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At least 253 records · Page 14
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NASA NTRS1985

Drift and observations in cosmic-ray modulation, 1

It is illustrated that a relative simple drift model can, in contrast with no drift models, simultaneously fit proton and electron spectra observed in 1965-66 and 1977, using a single set of modulation parameters except for a change in the IMF polarity. This result is interpreted together with the observation of Evenson and Meyer that electrons are recovering more rapidly than protons after 1980, in contrast with what Burger and Swanenburg observed in 1968-72, as a charge sign dependent effect due to the occurrence of drift in cosmic ray modulation. The same set of parameters produces a shift in the phase and amplitude of the diurnal anisotropy vector, consistent with observations in 1969-71 and 1980-81.

Potgieter, M. S.↗
NASA NTRS1985

Application of a variational method for generating adaptive grids

The application of variational methods for generating adaptive grids is not as straightforward as one is led to believe. Proper scaling, suitable weight functions and appropriate clustering on boundaries must be employed to obtain a satisfactory grid. This work, which is based on the framework developed by Brackbill and Saltzman, provides simple methods for determining scaling and investigates possible options for selecting the weight function and clustering points on the boundaries. The concepts developed here are applied to two two-dimensional problems: a model problem based on Burger's equation which contains two length scales and, transonic flow past airfoils using the Euler equations.

Kreis, R. I.↗
NASA NTRS1985

Higher order methods for convection-diffusion problems

This paper applies C1 cubic Hermite polynomials embedded in an orthogonal collocation scheme to the spatial discretization of the unsteady nonlinear Burgers equation as a model of the equations of fluid mechanics. The temporal discretization is carried out by means of either a noniterative finite difference or an iterative finite difference procedure. Results of this method are compared with those of a second-order finite difference scheme and a splined-cubic Taylor's series scheme. Stability limits are derived and the matrix structure of the several schemes are compared.

Murphy, J. D.↗
NASA NTRS1985

The effects of transient rheology on the interpretation of lower mantle viscosity

The role played by transient rheology in the interpretation of mantle viscosity is reexamined. The investigation has been carried out by comparing the amplitude responses with the data of secular variation of J(2), the relative sea-level histories at sites well within the ice margins and at the ice margin like the city of Boston. A linear Burgers body rheology has been assumed in ther lower mantle. The data near the edge of the ice load proves most sensitive to the transient viscosity structure. The non-monotonic behavior of sea-level data near Boston can be explained both by a steady-state lower mantle viscosity of 10 to the 22nd P with a thick lithosphere and by a transient lower mantle rheology but with a thin lithosphere. The long-term viscosity of the lower mantle in this second model has a steady-state value of around 5 x 10 to the 23rd P.

Sabadini, R.↗
NASA NTRS1985

High resolution TVD schemes using flux limiters

Roe (1981, 1985) has utilized flux limiters to obtain second order monotonicity preserving schemes. In the present paper, the foundation for flux limiters in the formulation of first order three-point schemes are discussed, and a systematic outline is provided of the method of using flux limiters to obtain second order accurate TVD schemes. Attention is given to Phi limiters, the Van Leer limiter, the Chakravarthy-Osher limiter, the linear advection equation and square wave data, the inviscid Burger's equation, and the extension of flux limiters to irregular grids, systems of equations, and implicit calculations.

Sweby, P. K.↗
NASA NTRS1986

Polynomial elimination theory and non-linear stability analysis for the Euler equations

Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.

Kennon, S. R.↗
NASA NTRS1986

The well-posedness of the Kuramoto-Sivashinsky equation

The Kuramoto-Sivashinsky equation arises in a variety of applications, among which are modeling reaction diffusion systems, flame propagation and viscous flow problems. It is considered here, as a prototype to the larger class of generalized Burgers equations: those consist of a quadratic nonlinearity and an arbitrary linear parabolic part. It is shown that such equations are well posed, thus admitting a unique smooth solution, continuously dependent on its initial data. As an attractive alternative to standard energy methods, existence and stability are derived in this case, by patching in the large short time solutions without 'loss of derivatives'.

