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NASA NTRS1982

Tenth NASTRAN User's Colloquium

The development of the NASTRAN computer program, a general purpose finite element computer code for structural analysis, was discussed. The application and development of NASTRAN is presented in the following topics: improvements and enhancements; developments of pre and postprocessors; interactive review system; the use of harmonic expansions in magnetic field problems; improving a dynamic model with test data using Linwood; solution of axisymmetric fluid structure interaction problems; large displacements and stability analysis of nonlinear propeller structures; prediction of bead area contact load at the tire wheel interface; elastic plastic analysis of an overloaded breech ring; finite element solution of torsion and other 2-D Poisson equations; new capability for elastic aircraft airloads; usage of substructuring analysis in the get away special program; solving symmetric structures with nonsymmetric loads; evaluation and reduction of errors induced by Guyan transformation.

Source record↗

NASA NTRS1983

Test results of modified electrical charged particle generator for application to fog dispersal

Modifications to a charged particle generator for use in fog dispersal applications were made and additional testing carried out. The modified nozzle, however, did not work as planned, and reported results are the unmodified nozzle. The addition of a positive displacement pump to supply the liquid water was highly successful. Measurements of the generator output current were made with a cylindrical collector system as well as with the needle probe used in previous studies. Measurements with the cylindrical collector and the needle probe showed identical agreement within the variability of the experiment. A high-voltage prove was purchased, and measurements of the corona voltage as well as the voltage variation in the charged particle jet were made. Electric fields in the vertical direction on the order of 1,000,000 v/m were measured. The voltage distribution along the centerline of the jet was compared with the numerical solutions of the Poisson equation and showed very good agreement. Velocity measurements using a pitot tube were made. The resulting measurements were compared with theoretical and other reported experimental results. The measured data showed the appropriate trends and agreed well with reported results. Based on the measured current-to-mass ratio from the charged particle generator, a calculation of the average droplet size was made. Droplet sizes were estimated to range between 0.8 and 0.4 microns. Using measured data, an analysis of the height to which the droplet can be dispersed by the charged particle generator was made. Although the mathematical model is highly simplified, the results indicated that particles would achieve heights on the order of 80 m.

Frost, W.↗

NASA NTRS1983

Solitary waves and double layers on auroral field lines

Time stationary solutions to the Vlasov-Poisson equations for ion holes and double layers are examined along with particle simulations that pertain to recent observations of small amplitude electric field structures on auroral field lines. Both the time stationary analysis and the simulations suggest that the observed double layers evolve from holes in ion phase space. Multiple small amplitude double layers, as seen in long simulation systems, are observed to propagate past the spacecraft and may account for the acceleration of plasma sheet electrons to produce inverted-V precipitation.

Hudson, M. K.↗

NASA NTRS1984

Vectorized multigrid Poisson solver for the CDC CYBER 205

The full multigrid (FMG) method is applied to the two dimensional Poisson equation with Dirichlet boundary conditions. This has been chosen as a relatively simple test case for examining the efficiency of fully vectorizing of the multigrid method. Data structure and programming considerations and techniques are discussed, accompanied by performance details.

Barkai, D.↗

NASA NTRS1982

An alternative to reduction of surface pressure to sea level

The pitfalls of the present method of reducing surface pressure to sea level are reviewed, and an alternative, adjusted pressure, P, is proposed. P is obtained from solution of a Poisson equation over a continental region, using the simplest boundary condition along the perimeter or coastline where P equals the sea level pressure. The use of P would avoid the empiricisms and disadvantages of pressure reduction to sea level, and would produce surface pressure charts which depict the true geostrophic wind at the surface.

Deardorff, J. W.↗

NASA NTRS1985

Spacecraft-environment interaction: The environmental plasma aspect

The effects involved in the interaction between an obstacle and a space plasma can be divided into: (1) effects on the obstacle itselt (i.e., its charging); and (2) effects on the environmental plasma due to the motion of the obstacle (i.e., the creation of shocks ahead of the obstacle and complicated wakes behind the obstacle). In the wake (or antisolar direction), plasma oscillations are excited and instabilities, wave-particle interactions, turbulence, etc., are believed to take place. The effects on the obstacle and on the environmental space plasma are coupled. Hence, simultaneous solutions to the Vlasov (or Boltzmann) and Poisson equations are sought. To obtain realistic solutions of practical use, three-dimensional and time-dependent models of the interaction are needed. Achieving the latter is indeed not simple.

