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At least 325 records · Page 18
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NASA NTRS1994

On the wavelet optimized finite difference method

When one considers the effect in the physical space, Daubechies-based wavelet methods are equivalent to finite difference methods with grid refinement in regions of the domain where small scale structure exists. Adding a wavelet basis function at a given scale and location where one has a correspondingly large wavelet coefficient is, essentially, equivalent to adding a grid point, or two, at the same location and at a grid density which corresponds to the wavelet scale. This paper introduces a wavelet optimized finite difference method which is equivalent to a wavelet method in its multiresolution approach but which does not suffer from difficulties with nonlinear terms and boundary conditions, since all calculations are done in the physical space. With this method one can obtain an arbitrarily good approximation to a conservative difference method for solving nonlinear conservation laws.

Jameson, Leland↗
NASA NTRS1994

Fourth order difference methods for hyperbolic IBVP's

Fourth order difference approximations of initial-boundary value problems for hyperbolic partial differential equations are considered. We use the method of lines approach with both explicit and compact implicit difference operators in space. The explicit operator satisfies an energy estimate leading to strict stability. For the implicit operator we develop boundary conditions and give a complete proof of strong stability using the Laplace transform technique. We also present numerical experiments for the linear advection equation and Burgers' equation with discontinuities in the solution or in its derivative. The first equation is used for modeling contact discontinuities in fluid dynamics, the second one for modeling shocks and rarefaction waves. The time discretization is done with a third order Runge-Kutta TVD method. For solutions with discontinuities in the solution itself we add a filter based on second order viscosity. In case of the non-linear Burger's equation we use a flux splitting technique that results in an energy estimate for certain different approximations, in which case also an entropy condition is fulfilled. In particular we shall demonstrate that the unsplit conservative form produces a non-physical shock instead of the physically correct rarefaction wave. In the numerical experiments we compare our fourth order methods with a standard second order one and with a third order TVD-method. The results show that the fourth order methods are the only ones that give good results for all the considered test problems.

Gustafsson, Bertil↗
NASA NTRS1994

Regional differences in lectin binding patterns of vestibular hair cells

Surface glycoconjugates of hair cells and supporting cells in the vestibular endorgans of the bullfrog were identified using biotinylated lectins with different carbohydrate specificities. Lectin binding in hair cells was consistent with the presence of glucose and mannose (CON A), galactose (RCA-I), N-acetylgalactosamine (VVA), but not fucose (UEA-I) residues. Hair cells in the bullfrog sacculus, unlike those in the utriculus and semicircular canals, did not stain for N-acetylglucosamine (WGA) or N-acetylgalactosamine (VVA). By contrast, WGA and, to a lesser extent, VVA, differentially stained utricular and semicircular canal hair cells, labeling hair cells located in peripheral, but not central, regions. In mammals, WGA uniformly labeled Type 1 hair cells while labeling, as in the bullfrog, Type 2 hair cells only in peripheral regions. These regional variations were retained after enzymatic digestion. We conclude that vestibular hair cells differ in their surface glycoconjugates and that differences in lectin binding patterns can be used to identify hair cell types and to infer the epithelial origin of isolated vestibular hair cells.

Baird, Richard A.↗
NASA NTRS1995

Analysis of developing laminar flows in circular pipes using a higher-order finite-difference technique

A higher-order finite-difference technique is developed to calculate the developing-flow field of steady incompressible laminar flows in the entrance regions of circular pipes. Navier-Stokes equations governing the motion of such a flow field are solved by using this new finite-difference scheme. This new technique can increase the accuracy of the finite-difference approximation, while also providing the option of using unevenly spaced clustered nodes for computation such that relatively fine grids can be adopted for regions with large velocity gradients. The velocity profile at the entrance of the pipe is assumed to be uniform for the computation. The velocity distribution and the surface pressure drop of the developing flow then are calculated and compared to existing experimental measurements reported in the literature. Computational results obtained are found to be in good agreement with existing experimental correlations and therefore, the reliability of the new technique has been successfully tested.

Gladden, Herbert J.↗
NASA NTRS1995

Convergence properties of finite-difference hydrodynamics schemes in the presence of shocks

We investigate the asymptotic convergence of finite-difference schemes for the Euler equations when the limiting solution contains shocks. The Lax-Wendroff theorem guarantees that certain conservative schemes converge to correct, physically valid solutions. We focus on two one-dimensional operator-split schemes with explicit artificial-viscosity terms. One, an internal-energy scheme, does not satisfy the assumptions of Lax-Wendroff; the other, a conservative total-energy scheme, does. With viscous lengths chosen proportional to the grid size, we find that both schemes converge to their zero-grid-size limits at the theoretically expected rate, but only the conversative scheme converges toward correct solutions of the inviscid fluid equations. We show that the difference in their behaviors results directly from the presence of shocks in the limiting solution. Empirically, we find that when the viscous lenghts tend toward zero more slowly than the grid size, however the nonconservative scheme also converges toward correct solutions. We characterize the asymptotic behavior of the total-energy scheme in a particular problem in which a shock forms. As the grid is refined, a Cauchy error approaches the expected rate of change slowly. We show that the changes in the artificial viscosity alter the diffusion of small-amplitude waves. The differences associated with such waves make the dominant contribution to the Cauchy error. We formulate an analytic model to relate the rate of approach to the effect of varying diffusion in waves and find quantitative agreement with our numerical results.