Tadmor, E.↗
NASA NTRS1986

Excitation of the earth's rotational axis by recent glacial discharges

The effects of present-day glacial discharges and the growth of the Antarctic ice sheet on exciting the earth's rotational axis are studied. Glacial forcing could cause a maximum change in J2 of about one-third of the observed amount, for the Maxwell rheology and for Burgers' body models with a long-term, lower-mantle viscosity greater than about 10 to the 23rd P. For transient rheologies the amount of excitation due to glacial melting decreases. Polar wander is not much excited by recent glacial melting for the various types of rheologies examined.

Gasperini, P.↗
NASA NTRS1986

Orientation and temperature dependence of some mechanical properties of the single-crystal nickel-base superalloy Rene N4. I - Tensile behavior

Single crystal specimens of a nickel-base superalloy with axes near 001, 011, and -112 were tested in tension at room temperature, 760, and 980 C. The alloy Rene N-4, was developed for gas turbine engine blades and has the nominal composition 3.7 Al, 4.2 Ti, 4 Ta, 0.5 Nb, 6 W, 1.5 Mo, 9 Cr, 7.5 Co, balance Ni, (all in weight percent). Analysis of slip band traces, specimen axis rotation, and dislocation Burgers vectors showed that at 760 and 980 C primary cube slip supplanted normal octahedral slip for the -112 line-oriented specimens. The other two orientations, which have lower resolved shear stresses on the cube system, exhibited octahedral slip at all three temperatures. The critical resolved shear stress is considerably greater on the cube system than on the octahedral system at room temperature. However, at 760 and 980 C the critical resolved shear stresses on the two systems are about the same. While the room temperature and 980 C yield strengths for the two orientations exhibiting octahedral slip could be rationalized on the basis of resolved shear stress, those at 760 C could not. Such violations of Schmid's law have previously been observed in other superalloys and single phase gamma-prime.

Miner, R. V.↗
NASA NTRS1987

An Exponential Finite Difference Technique for Solving Partial Differential Equations

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that were more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.

Handschuh, Robert F.↗
NASA NTRS1985

Recent developments in FEM-CFD

The current status of CFD with regard to unstructured grids employing finite element methods and Eulerian frames is reviewed. Algorithms suitable for the computation of large three-dimensional problems involving flow past arbitrary geometries are developed. Adaptive mesh refinement strategy is reviewed, and domain splitting or local time-stepping are briefly addressed. The development of search algorithms of optimal order, variable time-stepping Jacobi smoothers for elliptic problems, and transport concepts for hyperbolics to help achieve good performance for unstructured multigrid processes is discussed. As examples, transient supersonic flow in a channel, regular shock reflection of a wall, viscous flow past a protruberance, potential flow past a cylinder, and Burgers equation are considered.

Loehner, R.↗
NASA NTRS1985

Numerical solution of the Euler equation for compressible inviscid fluids

An effort is made to develop a satisfactory numerical method for the calculation of steady solutions of the Euler equations for inviscid compressible gas flows. The intended application is the prediction of the aerodynamic properties of aircraft flying at transonic speeds. Particular consideration is given to the modification of the equations to improve convergence to a steady state; finite volume formulation; adaptive dissipation; schemes designed to improve the resolution of shock waves; hybrid multistage time stepping schemes; residual averaging; a multigrid scheme; and trials with Burgers' equation. Results clearly demonstrate that the convergence of a time-dependent hyperbolic system to a steady state can be substantially accelerated by the introduction of multiple grids.

