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All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Finite Volume Methods: Foundation and Analysis

Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems. They are extensively used in fluid mechanics, porous media flow, meteorology, electromagnetics, models of biological processes, semi-conductor device simulation and many other engineering areas governed by conservative systems that can be written in integral control volume form. This article reviews elements of the foundation and analysis of modern finite volume methods. The primary advantages of these methods are numerical robustness through the obtention of discrete maximum (minimum) principles, applicability on very general unstructured meshes, and the intrinsic local conservation properties of the resulting schemes. Throughout this article, specific attention is given to scalar nonlinear hyperbolic conservation laws and the development of high order accurate schemes for discretizing them. A key tool in the design and analysis of finite volume schemes suitable for non-oscillatory discontinuity capturing is discrete maximum principle analysis. A number of building blocks used in the development of numerical schemes possessing local discrete maximum principles are reviewed in one and several space dimensions, e.g. monotone fluxes, E-fluxes, TVD discretization, non-oscillatory reconstruction, slope limiters, positive coefficient schemes, etc. When available, theoretical results concerning a priori and a posteriori error estimates are given. Further advanced topics are then considered such as high order time integration, discretization of diffusion terms and the extension to systems of nonlinear conservation laws.

Barth, Timothy↗
NASA NTRS1972

Charged-particle transport in turbulent astrophysical plasmas

The effect of electromagnetic fluctuations, or plasma turbulence, on the motion of the individual particles in a plasma is investigated. Two alternative methods are used to find a general equation governing the time-evolution of a distribution of charged particles subject to both an external force field and the random fields of the fluctuations. It is found that, for the high-temperature, low-density plasmas frequently encountered in the study of astrophysics, the presence of even a small amount of turbulence can have a very important effect on the behavior of the plasma. Two problems in which turbulence plays an important role are treated.

Newman, C. E., Jr.↗
NASA NTRS1977

Electromagnetic sounding of the moon using Apollo 16 and Lunokhod 2 surface magnetometer observations /preliminary results/

A technique of deep electromagnetic sounding of the moon using simultaneous magnetic-field measurements at two lunar surface sites is described. The method, used with the assumption that deep electrical conductivity is a function only of lunar radius, has the advantage of allowing calculation of the external driving field from two surface-site measurements only and therefore does not require data from a lunar orbiting satellite. A transient-response calculation is presented for the example of a magnetic-field discontinuity, measured simultaneously by Apollo 16 and Lunokhod 2 surface magnetometers.

Vanian, L. L.↗
NASA NTRS1983

Numerical computations on one-dimensional inverse scattering problems

An approximate method to determine the index of refraction of a dielectric obstacle is presented. For simplicity one dimensional models of electromagnetic scattering are treated. The governing equations yield a second order boundary value problem, in which the index of refraction appears as a functional parameter. The availability of reflection coefficients yield two additional boundary conditions. The index of refraction by a k-th order spline which can be written as a linear combination of B-splines is approximated. For N distinct reflection coefficients, the resulting N boundary value problems yield a system of N nonlinear equations in N unknowns which are the coefficients of the B-splines.

Dunn, M. H.↗
NASA NTRS1984

Numerical computations on one-dimensional inverse scattering problems

An approximate method to determine the index of refraction of a dielectric obstacle is presented. For simplicity one dimensional models of electromagnetic scattering are treated. The governing equations yield a second order boundary value problem, in which the index of refraction appears as a functional parameter. The availability of reflection coefficients yield two additional boundary conditions. The index of refraction by a k-th order spline which can be written as a linear combination of B-splines is approximated. For N distinct reflection coefficients, the resulting N boundary value problems yield a system of N nonlinear equations in N unknowns which are the coefficients of the B-splines.

Dunn, M. H.↗
NASA NTRS1987

Nonlinear dynamics of attractive magnetic bearings

The nonlinear dynamics of a ferromagnetic shaft suspended by the force of attraction of 1, 2, or 4 independent electromagnets is presented. Each model includes a state variable feedback controller which has been designed using the pole placement method. The constitutive relationships for the magnets are derived analytically from magnetic circuit theory, and the effects of induced eddy currents due to the rotation of the journal are included using Maxwell's field relations. A rotor suspended by four electro-magnets with closed loop feedback is shown to have nine equilibrium points within the bearing clearance space. As the rotor spin speed increases, the system is shown to pass through a Hopf bifurcation (a flutter instability). Using center manifold theory, this bifurcation can be shown to be of the subcritical type, indicating an unstable limit cycle below the critical speed. The bearing is very sensitive to initial conditions, and the equilibrium position is easily upset by transient excitation. The results are confirmed by numerical simulation.