Kimoto, Paul A.↗
NASA NTRS1995

The difference between radio-loud and radio-quiet active galaxies

The recent development of unified theories of active galactic nuclei (AGNs) has indicated that there are two physically distinct classes of these objects--radio-loud and radio-quiet. Despite differences, the (probable) thermal emissions from the AGNs (continua and lines from X-ray to infrared wavelengths) are quite similar to the two classes of object. We argue that this last result suggests that the black hole masses and mass accretion rates in the two classes are not greatly different, and that the difference between the classes is associated with the spin of the black hole. We assume that the normal process of accretion through a disk does not lead to rapidly spinning holes and propose that galaxies (e.g., spirals) which have not suffered a recent major merger event contain nonrotating or only slowly rotating black holes. When two such galaxies merge, the two black holes are known to form a binary and we assume that they eventually coalesce. The ratio of the number of radio-loud to radio-quiet AGNs at a given thermal (e.g., optical) luminosity is determined by the galaxy merger rate. Comparisons between the predicted and observed radio luminosity functions constrain the efficiencies with which jet power is extracted from the spinning hole and radio emission is produced by the jet.

Wilson, A. S.↗
NASA NTRS1995

Chemical studies of H chondrites. 6: Antarctic/non-Antarctic compositional differences revisited

We report data for the trace elements Au, Co, Sb, Ga, Rb, Ag, Se, Cs, Te, Zn, Cd, Bi, T1, and In (ordered by putative volatility during nebular condensation and accretion) determined by radiochemical neutron activation analysis of 14 additional H5 and H6 chondrite falls. Data for the 10 most volatile elements (Rb to In) treated by the multivariate techniques of linear discriminant analysis and logistic regression in these and 44 other falls are compared with those of 59 H4-6 chondrites from Antarctica. Various populations are tested by the multivariate techniques, using the previously developed method of randomization-simulation to assess significance levels. An earlier conclusion, based on fewer examples, that H4-6 chondrite falls are compositionally distinguishable from the Antarctic suite is verified by the additional data. This distinctiveness is highly significant because of the presence of samples from Victoria Land in the Antarctic population, which differ compositionally from falls beyond any reasonable doubt. However, it cannot be proven unequivocally that falls and Antarctic samples from Queen Maud Land are compositionally distinguishable. Trivial causes (e.g., analyst bias, weathering) cannot explain the Victoria Land (Antarctic)/non-Antarctic compositional difference for paradigmatic H4-6 chondrites. This seems to reflect a time-dependent variation of near-Earth meteoroid source regions differing in average thermal history.

Wolf, Stephen F.↗
NASA NTRS1996

Artificial Boundary Conditions Based on the Difference Potentials Method

While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears to be most significant in many areas of scientific computing, for example, in problems originating from acoustics, electrodynamics, solid mechanics, and fluid dynamics. In particular, in computational fluid dynamics (where external problems present a wide class of practically important formulations) the proper treatment of external boundaries may have a profound impact on the overall quality and performance of numerical algorithms. Most of the currently used techniques for setting the ABC's can basically be classified into two groups. The methods from the first group (global ABC's) usually provide high accuracy and robustness of the numerical procedure but often appear to be fairly cumbersome and (computationally) expensive. The methods from the second group (local ABC's) are, as a rule, algorithmically simple, numerically cheap, and geometrically universal; however, they usually lack accuracy of computations. In this paper we first present a survey and provide a comparative assessment of different existing methods for constructing the ABC's. Then, we describe a relatively new ABC's technique of ours and review the corresponding results. This new technique, in our opinion, is currently one of the most promising in the field. It enables one to construct such ABC's that combine the advantages relevant to the two aforementioned classes of existing methods. Our approach is based on application of the difference potentials method attributable to V. S. Ryaben'kii. This approach allows us to obtain highly accurate ABC's in the form of certain (nonlocal) boundary operator equations. The operators involved are analogous to the pseudodifferential boundary projections first introduced by A. P. Calderon and then also studied by R. T. Seeley. The apparatus of the boundary pseudodifferential equations, which has formerly been used mostly in the qualitative theory of integral equations and PDE'S, is now effectively employed for developing numerical methods in the different fields of scientific computing.

