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NASA NTRS1989

The nonlinear breakup of the sun's toroidal field

There are good reasons for believing that the sun has a strong toroidal magnetic field in the stably stratified region of convective overshoot sandwiched between the radiative zone and convective zone proper. The magnetic field in this region is modeled by studying the behavior of a layer of uniform field embedded in a subadiabatic atmosphere. Since the field can support extra mass, such a configuration is top-heavy, and instabilities of the Rayleigh-Taylor type can occur. Numerical integration of the two-dimensional compressible MHD equations makes it possible to follow the evolution of this instability into the nonlinear regime. The initial buoyancy-driven instability of the magnetic field gives rise to strong shearing motions, thereby exciting secondary Kelvin-Helmholtz instabilities which wrap the gas into regions of intense vorticity. The somewhat surprising subsequent motions are determined primarily by the strong interactions between vortices.

Hughes, D. W.↗

NASA NTRS1990

Recurrence in truncated Boussinesq models for nonlinear waves in shallow water

The rapid spatial recurrence of weakly nonlinear and weakly dispersive progressive shallow-water waves is examined using a numerical integration technique on the discretized and truncated form of the Boussinesq equations. This study primarily examines recurrence in wave fields with Ursell number O(1) and characterizes the sensitivity of recurrence to initial spectral shape and number of allowed frequency modes. It is shown that the rapid spatial recurrence is not an inherent property of the considered Boussinesq systems for evolution distances of 10-50 wavelengths. The main result of the study is that highly truncated Boussinesq models of resonant shallow-water ocean surface gravity waves predict rapid multiple recurrence cycles, but that this is an artifact dependent on the number of allowed modes. For initial conditions consisting of essentially all energy concentrated in a single mode, damping of the recurrence cycles increases as the number of low-power background modes increases. When more than 32 modes are allowed, the recurrence behavior is relatively insensitive to the number of allowed modes.

Elgar, Steve↗

NASA NTRS1990

Computation of convective flow with gravity modulation in rectangular cavities

In this work, a computational study is presented for the investigation of gravity modulation (g-jitter) effects in thermally driven cavity flows at terrestrial and microgravity environments. The two-dimensional, time-dependent Navier-Stokes equations are numerically integrated by a time-split method using direct matrix solvers. Computations at terrestrial gravity are utilized to assess the effects of adiabatic side-wall boundary conditions as well as the full nonlinearity of the governing equations on the sinusoidally forced Benard problem studied by Gresho and Sani. The low-g calculations focus on the establishment of critical frequency ranges and consider the effects of modulation direction and randomness. The applicability of linear analysis in the excitable frequency range at low g is also discussed.

Biringen, S.↗

NASA NTRS1990

A statistical study of the differential very long baseline interferometry delay rate error budget

The delta differential one-way Doppler (delta-DOD) error budget is assessed by analyzing 12 years of dual-frequency Deep Space Network very long baseline interferometry data. A typical delta-DOD observation is outlined, and the Magellan error budget along with tropospheric effects are considered. Formation of quasar-quasar observables, RMS delta-DOD residual, angular source separation and time separation between observations are discussed, along with elevation angle and atmospheric pathlength dependence, solar-plasma and ionospheric effects. It is concluded that the weak dependence of the delta-DOD error on angular source separation can mean that quasars with larger angular separation from a spacecraft may be used as navigation reference with little increase in the delta-DOD error. It is also indicated that the delta-DOD errors are dominated by wet troposphere fluctuations, and the results of numerical integrations for the single-station RMS delay rate at different elevation angles are presented.

Edwards, Charles D.↗

NASA NTRS1990

The application of Encke's method to long arc orbit determination solutions

The Laser Geodynamics Satellite (LAGEOS) was launched on May 4, 1976 to provide geophysical measurements by means of laser ranging techniques. To date, over twelve years of laser range measurements have been collected from various tracking stations located around the world. Laser range measurements to LAGEOS have contributed to studies of earth rotation, plate tectonics, global baseline, and the gravity field as well as many other areas. Some of these studies are based upon the determination of a single, continuous orbit for LAGEOS for time spans on the order of several years. Current studies at the University of Texas Center for Space Research include the precision orbit determination of LAGEOS for arc lengths of up to 12.8 years which represents over 31,000 orbital revolutions. These long arc studies have led to the implementation of Encke's method to improve the convergence of the batch filter while reducing numerical integration errors. While the technique has been successfully applied to arc lengths of up to 12.8 years, the results presented focus on the solution of a six-year arc.

Lundberg, J. B.↗

NASA NTRS1990

Comparisons of one- and two- interface methods for tunnel wall interference calculation

Tunnel wall interference in two-dimensional subsonic flow can be analytically calculated on the basis of the one- or two-interface method. The application of numerical integration by means of matrix multiplication to both methods has been found to significantly reduce CPU time in on-line operation. An investigation of the sensitivity of these methods to random velocity-measurement disturbances shows the one-interface method to be less sensitive to measurement errors, and therefore to be preferable for practical applications.

Lo, C. F.↗

NASA NTRS1990

The orbits of the satellites of Neptune

This article presents the results of a fit of numerically integrated Neptunian satellite orbits to earth-based astrometric observations and early Voyager spacecraft observations. Ephemerides based on these orbits were used by the Voyager project as the final pre-encounter ephemerides. As a by-product of the orbit fits, estimates of the Neptune mass, the second zonal harmonic of Neptune, and the pole orientation of Neptune were also obtained.