Jameson, A.↗
NASA NTRS1987

Large-scale fluctuations in the interplanetary medium

Power spectra of measurements of the magnetic field strength in the heliosphere obtained by Voyager 1 between 1 AU and 9 AU have the form of a power law f exp -a from periods of several hours to at least 6 days. The exponent was a = 2.0 + or - 0.05 for all of the spectra considered, which is the exponent for a series of steps and for Burgers' (1971) turbulence. Spectra of large-scale speed fluctuations also have the form f exp - b from a period of a few hours to periods greater than 13 days in the region from 1 AU to 8.9 AU. The exponent b is generally somewhat larger than b = 2, implying some 'persistence' of the speed fluctuations. The low-frequency cutoff (outer cutoff) of the power law increases from a period of 6.5 days at 1 AU to 26 days at (6.1-8.9) AU, which can be attributed to: (1) the coalescence of interaction regions and (2) a transfer of energy from the spectrum of large-scale speed fluctuations. The outer cutoff of the spectrum of speed fluctuations increases from a period of 13 days at 1 AU to 26 days between a few AU and 8.9 AU. Both the magnetic field strength fluctuations and the speed fluctuations have fractal behavior, suggesting that they are self affine rather than dominated by a few large discontinuities.

Burlaga, L. F.↗
NASA NTRS1987

TEM investigation of beta-SiC grown epitaxially on Si substrate by CVD

A transmission electron microscopy study is being conducted on the microstructure of beta-SiC films grown epitaxially on 001-plane silicon by chemical vapor deposition. Observations have been made in plain view and in cross-section. A high density of stacking faults has been found in the bulk of the epilayer which are bounded by partials of the Shockley type with Burgers vectors 1/6 211-line. Cross-sectional high resolution electron microscopy of the interface has shown it to be semicoherent with misfit dislocations to accommodate the lattice parameter difference between the substrate and the epilayer. In addition to misfit dislocations, a high density of twins and some stacking faults are present in the SiC near the interface. Mechanisms for the nucleation and growth of these defects are discussed.

Chorey, C. M.↗
NASA NTRS1987

Consequences of experimental transient rheology

Recent analyses of transient creep data for lower crustal and upper mantle substances are used to constrain the viscosity contrast across the 670 km discontinuity, and a 4-layer earth model in which both upper and lower mantles are described by a Burgers body rheology is assumed. Results indicate that the previously inferred viscosity variations would be reduced by a factor of ten using the new transient models. This result is in agreement with a revised viscosity estimate based on long-wavelength geoid anomalies and seismic tomography. Time-dependent perturbations to the gravity field from recent ice movements are shown to be significant.

Sabadini, Roberto↗
NASA NTRS1988

Analysis of the spectral vanishing viscosity method for periodic conservation laws

The convergence of the spectral vanishing method for both the spectral and pseudospectral discretizations of the inviscid Burgers' equation is analyzed. It is proven that this kind of vanishing viscosity is responsible for a spectral decay of those Fourier coefficients located toward the end of the computed spectrum; consequently, the discretization error is shown to be spectrally small independent of whether the underlying solution is smooth or not. This in turn implies that the numerical solution remains uniformly bounded and convergence follows by compensated compactness arguments.

Maday, Yvon↗
NASA NTRS1988

Non-oscillatory spectral Fourier methods for shock wave calculations

A non-oscillatory spectral Fourier method is presented for the solution of hyperbolic partial differential equations. The method is based on adding a nonsmooth function to the trigonometric polynomials which are the usual basis functions for the Fourier method. The high accuracy away from the shock is enhanced by using filters. Numerical results confirm that no oscillations develop in the solution. Also, the accuracy of the spectral solution of the inviscid Burgers equation is shown to be higher than a fixed order.

Cai, Wei↗
NASA NTRS1988

Mantle rheology and satellite signatures from present-day glacial forcings

Changes in the long-wavelength region of the earth's gravity field resulting from both present-day glacial discharges and the possible growth of the Antarctic ice sheet are considered. Significant differences in the responses between the Maxell and Burger body rheologies are found for time spans of less than 100 years. The quantitative model for predicting the secular variations of the gravitational potential, and means for incorporating glacial forcings, are described. Results are given for the excitation of the degree two harmonics. It is suggested that detailed satellite monitoring of present-day ice movements in conjunction with geodetic satellite missions may provide a reasonable alternative for the esimation of deep mantle viscosity.

Sabadini, Roberto↗