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NASA NTRS1987

A direct algorithm for solution of incompressible three-dimensional unsteady Navier-Stokes equations

A direct, implicit, numerical solution algorithm, with second-order accuracy in space and time, is constructed for the three-dimensional unsteady incompressible Navier-Stokes equations formulated in terms of velocity and vorticity, using generalized orthogonal coordinates to achieve the accurate solution of complex viscous flow configurations. A numerically stable, efficient, direct inversion procedure is developed for the computationally intensive divergence-curl elliptic velocity problem. This overdetermined partial differential operator is first formulated as a uniquely determined, nonsingular matrix-vector problem; this aspect of the procedure is a unique feature of the present analysis. The three-dimensional vorticity-transport equation is solved by a modified factorization technique which completely eliminates the need for any block-matrix inversions and only scalar tridiagonal matrices need to be inverted. The method is applied to the test problem of the three-dimensional flow within a shear-driven cubical box. Coherent streamwise vortex structures are observed within the steady-state flow at Re = 100.

Osswald, G. A.↗

NASA NTRS1987

Color graphics techniques for shaded surface displays of aerodynamic flowfield parameters

A variety of algorithms are presented that are useful in the color graphics displays of large sets of three-dimensional aerodynamic data. These methods augment established techniques for rapidly and interactively reviewing an assortment of smooth-shaded, color-coded illustrations for experimental and computational distributions of both scalar and vector quantities.

Weston, Robert P.↗

NASA NTRS1987

Analysis models for the estimation of oceanic fields

A general model for statistically optimal estimates is presented for dealing with scalar, vector and multivariate datasets. The method deals with anisotropic fields and treats space and time dependence equivalently. Problems addressed include the analysis, or the production of synoptic time series of regularly gridded fields from irregular and gappy datasets, and the estimate of fields by compositing observations from several different instruments and sampling schemes. Technical issues are discussed, including the convergence of statistical estimates, the choice of representation of the correlations, the influential domain of an observation, and the efficiency of numerical computations.

Carter, E. F.↗

NASA NTRS1987

A simplified derivation of stimulated emission by black holes

A black hole, when acting as a scatterer for quanta in a single mode of a massless scalar field, is known to convert any ingoing Gibbs state of that mode into an outgoing Gibbs state (with some other mean particle number). The paper presents a simple derivation for this property which may help to clarify what relation, if any, it bears to the microscopic structure of the black hole horizon.

Sorkin, Rafael D.↗

NASA NTRS1987

Macroscale particle simulation of kinetic Alfven waves

Two types of simulations of the kinetic Alfven wave are presented using a macroscale particle simulation code (Tanaka and Sato, 1986) which enables individual particle dynamics to be followed in the MHD scales. In this code, low frequency electromagnetic fields are solved by eliminating high frequency oscillations such as the light modes, and the scalar potential electric field is solved by eliminating Lagrangian oscillations. The dependences of the frequency and the Landau damping on the perpendicular wavenumber were studied, and good agreement was found between simulation and theoretical predictions. Some fundamental nonlinear interactions of the kinetic Alfven wave with the particles (parallel acceleration of the electrons) were also noted.

Tanaka, Motohiko↗

NASA NTRS1987

A new approach to the effect of sound on vortex dynamics

Analytical results are presented on the effect of acoustic radiation on three-dimensional vortex motions in a homogeneous, slightly compressible, inviscid fluid. The flow is considered as linear and irrotational everywhere except inside a very thin cylindrical core region around the vortex filament. In the outside region, a velocity potential is introduced that must be multivalued, and it is shown how to compute this scalar potential if the motion of the vortex filament is prescribed. To find the motion of this singularity in an external potential flow, a variational principle involving a volume integral that must exclude the singular region is considered. A functional of the external potential and vortex filament position is obtained whose extrema give equations to determine the sought-after evolution. Thus, a generalization of the Biot-Savart law to flows with constant sound speed at low Mach number is obtained.

