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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 775 records · Page 43
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NASA NTRS1993

An adaptive mesh-moving and refinement procedure for one-dimensional conservation laws

We examine the performance of an adaptive mesh-moving and /or local mesh refinement procedure for the finite difference solution of one-dimensional hyperbolic systems of conservation laws. Adaptive motion of a base mesh is designed to isolate spatially distinct phenomena, and recursive local refinement of the time step and cells of the stationary or moving base mesh is performed in regions where a refinement indicator exceeds a prescribed tolerance. These adaptive procedures are incorporated into a computer code that includes a MacCormack finite difference scheme wih Davis' artificial viscosity model and a discretization error estimate based on Richardson's extrapolation. Experiments are conducted on three problems in order to qualify the advantages of adaptive techniques relative to uniform mesh computations and the relative benefits of mesh moving and refinement. Key results indicate that local mesh refinement, with and without mesh moving, can provide reliable solutions at much lower computational cost than possible on uniform meshes; that mesh motion can be used to improve the results of uniform mesh solutions for a modest computational effort; that the cost of managing the tree data structure associated with refinement is small; and that a combination of mesh motion and refinement reliably produces solutions for the least cost per unit accuracy.

Biswas, Rupak↗
NASA NTRS1994

A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow

High order essentially non-oscillatory (ENO) schemes, originally designed for compressible flow and in general for hyperbolic conservation laws, are applied to incompressible Euler and Navier-Stokes equations with periodic boundary conditions. The projection to divergence-free velocity fields is achieved by fourth-order central differences through fast Fourier transforms (FFT) and a mild high-order filtering. The objective of this work is to assess the resolution of ENO schemes for large scale features of the flow when a coarse grid is used and small scale features of the flow, such as shears and roll-ups, are not fully resolved. It is found that high-order ENO schemes remain stable under such situations and quantities related to large scale features, such as the total circulation around the roll-up region, are adequately resolved.

Weinan, E.↗
NASA NTRS1994

Possible consequences of absence of Jupiters in planetary systems

The formation of the gas giant planets Jupiter and Saturn probably required the growth of massive approximately 15 Earth-mass cores on a time scale shorter than the approximately 10(exp 7) time scale for removal of nebular gas. Relatively minor variations in nebular parameters could preclude the growth of full-size gas giants even in systems in which the terrestrial planet region is similar to our own. Systems containing 'failed Jupiters,' resembling Uranus and Neptune in their failure to capture much nebular gas, would be expected to contain more densely populated cometary source regions. They will also eject a smaller number of comets into interstellar space. If systems of this kind were the norm, observation of hyperbolic comets would be unexpected. Monte Carlo calculations of the orbital evolution of region of such systems (the Kuiper belt) indicate that throughout Earth history the cometary impact flux in their terrestrial planet regions would be approximately 1000 times greater than in our Solar System. It may be speculated that this could frustrate the evolution of organisms that observe and seek to understand their planetary system. For this reason our observation of these planets in our Solar System may tell us nothing about the probability of similar gas giants occurring in other planetary systems. This situation can be corrected by observation of an unbiased sample of planetary systems.

Wetherill, George W.↗
NASA NTRS1994

Three-dimensional force-free looplike magnetohydrodynamic equilibria

Computations of three-dimensional force-free magnetohydrodynamic (MHD) equilibria, del x B = lambdaB with lambda = lambda(sub 0), a constant are presented. These equilibria are determined by boundary conditions on a surface corresponding to the solar photosphere. The specific boundary conditions used correspond to looplike magnetic fields in the corona. It is found that as lambda(sub 0) is increased, the loops of flux become kinked, and for sufficiently large lambda(sub 0), develop knots. The relationship between the kinking and knotting properties of these equilibria and the presence of a kink instability and related loss of equilibrium is explored. Clearly, magnetic reconnection must be involved for an unknotted loop equilibrium to become knotted, and speculations are made about the creation of a closed hyperbolic field line (X-line) about which this reconnection creating knotted field lines is centered.

Finn, John M.↗
NASA NTRS1994

System for locating the sources of wideband dE/dt from lightning

A system has been developed to measure wideband electic field derivatives (dE/dt) at five ground stations in a 15 km x 15 km network at Kennedy Space Center. Individual station responses are normalized using digital filters. Pulse-timing resolution is improved to much less than 50-ns sample interval by interpolation using packing in the frequency domain. A time tag for each pulse is defined as the mean of the times of the rising-edge half peak, peak, and falling-edge half peak. The standard deviation in these times defines the timing error and is shown to be a function of noise and bandwidth rather than digitization rate. Each of the four unknowns for a pulse source location (x,y,z) and time of occurrence (t) is found from the five time-tag measurements using different weightings for all five combinations of the four-station hyperbolic equations. Weighting factors and errors in x,y,z and t are estimated using error propagation techniques.