Samir, U.↗

NASA NTRS1986

Numerical simulation of spacecraft charging by impact-induced plasmas during a cometary flyby

A numerical model is developed for the interaction of a cometary probe, such as Giotto, with its environment, i.e., dust particles and gas. The spacecraft was set on a course to pass the comet at a velocity of 69 km/sec, so a chance existed that a potential field would form around the spacecraft and block lower energy particles from reaching the spacecraft instruments. The motion of electrons and ions is traced as a function of time to examine the evolution of the electric field, electric potential and the total space charge distributions on the surface of the spacecraft and its environment. Account is taken of the density of the particles and gas molecules at various distances from the comet, the collision energies involved, and the Giotto geometry. A solution is defined for the Poisson equation to describe the evolution of the plasma around Giotto, including the effects of ion collisions with the Al bumper protecting the spacecraft. The simulation predicts formation of an ion wake behind Giotto and the evolution of a positive potential on the order of 10 V around the spacecraft, i.e., sufficient for a positive potential barrier near the surface of the spacecraft.

Thiemann, H.↗

NASA NTRS1986

Theory of beat-resonant coupling of electrostatic modes

A general expression is derived for the beat-resonant coupling electrostatic modes in a Vlasov plasma. The result for the coupling of two modes has a simple structure: the appropriate momentum gradient of the equilibrium particle distribution is weighted by a positive coupling coefficient and averaged over the resonance surface in momentum space. The contributions of all the resonance surfaces are then summed. This basic structure had been previously exhibited only for specific homogeneous plasma models. The present theory, which unifies and greatly simplifies these individual treatments, is based on a variational formulation of the Vlasov-Poisson equations. Using Lie transforms, the variational principle is reexpressed in oscillation-center variables, and then the nonlinear wave dynamics are obtained from the independent variations of the wave phase and the wave amplitude. The power of the method is then applied to a strongly magnetized, strongly inhomogeneous, non-neutral plasma model.

Crawford, John David↗

NASA NTRS1987

Coupling finite element and spectral methods: First results

A Poisson equation on a rectangular domain is solved by coupling two methods: the domain is divided in two squares, a finite element approximation is used on the first square and a spectral discretization is used on the second one. Two kinds of matching conditions on the interface are presented and compared. In both cases, error estimates are proved.

Bernardi, Christine↗

NASA NTRS1987

Electrostatic charge on a dust size distribution in a plasma

The capacitance of a grain immersed in a steady state plasma containing a size distribution of dust particles is studied. The grain charge is determined by assuming the equilibrium potential has been obtained by a simple balance of electron and ion collection currents. It is shown that the validity of the analytical treatment given here for the linearized Poisson equation is confined to a certain region of space. Within this region and starting at very small plasma Debye length lambda(D), the capacitance at first exhibits a monotonic increase with increasing lambda(D). The capacitance eventually reaches a maximum, followed by a monotonic decrease. The charge density of the dust in the plasma is found to be only a function of the lambda(D); there is no significant dependence on the interparticle spacing.

Houpis, Harry L. F.↗

NASA NTRS1989

Application of internal gravitational field equations to geophysical measurement of G

The spherical harmonic equation for the gravitational potential inside the earth is presented. The equation satisfies Poisson's equation and converges uniformly. It obviates the need for downward continuation of the exterior potential with its attendant convergence difficulties but of course requires some knowledge of the earth's density distribution. The equation is used to derive the general expression for the geophysical measurement of the gravitational constant G made inside the earth, such as in boreholes and mine shafts. Numerical evidence is also presented to show that the long- to intermediate-wavelength gravity anomalies can masquerade as the 'fifth force' if not properly corrected for.

Rubincam, David Parry↗

NASA NTRS1990

Coupling finite element and spectral methods - First results

Bernardi, Christine↗

NASA NTRS1990

Theory of multicolor lattice gas - A cellular automaton Poisson solver

The present class of models for cellular automata involving a quiescent hydrodynamic lattice gas with multiple-valued passive labels termed 'colors', the lattice collisions change individual particle colors while preserving net color. The rigorous proofs of the multicolor lattice gases' essential features are rendered more tractable by an equivalent subparticle representation in which the color is represented by underlying two-state 'spins'. Schemes for the introduction of Dirichlet and Neumann boundary conditions are described, and two illustrative numerical test cases are used to verify the theory. The lattice gas model is equivalent to a Poisson equation solution.