Lund, Fernando↗

NASA NTRS1987

Extrapolation methods for vector sequences

This paper derives, describes, and compares five extrapolation methods for accelerating convergence of vector sequences or transforming divergent vector sequences to convergent ones. These methods are the scalar epsilon algorithm (SEA), vector epsilon algorithm (VEA), topological epsilon algorithm (TEA), minimal polynomial extrapolation (MPE), and reduced rank extrapolation (RRE). MPE and RRE are first derived and proven to give the exact solution for the right 'essential degree' k. Then, Brezinski's (1975) generalization of the Shanks-Schmidt transform is presented; the generalized form leads from systems of equations to TEA. The necessary connections are then made with SEA and VEA. The algorithms are extended to the nonlinear case by cycling, the error analysis for MPE and VEA is sketched, and the theoretical support for quadratic convergence is discussed. Strategies for practical implementation of the methods are considered.

Smith, David A.↗

NASA NTRS1987

Thermocapillary migration of a gas bubble in an arbitrary direction with respect to a plane surface

The thermocapillary migration of a gas bubble in an unbounded fluid in the presence of a neighboring rigid plane surface is considered in the limit of negligible Reynolds and Marangoni numbers. Results are given for a scalar interaction parameter defined as the ratio of the speed of the bubble in the presence of the plane surface to the speed in its absence. It is suggested that the weaker interaction effects noted for the case of thermocapillary migration relative to the case of motion due to a body force such as that caused by a gravitational field is attributable to the more rapid decay, away from the bubble, of the disturbance velocity and temperature gradient fields. The surface is found to exert the greatest influence in the case of motion normal to it, and the weakest influence in the case of parallel motion.

Meyyappan, M.↗

NASA NTRS1988

Ada Linear-Algebra Program

Routines provided for common scalar, vector, matrix, and quaternion operations. Computer program extends Ada programming language to include linear-algebra capabilities similar to HAS/S programming language. Designed for such avionics applications as software for Space Station.

Klumpp, A. R.↗

NASA NTRS1985

Aerothermal modeling program, phase 2

The main objectives of the Aerothermal Modeling Program, Phase 2 are: to develop an improved numerical scheme for incorporation in a 3-D combustor flow model; to conduct a benchmark quality experiment to study the interaction of a primary jet with a confined swirling crossflow and to assess current and advanced turbulence and scalar transport models; and to conduct experimental evaluation of the air swirler interaction with fuel injectors, assessments of current two-phase models, and verification the improved spray evaporation/dispersion models.

Mongia, H. C.↗

NASA NTRS1987

Time-domain robotic vision application

The quest for the highest resolution microwaves imaging and the principle of time-domain imaging is the primary motivation for recent developments in time-domain techniques. With the present technology fast time varying signals can now be measured and recorded both in magnitude and in phase. It has also enhanced the ability to extract relevant details concerning the scattering object. In the past, the inference of object geometry or shape from scattered signals has received substantial attention in radar technology. Various inverse scattering theories were proposed to develop analytical solutions to this problem. Furthermore, the random inversion, frequenty swept holography, and the synthetic radar imaging, all of which have two things in common: the physical optic far-field approximation and the utilization of the channels as an extra physical dimension, were also advanced significantly. Despite the inherent vectorial nature of electromagnetic waves, these scalar treatments have brought forth some promising results in practice with notable examples in subsurface and structure sounding. The use of time-domain imaging for space robotic vision applications was proposed. A multisensor approach to vision was shown to have several advantages over the video-only approach.

Tolliver, C. L.↗

NASA NTRS1988

Spectral dilation of L(B,H)-valued measures and its application to stationary dilation for Banach space valued processes

Let B be a Banach space and H and K two Hilbert spaces. The spectral dilation of L(B,H)-valued measures is studied and it is shown that the recent results of Makagon and Salehi (1986) and Rosenberg (1982) on the dilation of L(K,H)-valued measures can be extended to hold for the general Banach space setting of L(B,H)-valued measures. These L(B,H)-valued measures are closely connected to the Banach space valued processes. This connection is recalled and as application of spectral dilation of L(B,H)-valued measures the well known stationary dilation results for scalar valued processes is extended to the case of Banach space valued processes.

Miamee, A. G.↗

NASA NTRS1988

A vectorized Poisson solver over a spherical shell and its application to the quasi-geostrophic omega-equation

The quasi-geostrophic omega-equation in flux form is developed as an example of a Poisson problem over a spherical shell. Solutions of this equation are obtained by applying a two-parameter Chebyshev solver in vector layout for CDC 200 series computers. The performance of this vectorized algorithm greatly exceeds the performance of its scalar analog. The algorithm generates solutions of the omega-equation which are compared with the omega fields calculated with the aid of the mass continuity equation.

