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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

On the connection between multigrid and cyclic reduction

A technique is shown whereby it is possible to relate a particular multigrid process to cyclic reduction using purely mathematical arguments. This technique suggest methods for solving Poisson's equation in 1-, 2-, or 3-dimensions with Dirichlet or Neumann boundary conditions. In one dimension the method is exact and, in fact, reduces to cyclic reduction. This provides a valuable reference point for understanding multigrid techniques. The particular multigrid process analyzed is referred to here as Approximate Cyclic Reduction (ACR) and is one of a class known as Multigrid Reduction methods in the literature. It involves one approximation with a known error term. It is possible to relate the error term in this approximation with certain eigenvector components of the error. These are sharply reduced in amplitude by classical relaxation techniques. The approximation can thus be made a very good one.

Merriam, M. L.↗
NASA NTRS1983

Numerical simulations of plasma double layers

The results of analytical studies of quasi-static electric fields along geomagnetic field lines are discussed. The calculations were targeted at the structure, generation mechanisms and stability parameters. The field consists of two oppositely charged layers, either weakly or strongly charged, with an electric field between. Existence conditions are defined for the double layer field and balancing requirements are explored. Details of the simulation techniques, i.e., particle in cell and Vlasov simulations, for studying the double layer are outlined, noting that both periodic and quasi-periodic simulations are used. Solutions to Poisson's equation for fixed and floating point boundary conditions are generated. Finally, attention is also given to oblique and two-dimensional magnetic double layers.

Goertz, C. K.↗
NASA NTRS1986

The electrostatics of a dusty plasma

The potential distribution in a plasma containing dust grains were derived where the Debye length can be larger or smaller than the average intergrain spacing. Three models were treated for the grain-plasma system, with the assumption that the system of dust and plasma is charge-neutral: a permeable grain model, an impermeable grain model, and a capacitor model that does not require the nearest neighbor approximation of the other two models. A gauge-invariant form of Poisson's equation was used which is linearized about the average potential in the system. The charging currents to a grain are functions of the difference between the grain potential and this average potential. Expressions were obtained for the equilibrium potential of the grain and for the gauge-invariant capacitance between the grain and the plasma. The charge on a grain is determined by the product of this capacitance and the grain-plasma potential difference.

Whipple, E. C.↗
NASA NTRS1987

Integral method of wall interference correction in low-speed wind tunnels

The analytical solution of Poisson's equation, derived form the definition of vortex, was applied to the calculation of interference velocities due to the presence of wind tunnel walls. This approach, called the Integral Method, allows an accurate evaluation of wall interference for separated or more complicated flows without the need for considering any features of the model. All the information necessary for obtaining the wall correction is contained in wall pressure measurements. The correction is not sensitive to normal data-scatter, and the computations are fast enough for on-line data processing.

Zhou, Changhai↗
NASA NTRS1988

Vibrational Power Flow Analysis of Rods and Beams

A new method to model vibrational power flow and predict the resulting energy density levels in uniform rods and beams is investigated. This method models the flow of vibrational power in a manner analogous to the flow of thermal power in a heat conduction problem. The classical displacement solutions for harmonically excited, hysteretically damped rods and beams are used to derive expressions for the vibrational power flow and energy density in the rod and beam. Under certain conditions, the power flow in these two structural elements will be shown to be proportional to the energy density gradient. Using the relationship between power flow and energy density, an energy balance on differential control volumes in the rod and beam leads to a Poisson's equation which models the energy density distribution in the rod and beam. Coupling the energy density and power flow solutions for rods and beams is also discussed. It is shown that the resonant behavior of finite structures complicates the coupling of solutions, especially when the excitations are single frequency inputs. Two coupling formulations are discussed, the first based on the receptance method, and the second on the travelling wave approach used in Statistical Energy Analysis. The receptance method is the more computationally intensive but is capable of analyzing single frequency excitation cases. The traveling wave approach gives a good approximation of the frequency average of energy density and power flow in coupled systems, and thus, is an efficient technique for use with broadband frequency excitation.

Wohlever, James Christopher↗
NASA NTRS1989

Operator induced multigrid algorithms using semirefinement

A variant of multigrid, based on zebra relaxation, and a new family of restriction/prolongation operators is described. Using zebra relaxation in combination with an operator-induced prolongation leads to fast convergence, since the coarse grid can correct all error components. The resulting algorithms are not only fast, but are also robust, in the sense that the convergence rate is insensitive to the mesh aspect ratio. This is true even though line relaxation is performed in only one direction. Multigrid becomes a direct method if an operator-induced prolongation is used, together with the induced coarse grid operators. Unfortunately, this approach leads to stencils which double in size on each coarser grid. The use of an implicit three point restriction can be used to factor these large stencils, in order to retain the usual five or nine point stencils, while still achieving fast convergence. This algorithm achieves a V-cycle convergence rate of 0.03 on Poisson's equation, using 1.5 zebra sweeps per level, while the convergence rate improves to 0.003 if optimal nine point stencils are used. Numerical results for two and three dimensional model problems are presented, together with a two level analysis explaining these results.