Chen, H.↗

NASA NTRS1990

High voltage plasma sheath analysis related to TSS-1

On the first mission of the Tethered Satellite System (TSS-1), a 1.8 m diameter spherical satellite will be deployed a distance of 20 km above the Space Shuttle Orbiter on an insulated conducting tether. The satellite will be held at electric potentials up to 5000 volts positive with respect to the ambient plasma. Due to the passage of the conducting tether through the Earth's magnetic field, an electromagnetic field (EMF) will be created, driving electrons down the tether to the Orbiter, out through an electron gun into the ionosphere and back into the positive-biased satellite. The main problem addressed here is the current-voltage characteristics of the ionospheric interaction with the satellite. The first problem is that while the satellite will be capable of measuring charged particle flow to the surface at several locations, the detectors have a limited range of acceptance angle. The second problem is that the angle of incidence of the incoming electrons will have to be relative to the local normal. This will be important in order to predict the magnitude of the detectable current at each detector location so the detector gain can be pre-set to the correct range. The plasma sheath was analyzed mathematically, and subroutines were written to solve relevant finite element, Taylor-Vlasov, and Poisson equations.

Sheldon, John W.↗

NASA NTRS1990

Quadrature imposition of compatibility conditions in Chebyshev methods

This paper handles a problem encountered in the solution by way of Chebyshev spectral collocation discretization of the Poisson equation with homogeneous Neumann boundary conditions. When pseudospectral Chebyshev methodology is utilized to discretize the partial differential equation these integrals have to be approximated by an appropriate quadrature formula. The correct quadrature formula is developed for these problems, taking into account the degree of the polynomials involved. It is shown that this formula leads to a well-conditioned Chebyshev approximation to the differential equations and that the compatibility condition is automatically satisfied.

Gottlieb, D.↗

NASA NTRS1991

Lateral tunneling through voltage-controlled barriers

The paper reports on a detailed experimental investigation of lateral tunneling between electrodes of a two-dimensional electron gas separated by the voltage-controlled barrier of a nanometer Schottky gate. The experimental data are modeled using the WKB method to calculate the tunneling probability of electrons through a barrier whose shape is determined from a solution of the two-dimensional Poisson equation. This model is in excellent agreement with the experimental data over a two order of magnitude range of current.

Manion, S. J.↗

NASA NTRS1991

A two-dimensional, time-dependent, near-earth magnetotail

A kinetic approach is presented for obtaining slowly time-dependent, self-consistent plasma, and magnetic field configurations for this region, using anisotropic particle distributions. At present, a 2D configuration is used. The time variation of the plasma/field configuration is assumed to be driven by a slowly varying, externally imposed electric field (representing, for example, a change in solar wind conditions). The numerical approach involves solving a 2D nonlinear Poisson equation for the magnetic vector potential at each time step. The local current density is calculated from particle velocity distributions under the assumption of adiabatic particle motion. The obtained equations of state are compared with those of double-adiabatic theory. Numerical examples of self-consistent responses of the near-earth plasma and field to an externally imposed electric field pulse are presented.

Whipple, Elden↗

NASA NTRS1991

Structured background grids for generation of unstructured grids by advancing front method

A new method of background grid construction is introduced for generation of unstructured tetrahedral grids using the advancing-front technique. Unlike the conventional triangular/tetrahedral background grids which are difficult to construct and usually inadequate in performance, the new method exploits the simplicity of uniform Cartesian meshes and provides grids of better quality. The approach is analogous to solving a steady-state heat conduction problem with discrete heat sources. The spacing parameters of grid points are distributed over the nodes of a Cartesian background grid by interpolating from a few prescribed sources and solving a Poisson equation. To increase the control over the grid point distribution, a directional clustering approach is used. The new method is convenient to use and provides better grid quality and flexibility. Sample results are presented to demonstrate the power of the method.

Pirzadeh, Shahyar↗