Mullenmeister, Paul↗

NASA NTRS1987

A comparison of the Cray-2 performance before and after the installation of memory pseudo-banking

A suite of 13 large Fortran benchmark codes were run on a Cray-2 configured with memory pseudo-banking circuits, and floating point operation rates were measured for each under a variety of system load configurations. These were compared with similar flop measurements taken on the same system before installation of the pseudo-banking. A useful memory access efficiency parameter was defined and calculated for both sets of performance rates, allowing a crude quantitative measure of the improvement in efficiency due to pseudo-banking. Programs were categorized as either highly scalar (S) or highly vectorized (V) and either memory-intensive or register-intensive, giving 4 categories: S-memory, S-register, V-memory, and V-register. Using flop rates as a simple quantifier of these 4 categories, a scatter plot of efficiency gain vs Mflops roughly illustrates the improvement in floating point processing speed due to pseudo-banking. On the Cray-2 system tested this improvement ranged from 1 percent for S-memory codes to about 12 percent for V-memory codes. No significant gains were made for V-register codes, which was to be expected.

Schmickley, Ronald D.↗

NASA NTRS1988

Total Variation Diminishing (TVD) schemes of uniform accuracy

Explicit second-order accurate finite-difference schemes for the approximation of hyperbolic conservation laws are presented. These schemes are nonlinear even for the constant coefficient case. They are based on first-order upwind schemes. Their accuracy is enhanced by locally replacing the first-order one-sided differences with either second-order one-sided differences or central differences or a blend thereof. The appropriate local difference stencils are selected such that they give TVD schemes of uniform second-order accuracy in the scalar, or linear systems, case. Like conventional TVD schemes, the new schemes avoid a Gibbs phenomenon at discontinuities of the solution, but they do not switch back to first-order accuracy, in the sense of truncation error, at extrema of the solution. The performance of the new schemes is demonstrated in several numerical tests.

Hartwich, PETER-M.↗

NASA NTRS1988

Structure of a viscoplastic theory

The general structure of a viscoplastic theory is developed from physical and thermodynamical considerations. The flow equation is of classical form. The dynamic recovery approach is shown to be superior to the hardening function approach for incorporating nonlinear strain hardening into the material response through the evolutionary equation for back stress. A novel approach for introducing isotropic strain hardening into the theory is presented, which results in a useful simplification. In particular, the limiting stress for the kinematic saturation of state (not the drag stress) is the chosen scalar-valued state variable. The resulting simplification is that there is no coupling between dynamic and thermal recovery terms in each evolutionary equation. The derived theory of viscoplasticity has the structure of a two-surface plasticity theory when the response is plasticlike, and the structure of a Bailey-Orowan creep theory when the response is creeplike.

Freed, Alan D.↗

NASA NTRS1987

Spaceborne magnetometry

Low orbit (160 km altitude) satellite magnetometry is discussed. Magnetic field simulations and theoretical analyses were performed. They suggest that at 160 km, resolution value is 10, compared to 0.6 for Magsat, and that the satellite can reveal significant information on crustal tectonics. Vector and scalar magnetometers should be carried.

Taylor, P. T.↗

NASA NTRS1988

Some implications for cyclic plastic and viscoplastic equations based on nonproportional loading experiments

From cyclic, strain controlled, nonproportional tests on type 304 stainless steel and Hastelloy-X, the following statements may be made: (1) A dynamic recovery term is essential to properly model the backstress evolution. (2) From analysis of Hastelloy-X data obtained at 649 C, the inelastic strain rate appears to be a satisfactory directional index for direct hardening, but the backstress appears to be an inappropriate directional index of dynamic recovery. (3) Sinusoidal, 90 deg out-of-phase axial torsional tests can be very useful in aiding determination of backstress evolution functions, including both directional indices and scalar hardening functions, by virtue of the associated approximately constant magnitudes of overstress, inelastic strain rate, and effective stress. Such tests have previously been associated with the study of nonproportional hardening effects but have more far ranging applications.

Mcdowell, D. L.↗