Thomson, E. M.↗
NASA NTRS1994

Trajectory-based heating analysis for the European Space Agency/Rosetta Earth Return Vehicle

A coupled, trajectory-based flowfield and material thermal-response analysis is presented for the European Space Agency proposed Rosetta comet nucleus sample return vehicle. The probe returns to earth along a hyperbolic trajectory with an entry velocity of 16.5 km/s and requires an ablative heat shield on the forebody. Combined radiative and convective ablating flowfield analyses were performed for the significant heating portion of the shallow ballistic entry trajectory. Both quasisteady ablation and fully transient analyses were performed for a heat shield composed of carbon-phenolic ablative material. Quasisteady analysis was performed using the two-dimensional axisymmetric codes RASLE and BLIMPK. Transient computational results were obtained from the one-dimensional ablation/conduction code CMA. Results are presented for heating, temperature, and ablation rate distributions over the probe forebody for various trajectory points. Comparison of transient and quasisteady results indicates that, for the heating pulse encountered by this probe, the quasisteady approach is conservative from the standpoint of predicted surface recession.

RADIATIVE ABLATING FLOWFIELD A↗
NASA NTRS1995

qSmoothed particle interpolation

Smoothed particle hydrodynamics (SPH) discretization techniques are generalized to develop a method, smoothed particle interpolation (SPI), for solving initial value problems of systems of a nonhydrodynamical nature. Under this approach, SPH is viewed as strickly as interpolation scheme and, as such, suitable for solving general hyperbolic and parabolic equations. The SPI method is tested on (1) the wave equation with inhomogenous sound speed and (2) Burger's equation. The efficiency of SPI is studied by comparing SPI solutions to those obtained with standard finite-difference methods. It is shown that the power of SPI arises when the smoothing particles are free to move.

Laguna, Pablo↗
NASA NTRS1995

Generation of Venus' nightside ionospheric structure by particle streams from cosmoids

A newly discovered source of energetic particle streams directed at Venus' nightside may cause several exosphere phenomena. The streams evolve from dispersed cosmoids, a surreptitious population of meteoroids in nearly hyperbolic orbits, measured with three dust experiments on Pioneer 10/11. Loose fragile comet-like ensembles of frozen volatile material, they are orders of magnitude more populous than short-period meteoroids. Dispersion is forced near a planet masking the meteor signature at Earth, but recently terrestrial exosphere interactions have been detected principally from VLF radar returns and as suddenly formed layers of neutral sodium and iron probed by lidar. Venus influx is estimated greater than 10(exp -14)(g)/((sq cm)(s)) with nightside directed kinetic power of greater than 0.3 (erg)/((sq cm)s)). Compared to Earth, Venus, lacking a dipole field with almost no rotation, has a readily recognized set of nightside interaction signatures of these downward energetic particle streams: i.e., density depressions of the neutral thermosphere, hydrogen and helium bulges, a non-disappearing ionosphere, electron holes, nightglows, VLF bursty signals, and local magnetic fields. From Pioneer Venus Orbiter (PVO) measurements, the cosmoid population, its temporal and solar azimuthal variation may be determined.

Dubin, M.↗
NASA NTRS1995

Particle chaos and pitch angle scattering

Pitch angle scattering is a factor that helps determine the dawn-to-dusk current, controls particle energization, and it has also been used as a remote probe of the current sheet structure. Previous studies have interpreted their results under the exception that randomization will be greatest when the ratio of the two timescales of motion (gyration parallel to and perpendicular to the current sheet) is closet to one. Recently, the average expotential divergence rate (AEDR) has been calculated for particle motion in a hyperbolic current sheet (Chen, 1992). It is claimed that this AEDR measures the degree of chaos and therefore may be thought to measure the randomization. In contrast to previous expectations, the AEDR is not maximized when Kappa is approximately equal to 1 but instead increases with decreasing Kappa. Also contrary to previous expectations, the AEDR is dependent upon the parameter b(sub z). In response to the challenge to previous expectations that has been raised by this calculation of the AEDR, we have investigated the dependence of a measure of particle pitch angle scattering on both the parameters Kappa and b(sub z). We find that, as was previously expected, particle pitch angle scattering is maximized near Kappa = 1 provided that Kappa/b(sub z) greater than 1. In the opposite regime, Kappa/b(sub z) less than 1, we find that particle pitch angle scattering is still largest when the two timescales are equal, but the ratio of the timescales is proportional to b(sub z). In this second regime, particle pitch angle scattering is not due to randomization, but is instead due to a systematic pitch angle change. This result shows that particle pitch angle scattering need not be due to randomization and indicates how a measure of pitch angle scattering can exhibit a different behavior than a measure of chaos.