Decker, Naomi↗
NASA NTRS1988

Increased effective barrier heights in Schottky diodes by molecular-beam epitaxy of CoSi2 and Ga-doped Si on Si(111)

Increasing the effective Schottky-barrier height of epitaxial CoSi2/Si(111) diodes by the use of thin, highly doped Si layers in close proximity to the metal-semiconductor interface has been studied. Intrinsic Si, Si doped by coevaporation of Ga, and epitaxial CoSi2 layers have all been grown in the same molecular-beam epitaxy system. Current-voltage and photoresponse characterization yield barrier heights ranging from 0.61 eV for a sample with no p(+) layer to 0.89 eV for a sample with a 20-nm-thick p(+) layer. These results are compared to theoretical values based on a one-dimensional solution of Poisson's equation under the depletion approximation.

Fathauer, R. W.↗
NASA NTRS1989

Operator induced multigrid algorithms using semirefinement

A variant of multigrid, based on zebra relaxation, and a new family of restriction/prolongation operators is described. Using zebra relaxation in combination with an operator-induced prolongation leads to fast convergence, since the coarse grid can correct all error components. The resulting algorithms are not only fast, but are also robust, in the sense that the convergence rate is insensitive to the mesh aspect ratio. This is true even though line relaxation is performed in only one direction. Multigrid becomes a direct method if an operator-induced prolongation is used, together with the induced coarse grid operators. Unfortunately, this approach leads to stencils which double in size on each coarser grid. The use of an implicit three point restriction can be used to factor these large stencils, in order to retain the usual five or nine point stencils, while still achieving fast convergence. This algorithm achieves a V-cycle convergence rate of 0.03 on Poisson's equation, using 1.5 zebra sweeps per level, while the convergence rate improves to 0.003 if optimal nine point stencils are used. Numerical results for two- and three-dimensional model problems are presented, together with a two level analysis explaining these results.

Decker, Naomi Henderson↗
NASA NTRS1990

Double layers in contactor plasmas

The concept of using a hollow cathode to establish a low impedance contact between a spacecraft and the ambient plasma continues to gain in popularity, and is often then referred to as a plasma contactor. A growing number of studies indicate that large contact currents can be supported with small potential difference between the contactor and the ambient plasma. Results will be presented from a simple one-dimensional spherical model that obtains potentials from the solution of Poisson's equation, and particle densities from a turning point formalism that includes particle angular momentum. The neglect of collisions and magnetic field limits the realism. However, the results illustrate the effect of double layers that can form at the interface between contactor and ambient plasmas, when there is any voltage differential between the contactor and the ambient. The I-V characteristic of this model shows the usual space charge depends upon collection when the contactor flux is lower than some threshold; independence of I from variation in V when the flux is slightly greater than that threshold, and (numerical ?) instability for excessive flux suggesting the possibility of negative resistance. Even if a real I-V characteristic does not exhibit negative resistance, flat spots or high resistance regions may still be troublesome (or useful) to the total circuit.

Cooke, David L.↗
NASA NTRS1990

NASCAP/LEO calculations of current collection

NASCAP/LEO is a 3-dimensional computer code for calculating the interaction of a high-voltage spacecraft with the cold dense plasma found in Low Earth Orbit. Although based on a cubic grid structure, NASCAP/LEO accepts object definition input from standard computer aided design (CAD) programs so that a model may be correctly proportioned and important features resolved. The potential around the model is calculated by solving the finite element formulation of Poisson's equation with an analytic space charge function. Five previously published NASCAP/LEO calculations for three ground test experiments and two space flight experiments are presented. The three ground test experiments are a large simulated panel, a simulated pinhole, and a 2-slit experiment with overlapping sheaths. The two space flight experiments are a solar panel biased up to 1000 volts, and a rocket-mounted sphere biased up to 46 kilovolts. In all cases, the authors find good agreement between calculation and measurement.

Mandell, Myron J.↗
NASA NTRS1991

Improved millimeter-wave mixer performance analysis at cryogenic temperatures

The results of a 600-GHz mixer performance analysis using an improved model for computing the Schottky diode capacitance-voltage (C-V) relationship are presented. The computed C-V data for a realistic submillimeter-waver mixer diode are given as a function of physical temperature and compared to the standard analytic expression based on a solution of Poisson's equation. Both C-V relationships are used to predict the performance of an ideally terminated 600 GHz mixer operating at 300, 140, 80, and 30 K. It is shown that the drift-diffusion model more accurately describes the mixer performance when the physical temperature is reduced below roughly 100 K.

Siegel, Peter H.↗
NASA NTRS1991

A simulation of the collapse and fragmentation of cooling molecular clouds

The application of the Smoothed Particle Hydrodynamics method to the fragmentation of rotating cloud and disk systems is described, allowing for molecular cooling due to H2 and CO. A novel approach to solving Poisson's equation for disklike structures which exploits the multigrid algorithm is also described. Numerical studies are presented which investigate the evolution of both rotating clouds and Maclaurin disks, in each case with both an isothermal equation of state and with molecular cooling. The results establish the influence of molecular cooling on the fragmentation of molecular clouds. The isothermal sequences, if they fragment at all, do so into far fewer lumps than the cooling sequences. This is not due to a cooling instability as such, but rather to the reduced thermal support. One of the sequences shows a remarkable similarity to the W49A star-forming region.

