastewater is to selectively separate water in a process analogous to humidification-dehumidification (HDH). Only a few studies have investigated the use of HDH for wastewater treatment. In this study, a novel HDH system is introduced for treating highly contaminated water, such as oil and gas flowback and produced water. In this HDH process, a non-condensable gas, such as air, mixes with wastewater vapor to facilitate the separation of contaminants. As a result, clean water condenses from the multicomponent gaseous mixture while air carries organic contaminants out of the dehumidification section. A laboratory apparatus was constructed and experiments were performed to investigate the HDH process for wastewater treatment and to study the effects of flow dynamics including air flow rate on the composition of treated water. Different contaminants including benzene, toluene, 2-propanol and 2-butoxyethanol were tested. Experimental results showed that the system can be successfully applied for removing volatile and/or toxic organic contaminants from wastewater. A representative multicomponent mixture of fracking wastewater was successfully treated using the experimental setup and clean water with quality of 98.3% was obtained. It was revealed that increasing the air-to-vapor mass ratio improves purity of treated water. Quantitative analysis showed that by increasing the air-to-vapor mass ratio from 0.6 to 5.9, the fraction of separated 2-propanol through the air was improved from 43% to more than 96% of the initial amount. ASPEN software was employed to simulate equilibrium conditions. Finally, experimental results were observed to have lower mass fraction of residual contaminant in the treated water compared to equilibrium state.

42 ENGINEERING↗

NASA NTRS1979

Application of a microprocessor controlled lidar to tropospheric ozone measurements

A microprocessor controlled lidar system under construction at the NASA Goddard Space Flight Center is described and the problems in making space-based measurements of tropospheric ozone are considered. The differential absorption lidar using a dual wavelength, pulsed CO2 laser and direct detection receiver can significantly improve the existing global data base on tropospheric ozone burden. Sensitivity to tropospheric ozone can be obtained in the spaceborne version of lidar by selecting laser lines located in the wings of the target zone lines. Simulation studies using various laser line pairs in the P-branch of the CO2 9.4 micron band show that the ozone burden retrieval may be weighted to particular altitude regions. These simulation studies are based on numerical integration of differences in absorption coefficient at the two selected laser wavelengths using the AFGL absorption line parameter compilations, U.S. Standard Atmosphere ozone profile, and laser software. Simulation, data collection and reduction are performed by a microprocessor subsystem of the CO2 lidar.

Stewart, R. W.↗

DOE OSTI2022

A Visual Comparison of Silent Error Propagation

High-performance computing (HPC) systems play a critical role in facilitating scientific discoveries. Their scale and complexity (e.g., the number of computational units and software stack) continue to grow as new systems are expected to process increasingly more data and reduce computing time. However, with more processing elements, the probability that these systems will experience a random bit-flip error that corrupts a program's output also increases, which is often recognized as silent data corruption. Analyzing the resiliency of HPC applications in extreme-scale computing to silent data corruption is crucial but difficult. An HPC application often contains a large number of computation units that need to be tested, and error propagation caused by error corruption is complex and difficult to interpret. Here, to accommodate this challenge, we propose an interactive visualization system that helps HPC researchers understand the resiliency of HPC applications and compare their error propagation. Our system models an application's error propagation to study a program's resiliency by constructing and visualizing its fault tolerance boundary. Coordinating with multiple interactive designs, our system enables domain experts to efficiently explore the complicated spatial and temporal correlation between error propagations. At the end, the system integrated a nonmonotonic error propagation analysis with an adjustable graph propagation visualization to help domain experts examine the details of error propagation and answer such questions as why an error is mitigated or amplified by program execution.

