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At least 613 records · Page 34
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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

Cross-correlation of point series using a new method

Traditional methods of cross-correlation of two time series do not apply to point time series. Here, a new method, devised specifically for point series, utilizes a correlation measure that is based in the rms difference (or, alternatively, the median absolute difference) between nearest neightbors in overlapped segments of the two series. Error estimates for the observed locations of the points, as well as a systematic shift of one series with respect to the other to accommodate a constant, but unknown, lead or lag, are easily incorporated into the analysis using Monte Carlo techniques. A methodological restriction adopted here is that one series be treated as a template series against which the other, called the target series, is cross-correlated. To estimate a significance level for the correlation measure, the adopted alternative (null) hypothesis is that the target series arises from a homogeneous Poisson process. The new method is applied to cross-correlating the times of the greatest geomagnetic storms with the times of maximum in the undecennial solar activity cycle.

Strothers, Richard B.↗
NASA NTRS1994

The power spectrum of galaxies in the nearby universe

We compute the power spectrum of galaxy density fluctuations in a recently completed Southern Sky Redshift Survey of optically selected galaxies (SSRS2). The amplitude and shape of the SSRS2 power spectrum are consistent with results of the Center for Astrophysics redshift survey of the northern hemisphere (CfA2), including the abrupt change of slope on a scale of 30-50/h Mpc; these results are reproducible for independent volumes of space, and variations are consistent with the errors estimated from mock surveys. Taken together, the SSRS2 and the CfA2 form a complete sample of 14,383 galaxies which covers one-third of the sky. The power spectrum of this larger sample continues to rise on scales up to approximately 200/h Mpc, with weak evidence for flattening on the largest scales. The SSRS2 + CfA2 power spectrum and the power spectrum constraints implied by COBE are well matched by an Omega(h) is approximately 0.2, Omega + lambda(sub 0) = 1 cold dark matter model with minimal biasing of optically selected galaxies.

Da Costa, L. Nicolaci↗
NASA NTRS1995

Determination of plasma temperatures and luminosities using multiple extreme-ultraviolet and X-ray filters

We carefully examine the techniques used to infer temperatures of stellar coronal plasmas from the count rates of several broadband instruments in the X-ray and extreme-ultraviolet spectral ranges. In particular, we determine to what extent temperatures can be constrained and the corresponding uncertainties in the luminosities and emission measures lowered by fitting simultaneously count rates from the Einstein imaging proportional counter (IPC), the ROSAT Position Sensitive Proportional Counter (PSPC), the ROSAT Wide Field Camera (WFC) (both filters), and the EXOSAT Low Energy Telescope (LET) with the 3-Lex filter. We use published plasma emissivities with solar photospheric abundances. Since it has been found that single-temperature plasmas do not fit IPC data well, we assume a two-temperature plasma model. We find that, even with count rates from all of the above filters and overly optimistic error estimates, it is still not possible to determine a unique two-temperature solution. However, since the use of count rates from many filters can reduce substantially the number of possible solutions, temperature solutions determined by other means can be tested. We carry out such an analysis on a set of 18 nearby late-type stars to determine possible two-temperature solutions using multifilter photometry, and we compare these results with the temperature solutions derived by Schmitt et al. (1990) using IPC spectral data. In general, the two-temperature fits derived from the IPC spectral data are inconsistent with our results, with our data implying that, for many stars, the two temperatures derived by the IPC may be too low by about a factor of 2. The EXOSAT transmission grating Spectrometer (TGS) spectra of capella and sigma(exp 2) CrB support this conclusion. For Procyon and 70 Oph, though, the presence of a temperature component cooler than a million degress (not detected by the IPC) is deduced. While our analysis suggests the existence of more than one temperature in the coronae of late-type stars, in many instances our WFC data appear to be inconsistent with the presence of significant emission measure over a broad temperature distribution. This, together with the success of two-temperature plasmas in fitting IPC and TGS data, implies that for many stars, the coronal emission measure distribution may in fact be dominated by two distinct temperature regimes.