Hebbale, K. V.↗
NASA NTRS1999

Effects of an Applied Magnetic Field on the Directional Solidification of Hg(1-x)Zn(x)Se Alloys

Directionally solidified Hg(0.9)Zn(0.1)Se alloys were studied as an alternative to HgCdTe for the detection of electromagnetic radiation because of predicted improvements in lattice stability. Several boules were grown using a modified Bridgman-Stockbarger method and in an applied magnetic field. Axial compositional profiles showed mass transfer was primarily diffusion controlled. Radial compositional variations were greatly reduced when solidification occurred in an applied magnetic field. Microstructural characteristics and dislocation etch pit densities were greatly improved over HgTe based alloys. The extreme importance of processing conditions on defect generation was illustrated by comparing ampoule configurations and thermal profiles.

Cobb, S. D.↗
NASA NTRS1998

Experiments on Nucleation in Different Flow Regimes

The vast majority of metallic engineering materials are solidified from the liquid phase. Understanding the solidification process is essential to control microstructure, which in turn, determines the properties of materials. The genesis of solidification is nucleation, where the first stable solid forms from the liquid phase. Nucleation kinetics determine the degree of undercooling and phase selection. As such, it is important to understand nucleation phenomena in order to control solidification or glass formation in metals and alloys. Early experiments in nucleation kinetics were accomplished by droplet dispersion methods. Dilitometry was used by Turnbull and others, and more recently differential thermal analysis and differential scanning calorimetry have been used for kinetic studies. These techniques have enjoyed success; however, there are difficulties with these experiments. Since materials are dispersed in a medium, the character of the emulsion/metal interface affects the nucleation behavior. Statistics are derived from the large number of particles observed in a single experiment, but dispersions have a finite size distribution which adds to the uncertainty of the kinetic determinations. Even though temperature can be controlled quite well before the onset of nucleation, the release of the latent heat of fusion during nucleation of particles complicates the assumption of isothermality during these experiments. Containerless processing has enabled another approach to the study of nucleation kinetics. With levitation techniques it is possible to undercool one sample to nucleation repeatedly in a controlled manner, such that the statistics of the nucleation process can be derived from multiple experiments on a single sample. The authors have fully developed the analysis of nucleation experiments on single samples following the suggestions of Skripov. The advantage of these experiments is that the samples are directly observable. The nucleation temperature can be measured by noncontact optical pyrometry, the mass of the sample is known, and post-processing analysis can be conducted on the sample. The disadvantages are that temperature measurement must have exceptionally high precision, and it is not possible to isolate specific heterogeneous sites as in droplet dispersions. Levitation processing of refractory materials in ultra high vacuum provides an avenue to conduct these kinetic studies on single samples. Two experimental methods have been identified where ultra high vacuum experiments are possible; electrostatic levitation in ground-based experiments and electromagnetic processing in low earth orbit on TEMPUS. Such experiments, reported here, were conducted on zirconium. Liquid zirconium is an excellent solvent and has a high solubility for contaminants contained in the bulk material as well as those contaminants found in the vacuum environment. Oxides, nitrides, and carbides do not exist in the melt, and do not form on the surface of molten zirconium, for the materials and vacuum levels used in this study. Ground-based experiments with electrostatic levitation have shown that the statistical nucleation kinetic experiments are viable and yield results which are consistent with classical nucleation theory. The advantage of low earth orbit experiments is the ability to vary the flow conditions in the liquid prior to nucleation. The put-pose of nucleation experiments in TEMPUS was to examine.