Burkhart, G. R.↗
NASA NTRS1995

Nightside electron flux measurements at Mars by the Phobos-2 HARP instrument

All the available nightside electron data obtained during circular orbits at Mars from the Phobos-2 Hyperbolic Retarded Potential Analyzer (HARP) instrument have been examined in detail and are summarized in this paper. An electron flux component with energies exceeding that of the unperturbed solar wind was observed inside the magnetosheath, indicating the presence of acceleration mechanism(s). The character of the electron fluxes measured in the magnetotail cannot be classified in any simple manner, however, there is a correlation between the electron fluxes measured well inside this region and the unperturbed solar wind ram pressure.

Shutte, N.↗
NASA NTRS1995

Explicit and implicit compact high-resolution shock-capturing methods for multidimensional Euler equations 1: Formulation

Two classes of explicit compact high-resolution shock-capturing methods for the multidimensional compressible Euler equations for fluid dynamics are constructed. Some of these schemes can be fourth-order accurate away from discontinuities. For the semi-discrete case their shock-capturing properties are of the total variation diminishing (TVD), total variation bounded (TVB), total variation diminishing in the mean (TVDM), essentially nonoscillatory (ENO), or positive type of scheme for 1-D scalar hyperbolic conservation laws and are positive schemes in more than one dimension. These fourth-order schemes require the same grid stencil as their second-order non-compact cousins. One class does not require the standard matrix inversion or a special numerical boundary condition treatment associated with typical compact schemes. Due to the construction, these schemes can be viewed as approximations to genuinely multidimensional schemes in the sense that they might produce less distortion in spherical type shocks and are more accurate in vortex type flows than schemes based purely on one-dimensional extensions. However, one class has a more desirable high-resolution shock-capturing property and a smaller operation count in 3-D than the other class. The extension of these schemes to coupled nonlinear systems can be accomplished using the Roe approximate Riemann solver, the generalized Steger and Warming flux-vector splitting or the van Leer type flux-vector splitting. Modification to existing high-resolution second- or third-order non-compact shock-capturing computer codes is minimal. High-resolution shock-capturing properties can also be achieved via a variant of the second-order Lax-Friedrichs numerical flux without the use of Riemann solvers for coupled nonlinear systems with comparable operations count to their classical shock-capturing counterparts. The simplest extension to viscous flows can be achieved by using the standard fourth-order compact or non-compact formula for the viscous terms.

Yee, H. C.↗
NASA NTRS1994

Replicate Wolter-I x-ray mirrors

Cylindrical (hyperbolic - parabolic Wolter I) mirrors have been electroformed from nickel over an electroless nickel-phosphorous (NiP) plated aluminum mandrel in support of the NASA AXAF-S x-ray spectrometer program. The electroless nickel was diamond turned and polished to achieve a surface finish of 10 angstroms rms or better. Gold was then plated on the nickel alloy after an electrochemical passivation step. Next a heavy layer of pure nickel was plated one millimeter thick with controlled stress at zero using a commercial PID program to form the actual mirror. This shell was removed from the NiP alloy coated mandrel by cryogenic cooling and contraction of the aluminum to release the mirror. It is required that the gold not adhere well to the NiP but all other plated coatings must exhibit good adherence. Four mirrors were fabricated from two mandrels prepared by this method. The area of each part is 0.7 square meters (7.5 square feet).

Engelhaupt, D. E.↗
NASA NTRS1995

Progressive wave expansions and open boundary problems

In this paper we construct progressive wave expansions and asymptotic boundary conditions for wave-like equations in exterior domains, including applications to electromagnetics, compressible flows and aero-acoustics. The development of the conditions will be discussed in two parts. The first part will include derivations of asymptotic conditions based on the well-known progressive wave expansions for the two-dimensional wave equations. A key feature in the derivations is that the resulting family of boundary conditions involves a single derivative in the direction normal to the open boundary. These conditions are easy to implement and an application in electromagnetics will be presented. The second part of the paper will discuss the theory for hyperbolic systems in two dimensions. Here, the focus will be to obtain the expansions in a general way and to use them to derive a class of boundary conditions that involve only time derivatives or time and tangential derivatives. Maxwell's equations and the compressible Euler equations are used as examples. Simulations with the linearized Euler equations are presented to validate the theory.