Jacobson, R. A.↗

NASA NTRS1991

Faster Algorithm For Computation Of Incompressible Flow

Improved algorithm yields faster numerical solutions of Navier-Stokes equations of steady or unsteady three-dimensional flow of incompressible fluid. In artificial-compressibility method, unsteady flow treated as incompressible in advancing from one time step to next, but at each time step (or in steady state), fluid treated as having variable compressibility enabling propagation of flow field, and subiterations performed in increments of pseudotime until effects of compressibility subside. Directly couples pressure and velocity fields at same time step and converts elliptic incompressible Navier-Stokes equations to hyperbolic form more amenable to numerical integration.

Rogers, S. E.↗

NASA NTRS1991

Simulation Of Flow In A Turbine Cascade

Report discusses application of lower-upper (LU) implicit numerical-integration scheme, together with interactive grid-generation method, to simulation of inviscid, compressible flow in two-dimensional model of turbine cascade. Study part of continuing effort to develop techniques for computation of complicated three-dimensional flows in turbomachinery.

Choo, Yung K.↗

NASA NTRS1991

Calculating Transient Vibrations Of Coupled Substructures

Finite-element, numerical-integration method for estimating transient vibrational response of structure composed of coupled substructures entails less computation. Responses of substructures to external forces and to forces of interaction between substructures computed. Equations of motion of each substructure solved independently. Applicable to any number and configuration of linearly responding substructures and to both determinate and indeterminate boundary conditions at interfaces between substructures. Also applicable to changing interface boundary conditions.

Admire, J. R.↗

NASA NTRS1991

Overview Of Methods For Computation Of Shocks

NASA technical memorandum provides systematic overview of class of conservative finite-difference shock-capturing numerical-integration methods for solution of hyperbolic conservation laws. Unified and generalized formulation for one class of methods presented.

Yee, H. C.↗

NASA NTRS1991

Speeding Convergence In Simulations Of Hypersonic Flow

Report describes study aimed at accelerating rates of convergence of iterative schemes for numerical integration of equations of hypersonic flow of viscous and inviscid fluids. Richardson-type overrelaxation method applied.

Flores, J.↗

NASA NTRS1991

Navier-Stokes Simulation Of Wind-Tunnel Flow

Report describes three-dimensional Navier-Stokes simulation of transonic flow past model wing in wind tunnel and in free air. Numerical integration performed by LU-ADI factorization algorithm. Simulation shows effects of walls of tunnel.

Obayashi, S.↗

NASA NTRS1991

Navier-Stokes Computations On Zonal Grids

Report describes numerical simulations of transonic flow of air about isolated wing and about wing and fuselage (not tail assembly) of F-16A aircraft. Fast, diagonalized Beam-Warming numerical-integration algorithm for solution of Euler and Navier-Stokes equations applied via Transonic Navier-Stokes computer program, using computational grids divided into zones of coarse and finer meshes.

Flores, Jolen↗

NASA NTRS1991

Direct Finite-Difference Simulations Of Turbulent Flow

Report discusses use of upwind-biased finite-difference numerical-integration scheme to simulate evolution of small disturbances and fully developed turbulence in three-dimensional flow of viscous, incompressible fluid in channel. Involves use of computational grid sufficiently fine to resolve motion of fluid at all relevant length scales.

Rai, Man Mohan↗

NASA NTRS1990

A piloted simulator evaluation of a ground-based 4-D descent advisor algorithm

A ground-based, four dimensional (4D) descent-advisor algorithm is under development at NASA-Ames. The algorithm combines detailed aerodynamic, propulsive, and atmospheric models with an efficient numerical integration scheme to generate 4D descent advisories. The ability is investigated of the 4D descent advisor algorithm to provide adequate control of arrival time for aircraft not equipped with on-board 4D guidance systems. A piloted simulation was conducted to determine the precision with which the descent advisor could predict the 4D trajectories of typical straight-in descents flown by airline pilots under different wind conditions. The effects of errors in the estimation of wind and initial aircraft weight were also studied. A description of the descent advisor as well as the result of the simulation studies are presented.

Davis, Thomas J.↗

NASA NTRS1990

Dynamic Analysis and Control of Lightweight Manipulators with Flexible Parallel Link Mechanisms

The objective is the theoretical analysis and the experimental verification of dynamics and control of a two link flexible manipulator with a flexible parallel link mechanism. Nonlinear equations of motion of the lightweight manipulator are derived by the Lagrangian method in symbolic form to better understand the structure of the dynamic model. The resulting equation of motion have a structure which is useful to reduce the number of terms calculated, to check correctness, or to extend the model to higher order. A manipulator with a flexible parallel link mechanism is a constrained dynamic system whose equations are sensitive to numerical integration error. This constrained system is solved using singular value decomposition of the constraint Jacobian matrix. Elastic motion is expressed by the assumed mode method. Mode shape functions of each link are chosen using the load interfaced component mode synthesis. The discrepancies between the analytical model and the experiment are explained using a simplified and a detailed finite element model.

Lee, Jeh Won↗

NASA NTRS1990

Thermal-structural finite element analysis using linear flux formulation

A linear flux approach is developed for a finite element thermal-structural analysis of steady state thermal and structural problems. The element fluxes are assumed to vary linearly in the same form as the element unknown variables, and the finite element matrices are evaluated in closed form. Since numerical integration is avoided, significant computational time saving is achieved. Solution accuracy and computational speed improvements are demonstrated by solving several two and three dimensional thermal-structural examples.

Pandey, Ajay K.↗