Tsynkov, Semyon V.↗
NASA NTRS1996

Nonstandard Finite Difference Schemes: Relations Between Time and Space Step-Sizes in Numerical Schemes for PDE's That Follow from Positivity Condition

A large class of physical phenomena can be modeled by evolution and wave type Partial Differential Equations (PDE). Few of these equations have known explicit exact solutions. Finite-difference techniques are a popular method for constructing discrete representations of these equations for the purpose of numerical integration. However, the solutions to the difference equations often contain so called numerical instabilities; these are solutions to the difference equations that do not correspond to any solution of the PDE's. For explicit schemes, the elimination of this behavior requires functional relations to exist between the time and space steps-sizes. We show that such functional relations can be obtained for certain PDE's by use of a positivity condition. The PDE's studied are the Burgers, Fisher, and linearized Euler equations.

Mickens, Ronald E.↗
NASA NTRS1995

The Effect of Different Materials on the Accuracy of the HYDRA Optical-Fiber-Coupled Coherent Range/Pressure Measurement System and the Development of the Health Care Database System at Old Dominion University

The objective of the first project involving the HYDRA laser system was to determine what effects, if any, could been seen in the system's measurements when testing was done with objects composed of different materials. Ideally we would like to have seen that the range of measurements were all within the accepted 0.4 millimeter accuracy of the system. Unfortunately our results were not as we had hoped, and there did appear to be some significant difference in the measurements made on objects composed of different materials. The second project is a continuing project at Old Dominion University. The ultimate goal is to develop a medical database that allows a doctor or hospital to keep medical records on line. The current data of the system consisted of one patient whose medical data had been hard coded to allow for a demonstration of the potentials of the system. The short term goal for this summer was to add additional patients to the system for testing, and to eliminate the hard coding of data by creating a database where data could be stored and queried to produce the results seen in the current state.

Johnson, Kimberly D.↗
NASA NTRS1996

Performance Trend of Different Algorithms for Structural Design Optimization

Nonlinear programming algorithms play an important role in structural design optimization. Fortunately, several algorithms with computer codes are available. At NASA Lewis Research Center, a project was initiated to assess performance of different optimizers through the development of a computer code CometBoards. This paper summarizes the conclusions of that research. CometBoards was employed to solve sets of small, medium and large structural problems, using different optimizers on a Cray-YMP8E/8128 computer. The reliability and efficiency of the optimizers were determined from the performance of these problems. For small problems, the performance of most of the optimizers could be considered adequate. For large problems however, three optimizers (two sequential quadratic programming routines, DNCONG of IMSL and SQP of IDESIGN, along with the sequential unconstrained minimizations technique SUMT) outperformed others. At optimum, most optimizers captured an identical number of active displacement and frequency constraints but the number of active stress constraints differed among the optimizers. This discrepancy can be attributed to singularity conditions in the optimization and the alleviation of this discrepancy can improve the efficiency of optimizers.

Patnaik, Surya N.↗
NASA NTRS1996

Time-Dependent Parabolic Finite Difference Formulation for Harmonic Sound Propagation in a Two-Dimensional Duct with Flow

An explicit finite difference real time iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for future large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable for a harmonic monochromatic sound field, a parabolic (in time) approximation is introduced to reduce the order of the governing equation. The analysis begins with a harmonic sound source radiating into a quiescent duct. This fully explicit iteration method then calculates stepwise in time to obtain the 'steady state' harmonic solutions of the acoustic field. For stability, applications of conventional impedance boundary conditions requires coupling to explicit hyperbolic difference equations at the boundary. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Kreider, Kevin L.↗
NASA NTRS1997

Experimental Data for Two Different Alternator Configurations in a Solar Brayton Power System

A solar dynamic (SD) space power system has been under test at the NASA Lewis Research Center since 1994. The SD Ground Test Demonstration (GTD) system includes a solar concentrator, heat receiver with thermal energy storage, Brayton power conversion unit, and radiator installed in a thermal-vacuum chamber with a solar simulator. The Brayton unit has been operated with two different turboalternator compressor (TAC) assemblies, one which included a Rice Lundell alternator and another which incorporated a permanent magnet (PM) alternator. The Rice alternator was part of the mini-Brayton rotating unit, designed and built during the 1970's and refurbished for the GTD. The PM TAC was a development unit from the Joint US/Russian SD Flight Project. This paper highlights the operational differences (and similarities) between the Rice and PM TAC configurations including a comparative evaluation of startup characteristics and operating performance. The two alternator configurations were tested under similar thermal conditions, as an interchangeable component within the SD system. The electrical characteristics of the two units, however, dictated the use of significantly different power conditioning and control strategies. The electrical control architectures are described and compared. Test data are presented on TAC startup and system operating performance for both configurations.