Hagstrom, T.↗
NASA NTRS1995

SeaWiFS Technical Report Series: The SeaWiFS CZCS-Type Pigment Algorithm - Volume 29

The Sea-viewing Wide Field-of-view Sensor (SeaWiFS) mission will provide operational ocean color that will be superior to the previous Coastal Zone Color Sensor (CZCS) proof-of-concept mission. An algorithm is needed that exploits the full functionality of SeaWiFS whilst remaining compatible in concept with algorithms used for the CZCS. This document describes the theoretical rationale of radiance band-ratio methods for determining chlorophyll-a and other important biogeochemical parameters, and their implementation for the SeaWIFS mission. Pigment interrelationships are examined to explain the success of the CZCS algorithms. In the context where chlorophyll-a absorbs only weakly at 520 nm, the success of the 520 nm to 550 nm CZCS band ratio needs to be explained. This is explained by showing that in pigment data from a range of oceanic provinces chlorophyll-a (absorbing at less than 490 nm), carotenoids (absorbing at greater than 460 nm), and total pigment are highly correlated. Correlations within pigment groups particularly photoprotectant and photosynthetic carotenoids are less robust. The sources of variability in optical data are examined using the NIMBUS Experiment Team (NET) bio-optical data set and bio-optical model. In both the model and NET data, the majority of the variance in the optical data is attributed to variability in pigment (chlorophyll-a), and total particulates, with less than 5% of the variability resulting from pigment assemblage. The relationships between band ratios and chlorophyll is examined analytically, and a new formulation based on a dual hyperbolic model is suggested which gives a better calibration curve than the conventional log-log linear regression fit. The new calibration curve shows the 490:555 ratio is the best single-band ratio and is the recommended CZCS-type pigment algorithm. Using both the model and NET data, a number of multiband algorithms are developed; the best of which is an algorithm based on the 443:555 and 490:555 ratios. From model data, the form of potential algorithms for other products, such as total particulates and dissolved organic matter (DOM), are suggested.

Hooker, Stanford B.↗
NASA NTRS1996

GENIE(++): A Multi-Block Structured Grid System

The computer code GENIE++ is a continuously evolving grid system containing a multitude of proven geometry/grid techniques. The generation process in GENIE++ is based on an earlier version. The process uses several techniques either separately or in combination to quickly and economically generate sculptured geometry descriptions and grids for arbitrary geometries. The computational mesh is formed by using an appropriate algebraic method. Grid clustering is accomplished with either exponential or hyperbolic tangent routines which allow the user to specify a desired point distribution. Grid smoothing can be accomplished by using an elliptic solver with proper forcing functions. B-spline and Non-Uniform Rational B-splines (NURBS) algorithms are used for surface definition and redistribution. The built in sculptured geometry definition with desired distribution of points, automatic Bezier curve/surface generation for interior boundaries/surfaces, and surface redistribution is based on NURBS. Weighted Lagrance/Hermite transfinite interpolation methods, interactive geometry/grid manipulation modules, and on-line graphical visualization of the generation process are salient features of this system which result in a significant time savings for a given geometry/grid application.

Williams, Tonya↗
NASA NTRS1996

Homotopy Solutions of Kepler's Equations

Kepler's Equation is solved using an integrative algorithm developed using homotropy theory. The solution approach is applicable to both elliptic and hyperbolic forms of Kepler's Equation. The results from the proposed algorithm compare quite favorably with those from existing iterative schemes.

Fitz-Coy, Norman↗
NASA NTRS1996

Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation

We study parallel two-level overlapping Schwarz algorithms for solving nonlinear finite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The overall algorithm, Newton-Krylov-Schwarz (NKS), employs an inexact finite-difference Newton method and a Krylov space iterative method, with a two-level overlapping Schwarz method as a preconditioner. We demonstrate that NKS, combined with a density upwinding continuation strategy for problems with weak shocks, is robust and, economical for this class of mixed elliptic-hyperbolic nonlinear partial differential equations, with proper specification of several parameters. We study upwinding parameters, inner convergence tolerance, coarse grid density, subdomain overlap, and the level of fill-in in the incomplete factorization, and report their effect on numerical convergence rate, overall execution time, and parallel efficiency on a distributed-memory parallel computer.

Cai, Xiao-Chuan↗
NASA NTRS1995

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations: Global Asymptotic Behavior of Time Discretizations - 2

The global asymptotic nonlinear behavior of 1 1 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODES) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDES.

Yee, H. C.↗