Bayuzick, R. J.↗
NASA NTRS1999

Progress of Cometary Science in the Past 100 Years

Enormous strides made by cometary science during the 20th century defy any meaningful comparison of its state 100 years ago and now. The great majority of the subfields enjoying much attention nowadays did not exist in the year 1900. Dramatic developments, especially in the past 30-50 years, have equally affected observational and theoretical studies of comets. The profound diversification of observing techniques has been documented by the ever widening limits on the electromagnetic spectrum covered. While the time around 1900 marked an early period of slow and painful experimentation with photographic methods in cometary studies, observations of comets from the x-ray region to the radio waves have by now become routine. Many of the new techniques, and all those involved with the wavelengths shorter than about 300 nm, were made possible by another major breakthrough of this century - observing from space. Experiments on dedicated Earth-orbiting satellites as well as several deep-space probes have provided fascinating new information on the nature and makeup of comets. In broader terms, much of the progress has been achieved thanks to fundamental discoveries and major advances in electronics, whose applications resulted in qualitatively new instruments (e.g. radiotelescopes) and sensors or detectors (e.g. CCD arrays). The most universal effect on the entire cometary science, from observing to data handling to quantitative interpretations, has been, as in any other branch of science, due to the introduction of electronic computers, with their processing capabilities not only unheard of, but literally unimaginable, in the age of classical desk calculators. As if all this should not be enough, the today's generations of comet scientists have, in addition, been blessed with nature's highly appreciated cooperation. Indeed, in the span of a dozen years, between 1985 and 1997, we were privileged to witness four remarkable cometary events: (i) a return of Halley's celebrated comet; (ii) the impact of an extensively fragmented comet Shoemaker-Levy 9 into Jupiter - a once-in-a-millenium episode; (iii) a closeup, appearance of a small but very active Earth-approaching comet Hyakutake; and (iv) an unforgettable celestial show of comet Hale-Bopp, one of the brightest and the most massive comets ever observed. We have been - and for many years to come will be - harvesting scientifically lucrative findings based on the flood of data accumulated during observational campaigns organized for these and other recent objects. Our understanding of cometary phenomena will continue to grow as observing techniques are further being improved and as more sophisticated theories are being developed. Recent accomplishments achieved in the rapidly expanding field of comets are certain to stimulate the members of this astronomical community in their quest for new discoveries in the 21st century!

Sekanina, Zdenek↗
NASA NTRS2007

The Potential for Imaging in Situ Damage in Inflatable Space Structures

NASA is investigating the use of inflatable habitat structures for orbital transfer and planetary applications. Since space structures are vulnerable to damage from micrometeoroid and orbital debris, it is important to investigate means of detecting such damage. This study is an investigation into methods for performing non-destructive evaluation (NDE) on inflatable habitat modules. Results of this work showed that various electromagnetic imaging modalities from microwaves to terahertz imaging have the greatest potential for a viable, portable, NDE tool which could possibly be deployed aboard an inflatable habitat module.

Madaras, Eric I.↗
NASA NTRS2006

Deployable antenna

A deployable antenna and method for using wherein the deployable antenna comprises a collapsible membrane having at least one radiating element for transmitting electromagnetic waves, receiving electromagnetic waves, or both.

Fink, Patrick W.↗
NASA NTRS2002

Signal-to-Noise Ratio Prediction and Validation for Space Shuttle GPS Flight Experiment

A deterministic method for Space Station Global Positioning System (GPS) Signal-To- Noise Ratio (SNR) predictions is proposed. The complex electromagnetic interactions between GPS antennas and surrounding Space Station structures are taken into account by computational electromagnetic technique. This computer simulator is capable of taking into account multipath effects from dynamically changed solar panels and thermal radiators. A comparison with recent collected Space Station GPS system flight experiment data is presented. The simulation results are in close agreement with flight data.

Hwu, Shian U.↗
NASA NTRS2005

Issues and Methods Concerning the Evaluation of Hypersingular and Near-Hypersingular Integrals in BEM Formulations

It is known that higher order modeling of the sources and the geometry in Boundary Element Modeling (BEM) formulations is essential to highly efficient computational electromagnetics. However, in order to achieve the benefits of hIgher order basis and geometry modeling, the singular and near-singular terms arising in BEM formulations must be integrated accurately. In particular, the accurate integration of near-singular terms, which occur when observation points are near but not on source regions of the scattering object, has been considered one of the remaining limitations on the computational efficiency of integral equation methods. The method of singularity subtraction has been used extensively for the evaluation of singular and near-singular terms. Piecewise integration of the source terms in this manner, while manageable for bases of constant and linear orders, becomes unwieldy and prone to error for bases of higher order. Furthermore, we find that the singularity subtraction method is not conducive to object-oriented programming practices, particularly in the context of multiple operators. To extend the capabilities, accuracy, and maintainability of general-purpose codes, the subtraction method is being replaced in favor of the purely numerical quadrature schemes. These schemes employ singularity cancellation methods in which a change of variables is chosen such that the Jacobian of the transformation cancels the singularity. An example of the sin,oularity cancellation approach is the Duffy method, which has two major drawbacks: 1) In the resulting integrand, it produces an angular variation about the singular point that becomes nearly-singular for observation points close to an edge of the parent element, and 2) it appears not to work well when applied to nearly-singular integrals. Recently, the authors have introduced the transformation u(x(prime))= sinh (exp -1) x(prime)/Square root of ((y prime (exp 2))+ z(exp 2) for integrating functions of the form I = Integral of (lambda(r(prime))((e(exp -jkR))/(4 pi R) d D where A (r (prime)) is a vector or scalar basis function and R = Square root of( (x(prime)(exp2) + (y(prime)(exp2) + z(exp 2)) is the distance between source and observation points. This scheme has all of the advantages of the Duffy method while avoiding the disadvantages listed above. In this presentation we will survey similar approaches for handling singular and near-singular terms for kernels with 1/R(exp 2) type behavior, addressing potential pitfalls and offering techniques to efficiently handle special cases.