97 MATHEMATICS AND COMPUTING↗

NASA NTRSDate not supplied

Computer Controlled High Vacuum Gas Purification and Analysis Line

Light stable isotope work requires the handling of gasses such a way that does not alter isotopic composition. To do this, there are a large number of analytical and experimental procedures which involve the use of a vacuum line, numerous “egg timers” and a human hand on a valve. Unfortunately, the human hand is inconsistent and inadvertent small, and commonly large, differences in timing can have a measurable effect on outcomes. We have constructed a computer controlled high-vacuum line to be used as an expandable platform for future experimental and analytical procedures. The vacuum line consists of an electropolished 316 stainless steel system of cryogenic u-traps partitioned by pneumatic valves. The code to operate the line has been developed using the LabView platform and will allow for automated timing, consistent valve opening speed and unattended operation of long analytical procedures. The aim of this project is to address a need in the light stable isotope laboratory for a general-purpose vacuum line for handling and manipulation of gasses. When combined with existing instrumentation it allows for a significant expansion of current analytical capabilities. The system allows for better handling of standards, gas conversion techniques and gas sample collection for interlaboratory comparisons. The basic structure of the line, automation hardware and software were chosen and designed to provide a base for future expansion of the system to incorporate new automated analytical techniques as laboratory instrumentation and analytical needs expand.

High vacuum↗

NASA NTRS2001

Accuracy for detection of simulated lesions: comparison of fluid-attenuated inversion-recovery, proton density--weighted, and T2-weighted synthetic brain MR imaging

OBJECTIVE: The objective of our study was to determine the effects of MR sequence (fluid-attenuated inversion-recovery [FLAIR], proton density--weighted, and T2-weighted) and of lesion location on sensitivity and specificity of lesion detection. MATERIALS AND METHODS: We generated FLAIR, proton density-weighted, and T2-weighted brain images with 3-mm lesions using published parameters for acute multiple sclerosis plaques. Each image contained from zero to five lesions that were distributed among cortical-subcortical, periventricular, and deep white matter regions; on either side; and anterior or posterior in position. We presented images of 540 lesions, distributed among 2592 image regions, to six neuroradiologists. We constructed a contingency table for image regions with lesions and another for image regions without lesions (normal). Each table included the following: the reviewer's number (1--6); the MR sequence; the side, position, and region of the lesion; and the reviewer's response (lesion present or absent [normal]). We performed chi-square and log-linear analyses. RESULTS: The FLAIR sequence yielded the highest true-positive rates (p < 0.001) and the highest true-negative rates (p < 0.001). Regions also differed in reviewers' true-positive rates (p < 0.001) and true-negative rates (p = 0.002). The true-positive rate model generated by log-linear analysis contained an additional sequence-location interaction. The true-negative rate model generated by log-linear analysis confirmed these associations, but no higher order interactions were added. CONCLUSION: We developed software with which we can generate brain images of a wide range of pulse sequences and that allows us to specify the location, size, shape, and intrinsic characteristics of simulated lesions. We found that the use of FLAIR sequences increases detection accuracy for cortical-subcortical and periventricular lesions over that associated with proton density- and T2-weighted sequences.

NASA Discipline Neuroscience↗

NASA NTRS2006

NASA Tech Briefs, November 2006

Topics include: Simulator for Testing Spacecraft Separation Devices; Apparatus for Hot Impact Testing of Material Specimens; Instrument for Aircraft-Icing and Cloud-Physics Measurements; Advances in Measurement of Skin Friction in Airflow; Improved Apparatus for Testing Monoball Bearings; High-Speed Laser Scanner Maps a Surface in Three Dimensions; Electro-Optical Imaging Fourier-Transform Spectrometer; Infrared Instrument for Detecting Hydrogen Fires; Modified Coaxial Probe Feeds for Layered Antennas; Detecting Negative Obstacles by Use of Radar; Cryogenic Pound Circuits for Cryogenic Sapphire Oscillators; PixelLearn; New Software for Predicting Charging of Spacecraft; Conversion Between Osculating and Mean Orbital Elements; Generating a 2D Representation of a Complex Data Structure; Making Activated Carbon by Wet Pressurized Pyrolysis; Composite Solid Electrolyte Containing Li+- Conducting Fibers; Electrically Conductive Anodized Aluminum Surfaces; Rapid-Chill Cryogenic Coaxial Direct-Acting Solenoid Valve; Variable-Tension-Cord Suspension/Vibration- Isolation System; Techniques for Connecting Superconducting Thin Films; Versatile Friction Stir Welding/Friction Plug Welding System; Thermal Spore Exposure Vessels; Enumerating Spore-Forming Bacteria Airborne with Particles; Miniature Oxidizer Ionizer for a Fuel Cell; Miniature Ion-Array Spectrometer; Promoted-Combustion Chamber with Induction Heating Coil; Miniature Ion-Mobility Spectrometer; Mixed-Salt/Ester Electrolytes for Low-Temperature Li+ Cells; Miniature Free-Space Electrostatic Ion Thrusters; Miniature Bipolar Electrostatic Ion Thruster; Holographic Plossl Retroreflectors; Miniature Electrostatic Ion Thruster With Magnet; Using Apex To Construct CPM-GOMS Models; Sequence Detection for PPM Optical Communication With ISI; Algorithm for Rapid Searching Among Star-Catalog Entries; Expectation-Based Control of Noise and Chaos; Radio Heating of Lunar Soil to Release Gases; Using Electrostriction to Manipulate Ullage in Microgravity; Equations for Scoring Rules When Data Are Missing; Insulating Material for Next-Generation Spacecraft; and Pseudorandom Switching for Adding Radar to the AFF Sensor.