Wood, Brian E.↗
NASA NTRS1994

A comparison of cosmological hydrodynamic codes

We present a detailed comparison of the simulation results of various hydrodynamic codes. Starting with identical initial conditions based on the cold dark matter scenario for the growth of structure, with parameters h = 0.5 Omega = Omega(sub b) = 1, and sigma(sub 8) = 1, we integrate from redshift z = 20 to z = O to determine the physical state within a representative volume of size L(exp 3) where L = 64 h(exp -1) Mpc. Five indenpendent codes are compared: three of them Eulerian mesh-based and two variants of the smooth particle hydrodynamics 'SPH' Lagrangian approach. The Eulerian codes were run at N(exp 3) = (32(exp 3), 64(exp 3), 128(exp 3), and 256(exp 3)) cells, the SPH codes at N(exp 3) = 32(exp 3) and 64(exp 3) particles. Results were then rebinned to a 16(exp 3) grid with the exception that the rebinned data should converge, by all techniques, to a common and correct result as N approaches infinity. We find that global averages of various physical quantities do, as expected, tend to converge in the rebinned model, but that uncertainites in even primitive quantities such as (T), (rho(exp 2))(exp 1/2) persists at the 3%-17% level achieve comparable and satisfactory accuracy for comparable computer time in their treatment of the high-density, high-temeprature regions as measured in the rebinned data; the variance among the five codes (at highest resolution) for the mean temperature (as weighted by rho(exp 2) is only 4.5%. Examined at high resolution we suspect that the density resolution is better in the SPH codes and the thermal accuracy in low-density regions better in the Eulerian codes. In the low-density, low-temperature regions the SPH codes have poor accuracy due to statiscal effects, and the Jameson code gives the temperatures which are too high, due to overuse of artificial viscosity in these high Mach number regions. Overall the comparison allows us to better estimate errors; it points to ways of improving this current generation ofhydrodynamic codes and of suiting their use to problems which exploit their best individual features.

Kang, Hyesung↗
NASA NTRS1993

Targeting an asteroid: The DSPSE encounter with asteroid 1620 Geographos

Accurate targeting of the Deep Space Program Science Experiment (DSPSE) spacecraft to achieve a 100 km sunward flyby of asteroid 1620 Geographos will require that the ground-based ephemeris of Geographos be well known in advance of the encounter. Efforts are underway to ensure that precision optical and radar observations are available for the final asteroid orbit update that takes place several hours prior to the DSPSE flyby. Because the asteroid passes very close to the Earth six days prior to the DSPSE encounter, precision ground-based optical and radar observations should be available. These ground-based data could reduce the asteroid's position uncertainties (1-sigma) to about 10 km. This ground-based target ephemeris error estimate is far lower than for any previous comet or asteroid that has been under consideration as a mission target.

Yeomans, Donald K.↗
NASA NTRS1994

Venus' center of figure-center of mass offset

Magellan altimetry data reveal that the center of figure (CF) of Venus is displaced approximately 280 m from its center of mass (CM) toward 4.4 deg S, 135.8 deg E, a location in Aphrodite Terra. This offset is smaller than those of other terrestrial planets but larger than the estimated error, which is no more than a few tens of meters. We examine the possibility that the CF-CM offset is related to specific geologic provinces on Venus by deriving three simple models for the offset: a thick-crust model, a hotspot model, and a thick-lithosphere model. The offset caused by a region of thick crust depends upon the region's extent, the crust-mantle density contrast, and the thickness of excess crust. A hotspot-related offset depends on the extent of the thermally anomalous region and the magnitude of the thermal anomaly. Offset due to a region of thick lithosphere depends upon the extent of the region, the average temperature contrast across the lithosphere, and the amount of excess lithosphere. We apply the three models to Venus plateau-shaped highlands, volcanic rises, and lowlands, respectively, in an attempt to match the observed CF-CM offset location and magnitude. The influence of most volcanic rises and of Ishtar Terra on the CF-CM offset must be quite small if we are to explain the direction of the observed offset. The lack of influence of volcanic rises can be explained if the related thermal anomalies are limited to a few hundred degrees or less and are plume-shaped (i.e., characterized by a flattened sublithospheric `head' with a narrow cylindrical feeder `tail'). The unimportance of Ishtar Terra is most easily explained if it lies atop a significant mantle downwelling.