Fink, P. W.↗
NASA NTRS1993

Concept definition study for an extremely large aerophysics range facility

A conceptual design of a very large aeroballistic range is presented, as are its operational characteristics and procedures. The proposed model launcher is a two-stage light-gas gun, having a launch tube diameter of 254 mm, and the capability of accelerating a 14 kg launch mass to 6.1 km/sec. The gun's 91.4 cm diameter piston is driven by pressurized helium. High pressures in the central breech are contained by a multiple disk arrangement. The blast tank and sabot separation tank are described, as are methods for arresting sabot segments. The conceptual design of the range itself includes a 3.3 m diameter test or flight chamber some 330 m in length. Provisions are made for testing of free flight models and tests in which the model is confined by a track system. Methods for model deceleration and recovery are described. Provisions required for future addition of advanced model launchers such as an electromagnetic launcher or ram accelerator are addressed. Siting and safety issues are also addressed.

Swift, Hallock F.↗
NASA NTRS2007

Interfacing WIPL-D with Mechanical CAD Software

of almost any popular CAD format, e.g. IGES, Parasolid, DXF, ACIS etc. The solid models are processed (simplified) and meshed in GiD(R), and then converted into WIPL-D Pro input file by simple Fortran or Matlab code. This algorithm allows the user to control the mesh of imported geometry, and to assign electric p~perties to metalic and dielectric surfaces. Implementation of the algorithm is demonstrated by examples obtained from the NASA Discovery mission, Phoenix Lander 2008. Results for radiation pattern of Phoenix Lander UHF relay antenna with effect of Martian surface, both simulated in WIPL-D Pro and measured, are shown for comparison.

method of moments (MoM)↗
NASA NTRS2011

Method to Create Arbitrary Sidewall Geometries in 3-Dimensions Using Liga with a Stochastic Optimization Framework

Disclosed herein is a method of making a three dimensional mold comprising the steps of providing a mold substrate; exposing the substrate with an electromagnetic radiation source for a period of time sufficient to render the portion of the mold substrate susceptible to a developer to produce a modified mold substrate; and developing the modified mold with one or more developing reagents to remove the portion of the mold substrate rendered susceptible to the developer from the mold substrate, to produce the mold having a desired mold shape, wherein the electromagnetic radiation source has a fixed position, and wherein during the exposing step, the mold substrate is manipulated according to a manipulation algorithm in one or more dimensions relative to the electromagnetic radiation source; and wherein the manipulation algorithm is determined using stochastic optimization computations.

Eyre, Francis B.↗
NASA NTRS2004

Analysis of a Lunar Base Electrostatic Radiation Shield Concept

Space weather can be defined as the total ensemble of radiation in space, as well as on the surface of moons and asteroids. It consists of electromagnetic, charged-particle, and neutral particle radiation. The fundamental goal behind this NIAC Phase I research is to investigate methods of generating a static electric-field potential phi(x, y, z) in the volume above and around a "safe" or protected area on the lunar surface so that trajectories of harmful charged particle radiation are modified (deflected or reflected), thus creating a shadow over that region. Since the charged particles are not neutralized but merely redirected, there will be areas outside of the shadowed protected region that will have a higher flux concentration of radiation. One of the fundamental limitations of the static electric (electrostatic)-field approach to radiation shielding is that complete shadowing is accomplished only by complete reflection, which can only occur for shield voltages greater than or equal to the kinetic energy (in electron volts) of the incoming charged particles. Just as habitats on Earth are protected from severe weather events and conditions, such as extreme temperatures, high winds, and UV radiation, using multiple methods of shielding protection from severe space weather will undoubtedly require multiple strategies. The electrostatic shield concept may be one of many methods employed to protect astronaut habitats on the lunar surface from some of the harmful effects of space weather.

Buhler, Charles R.↗