Source record↗

DOE OSTI2015

Performance of a Low Activity Beta-Sensitive SR{sup 90} Water Monitor for Fukushima

There are large volumes of contaminated water from the stabilization efforts at the damaged Fukushima Nuclear Power Plants. This water is being processed to remove radioactivity for eventual release to the environment. An on-line continuously operating system to confirm that the clean-up system is working properly, and to provide prompt feedback of the results is required by the system operator. While gamma emitting nuclides allow for the straight forward approach of gamma spectroscopy to identify and quantify radioactivity in water, pure beta emitting nuclides such as Sr{sup 90} pose a challenging problem. The relatively short range of beta radiation in water requires optimization of the measurement geometry in terms of the source-detector distance and source-detector interface while retaining a background sensitivity low enough to meet the Minimum Detectable Concentration (MDC) of 10 Bq/kg in 180 minutes. This issue is complicated by the continuum nature of the beta spectrum which does not allow for simple nuclide identification. The use of the Monte-Carlo code MCNP to estimate system performance before prototyping vastly increases the success of the end product. Various parameters such as detector size and thickness, water chamber size, water chamber construction materials were evaluated to help choose the optimum geometry. The final design was a system consisting of two large-area (16 x 35 cm) and thin (0.15 mm) plastic scintillators placed very close to a sealed a water chamber. The size of the chamber was optimized to obtain the maximum efficiency for the nuclide being measured (Sr/Y{sup 90}) but to minimize the efficiency for possible interferences (Ru/Rh{sup 106}, Cs{sup 137}). A thin carbon fiber window was selected with adequate material and thickness to contain the water under pressure, but also thin enough (0.5 mm) to allow enough beta radiation to pass through to the active detector volume. The entire measurement geometry is then housed in a thick lead shield to reduce contributions from external sources to an acceptable level. Data acquisition is accomplished through customized application-specific software that allows for long counting times to attain a low MDC, but also simultaneously provides alarms on short averaging times to achieve a fast response to sudden changes in activity concentration. Multiple monitors are then linked to supervisory software where real time data and alarms are available for analysis in remote locations. The system also allows for remote operation of the unit; check sources, background checks, systems settings and more may be accessed remotely. Testing of the production devices has shown that we can achieve the 10 Bk/kg MDC requirement for Sr{sup 90} in equilibrium with Y{sup 90} with a count time of approximately 20 minutes. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2023