Monaghan, Joe J.↗
NASA NTRS1991

Model of electron collecting plasma contactors

In laboratory experiments, plasma contactors are observed to collect ampere-level electron currents with low impedance. In order to extend the laboratory experience to the low-earth-orbit environment, a model of plasma contactors is being developed. Laboratory results are being used to support and validate the model development. The important physical processes observed in the laboratory are that the source plasma is separated from the background plasma by a double layer and that ionization of the expellant gas by the collected electrons creates the bulk of the ions that leave the source plasma. The model, which uses Poisson's equation with a physical charge density that includes the ion and electron components of both the source and the ambient plasmas, reproduces this phenomenon for typical experimental parameters. The calculations, in agreement with the laboratory results, show little convergence of the accelerated electrons. The angular momentum of the incoming electrons dramatically reduces the peak electron density. These electrons ionize enough gas to generate the source plasma. Calculations show that the increase in ionization rate with potential produces a steep rise in collected current with increasing potential as seen in the laboratory.

Davis, V. A.↗
NASA NTRS1992

More About Generating Three-Dimensional Grids About Anything

Report presents additional details of mathematical basis and potential applications of method of generating three-dimensional grids fitted to bodies having arbitrary, complicated shapes. Grids used in finite-difference or finite-volume computations of flows around bodies. Grid-generation method involves numerical solutions of Poisson's equations described in "Generating Three-Dimensional Grids About Anything" (ARC-12620).

Sorenson, Reese L.↗
NASA NTRS1992

Validation and applications of the POLAR code

The Potentials of Large Objects in the Auroral Region (POLAR) code was written to model the charging of large spacecraft by auroral electrons in low polar orbit. It has also proven to be a powerful tool for analysis of active and voltage-plasma interactions. POLAR combines 3-D object definition, direct solution to Poisson's equation, space charge transport, and surface charge computation. Physical effects treated by POLAR include the plasma wake and ram, the geomagnetic field, ionization, sheath and barrier formation, and photo and secondary electron generation and transport. Polar development is complete and it is now available to the aerospace community. The methodology of POLAR is reviewed but concentration is on the applications of POLAR to physical problems and observations with the intent of demonstrating both the code's capabilities, and its limitations. These applications include the Space Shuttle, the Defense Meteorological Satellite Program (DMSP) satellites, sounding rockets, plasma chamber experiments, and things not yet flown.

Cooke, David L.↗
NASA NTRS1992

Comparison between the PISO algorithm and preconditioning methods for compressible flow

Two widely used family of algorithms, pressure-based and density-based methods, have been developed for computational fluid dynamics (CFD) problems over the years. Pressure-based methods (such as SIMPLE and PISO) use a Poisson-like equation for updating pressure instead of the continuity equation, while density-based methods use the continuity equation to update density (an equation of state is used to provide density in pressure based schemes and pressure in density based schemes). Pressure-based methods were developed originally for incompressible flows at low Reynolds numbers and were then extended to high Reynolds numbers and compressible applications. On the other hand, density based methods were originally developed for transonic flows and have been extended down to low Mach numbers through the use of preconditioning techniques. We compare these two very different approaches to solving the Navier-Stokes equations in order to gain an understanding of their similarities and differences. Specifically, we consider the PISO scheme as a representative pressure-based method and contrast it with a recently developed preconditioning scheme. We also compare the relative performance of the PISO algorithm with a Euler implicit algorithm that is employed to solve the preconditioned equations by means of a vector stability analysis.

Merkle, Charles L.↗
NASA NTRS1992

Multigrid acceleration of a fractional-step solver in generalized curvilinear coordinate systems

The efficiency of the INS3D-fractional step (FS) code has been significantly enhanced by accelerating the Poisson solver with a multigrid (MG) method. This is apparently the first implementation of the MG method for solving the 3D discrete Poisson-like equation obtained in the derivation of FS solution methods for the incompressible Navier-Stokes equations in generalized nonorthogonal coordinate systems using a staggered arrangement of the variables. The MG solver is insensitive to the geometry, even in cases of highly nonorthogonal clustered meshes, as well as to the free parameters of MG methods.

Rosenfeld, Moshe↗
NASA NTRS1992

The scaling of relativistic double-year widths - Poisson-Vlasov solutions and particle-in-cell simulations

The study of relativistic plasma double layers is described through the solution of the one-dimensional, unmagnetized, steady-state Poisson-Vlasov equations and by means of one-dimensional, unmagnetized, particle-in-cell simulations. The thickness vs potential-drop scaling law is extended to relativistic potential drops and relativistic plasma temperatures. The transition in the scaling law for 'strong' double layers suggested by analytical two-beam models by Carlqvist (1982) is confirmed, and causality problems of standard double-layer simulation techniques applied to relativistic plasma systems are discussed.

Sulkanen, Martin E.↗