Mason, Lee S.↗
NASA NTRS1996

Comparative Evaluation of Different Optimization Algorithms for Structural Design Applications

Non-linear programming algorithms play an important role in structural design optimization. Fortunately, several algorithms with computer codes are available. At NASA Lewis Research Centre, a project was initiated to assess the performance of eight different optimizers through the development of a computer code CometBoards. This paper summarizes the conclusions of that research. CometBoards was employed to solve sets of small, medium and large structural problems, using the eight different optimizers on a Cray-YMP8E/8128 computer. The reliability and efficiency of the optimizers were determined from the performance of these problems. For small problems, the performance of most of the optimizers could be considered adequate. For large problems, however, three optimizers (two sequential quadratic programming routines, DNCONG of IMSL and SQP of IDESIGN, along with Sequential Unconstrained Minimizations Technique SUMT) outperformed others. At optimum, most optimizers captured an identical number of active displacement and frequency constraints but the number of active stress constraints differed among the optimizers. This discrepancy can be attributed to singularity conditions in the optimization and the alleviation of this discrepancy can improve the efficiency of optimizers.

Patnaik, Surya N.↗
NASA NTRS1959

Some Finite Difference Solutions of the Laminar Compressible Boundary Layer Showing the Effects of Upstream Transpiration Cooling

Three numerical solutions of the partial differential equations describing the compressible laminar boundary layer are obtained by the finite difference method described in reports by I. Flugge-Lotz, D.C. Baxter, and this author. The solutions apply to steady-state supersonic flow without pressure gradient, over a cold wall and over an adiabatic wall, both having transpiration cooling upstream, and over an adiabatic wall with upstream cooling but without upstream transpiration. It is shown that for a given upstream wall temperature, upstream transpiration cooling affords much better protection to the adiabatic solid wall than does upstream cooling without transpiration. The results of the numerical solutions are compared with those of approximate solutions. The thermal results of the finite difference solution lie between the results of Rubesin and Inouye, and those of Libby and Pallone. When the skin-friction results of one finite difference solution are used in the thermal analysis of Rubesin and Inouye, improved agreement between the thermal results of the two methods of solution is obtained.

Howe, John T.↗
NASA NTRS1998

Stressed-Oxidation Lifetime of Different SiC Fiber, CVI Matrix SiC Minicomposites in Air

The stressed-oxidation lifetime properties of several minicomposites composed of single fiber tows with a CVI SiC matrix were compared. The minicomposites were made up of Nicalon(Tm) and Hi-Nicalon(Tm) SiC fibers with carbon or BN interphases. Constant load stress-rupture tests were performed between 600 and 13000 C in air for all of the minicomposite systems. Cyclic load testing was performed on the Hi-Nicalon minicomposite systems. The factors controlling the different lifetime behaviors: fiber rupture properties, interphase oxidation, fiber degradation, and fiber-matrix bonding, are discussed in light of different minicomposite constituents. All of the systems were subject to intermediate temperature embrittlement. The Hi-Nicalon fiber, BN interphase system, performed the best for constant load conditions. For cyclic load conditions, both the BN- interphase and C-interphase minicomposites displayed poor, but different failure behavior.

Morscher, Gregory N.↗
NASA NTRS1999

Land-Ocean Differences in LIS and OTD Tropical Lightning Observations

Significant differences are known to exist on a global scale between continental and oceanic total lightning regional flash rates, suggesting differences in the properties of convective storms in these regimes. Lightning properties observed by the Optical Transient Detector (OTD) and Lightning Imaging Sensor (LIS) over land and ocean are compared, limited to analysis over the tropics in order to simplify physical interpretation. We find that the mean flash rates of individual storms over tropical land only exceed those over ocean by a factor of 2 (far less than the observed differences in regional flash rates). However, the average nearest neighbor distance of continental thunderstorms in half that over oceans. Cloud-top lightning optical radiance in oceanic storms is also twice as large as over land, suggesting either more energetic flashes over the oceans or less intervening cloud particles.

Boccippio, Dennis J.↗
NASA NTRS1999

Land-Ocean Differences in LIS and OTD Tropical Lightning Observations

Significant differences are known to exist on a global scale between continental and oceanic total lightning regional flash rates, suggesting differences in the properties of convective storms in these regimes. Lightning properties observed by the Optical Transient Detector (OTD) and Lightning Imaging Sensor (LIS) over land and ocean are compared, limited to analysis over the tropics in order to simplify physical interpretation. We find that the mean flash rates of individual storms over tropical land only exceed those over ocean by a factor of 2 (far less than the observed differences in regional flash rates). However, the average nearest neighbor distance of continental thunderstorms is half that over oceans. Cloud-top lightning optical radiance in oceanic storms is also twice as large as over land, suggesting either more energetic flashes over the oceans or less intervening cloud particles.

Boccippio, D. J.↗