A differentiable perturbation-based weak lensing shear estimator

Upcoming imaging surveys will use weak gravitational lensing to study the large-scale structure of the Universe, demanding sub-per cent accuracy for precise cosmic shear measurements. We present a new differentiable implementation of our perturbation-based shear estimator (fpfs), using jax, which is publicly available as part of a new suite of analytic shear algorithms called anacal. This code can analytically calibrate the shear response of any non-linear observable constructed with the fpfs shapelets and detection modes utilizing autodifferentiation (ad), generalizing the formalism to include a family of shear estimators with corrections for detection and selection biases. Using the ad capability of jax, it calculates the full Hessian matrix of the non-linear observables, which improves the previously presented second-order noise bias correction in the shear estimation. As an illustration of the power of the new anacal framework, we optimize the effective galaxy number density in the space of the generalized shear estimators using an LSST-like galaxy image simulation for the 10 yr LSST. For the generic shear estimator, the magnitude of the multiplicative bias |m| is below 3 × 10 –3 (99.7 per cent confidence interval), and the effective galaxy number density is improved by 5 per cent. We also discuss some planned future additions to the anacal software suite to extend its applicability beyond the fpfs measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS2004

Lunar and Planetary Science XXXV: Undergraduate Education and Research Programs, Facilities, and Information Access

The titles in this section include: 1) GRIDVIEW: Recent Improvements in Research and Education Software for Exploring Mars Topography; 2) Software and Hardware Upgrades for the University of North Dakota Asteroid and Comet Internet Telescope (ACIT); 3) Web-based Program for Calculating Effects of an Earth Impact; 4) On-Line Education, Web- and Virtual-Classes in an Urban University: A Preliminary Overview; 5) Modelling Planetary Material's Structures: From Quasicrystalline Microstructure to Crystallographic Materials by Use of Mathematica; 6) How We Used NASA Lunar Set in Planetary and Material Science Studies: Textural and Cooling Sequences in Sections of Lava Column from a Thin and a Thick Lava-Flow, from the Moon and Mars with Terrestrial Analogue and Chondrule Textural Comparisons; 7) Classroom Teaching of Space Technology and Simulations by the Husar Rover Model; 8) New Experiments (In Meteorology, Aerosols, Soil Moisture and Ice) on the New Hunveyor Educational Planetary Landers of Universities and Colleges in Hungary; 9) Teaching Planetary GIS by Constructing Its Model for the Test Terrain of the Hunveyor and Husar; 10) Undergraduate Students: An Untapped Resource for Planetary Researchers; 11) Analog Sites in Field Work of Petrology: Rock Assembly Delivered to a Plain by Floods on Earth and Mars; 12) RELAB (Reflectance Experiment Laboratory): A NASA Multiuser Spectroscopy Facility; 13) Full Text Searching and Customization in the NASA ADS Abstract Service.

Source record↗

NASA NTRS2010

Parameterizing Coefficients of a POD-Based Dynamical System

A method of parameterizing the coefficients of a dynamical system based of a proper orthogonal decomposition (POD) representing the flow dynamics of a viscous fluid has been introduced. (A brief description of POD is presented in the immediately preceding article.) The present parameterization method is intended to enable construction of the dynamical system to accurately represent the temporal evolution of the flow dynamics over a range of Reynolds numbers. The need for this or a similar method arises as follows: A procedure that includes direct numerical simulation followed by POD, followed by Galerkin projection to a dynamical system has been proven to enable representation of flow dynamics by a low-dimensional model at the Reynolds number of the simulation. However, a more difficult task is to obtain models that are valid over a range of Reynolds numbers. Extrapolation of low-dimensional models by use of straightforward Reynolds-number-based parameter continuation has proven to be inadequate for successful prediction of flows. A key part of the problem of constructing a dynamical system to accurately represent the temporal evolution of the flow dynamics over a range of Reynolds numbers is the problem of understanding and providing for the variation of the coefficients of the dynamical system with the Reynolds number. Prior methods do not enable capture of temporal dynamics over ranges of Reynolds numbers in low-dimensional models, and are not even satisfactory when large numbers of modes are used. The basic idea of the present method is to solve the problem through a suitable parameterization of the coefficients of the dynamical system. The parameterization computations involve utilization of the transfer of kinetic energy between modes as a function of Reynolds number. The thus-parameterized dynamical system accurately predicts the flow dynamics and is applicable to a range of flow problems in the dynamical regime around the Hopf bifurcation. Parameter-continuation software can be used on the parameterized dynamical system to derive a bifurcation diagram that accurately predicts the temporal flow behavior.

Kalb, Virginia L.↗