Bindschadler, Duane L.↗
NASA NTRS1995

Hydromagnetic conditions near the core-mantle boundary

The main results of the grant were (1) finishing the manuscript of a proof of completeness of the Poincare modes in an incompressible nonviscous fluid corotating with a rigid ellipsoidal boundary, (2) partial completion of a manuscript describing a definition of helicity that resolved questions in the literature about calculating the helicities of vector fields with complicated topologies, and (3) the beginning of a reexamination of the inverse problem of inferring properties of the geomagnetic field B just outside the core-mantle boundary (CMB) from measurements of elements of B at and above the earth's surface. This last work has led to a simple general formalism for linear and nonlinear inverse problems that appears to include all the inversion schemes so far considered for the uniqueness problem in geomagnetic inversion. The technique suggests some new methods for error estimation that form part of this report.

Backus, George E.↗
NASA NTRS1996

First-Order System Least-Squares for the Navier-Stokes Equations

This paper develops a least-squares approach to the solution of the incompressible Navier-Stokes equations in primitive variables. As with our earlier work on Stokes equations, we recast the Navier-Stokes equations as a first-order system by introducing a velocity flux variable and associated curl and trace equations. We show that the resulting system is well-posed, and that an associated least-squares principle yields optimal discretization error estimates in the H(sup 1) norm in each variable (including the velocity flux) and optimal multigrid convergence estimates for the resulting algebraic system.

Bochev, P.↗
NASA NTRS1996

First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity

Following our earlier work on general second-order scalar equations, here we develop a least-squares functional for the two- and three-dimensional Stokes equations, generalized slightly by allowing a pressure term in the continuity equation. By introducing a velocity flux variable and associated curl and trace equations, we are able to establish ellipticity in an H(exp 1) product norm appropriately weighted by the Reynolds number. This immediately yields optimal discretization error estimates for finite element spaces in this norm and optimal algebraic convergence estimates for multiplicative and additive multigrid methods applied to the resulting discrete systems. Both estimates are uniform in the Reynolds number. Moreover, our pressure-perturbed form of the generalized Stokes equations allows us to develop an analogous result for the Dirichlet problem for linear elasticity with estimates that are uniform in the Lame constants.

Cai, Z.↗
NASA NTRS1996

Utilization of STRAT Data

One of the goals of the STRAT mission was to improve our understanding of transport in the stratosphere. We have used our coupled 2-D model to analyse transport between the tropics and midlatitudes using aircraft measurements of (CO2) and (N2O) made during the SPADE and ASHOE/MAESA campaigns (Boering et al. 1994) for model validation. We have further used the model to estimate errors in the experimental determination of the age of stratospheric air that arise from nonlinear increases of real tracers such as (CO2) and (SF6). The interpretation of measurements made during STRAT is still in progress. Most of the work performed under this contract has been described in the second year progress report, submitted in April of 1996. In the following, the research is summarized and some additional work that has become relevant in the meantime is described. We have developed an interactive model of the dynamics, chemistry and radiation of the stratosphere with partial support from this contract. The dynamics module integrates the primitive equations on a sphere. Lower boundary zonal winds and eddy geopotential heights are specified from observations. Chemistry and tracer transport are done in two dimensions. The chemistry model is a family model. Long lived species are transported and short lived species are determined in intervals of 5 to 10 days by assuming photochemical steady state. Full diurnal integrations with the fast species are performed periodically and diurnal coefficients, derived from the explicit integration are used to determine the steady state solution. Heating rates in the stratosphere are calculated from model ozone and the model temperatures and circulation fields are used in the chemistry transport module.

Source record↗
NASA NTRS1998

Automated Track Recognition and Event Reconstruction in Nuclear Emulsion

The major advantages of nuclear emulsion for detecting charged particles are its submicron position resolution and sensitivity to minimum ionizing particles. These must be balanced, however, against the difficult manual microscope measurement by skilled observers required for the analysis. We have developed an automated system to acquire and analyze the microscope images from emulsion chambers. Each emulsion plate is analyzed independently, allowing coincidence techniques to be used in order to reject back- ground and estimate error rates. The system has been used to analyze a sample of high-multiplicity Pb-Pb interactions (charged particle multiplicities approx. 1100) produced by the 158 GeV/c per nucleon Pb-208 beam at CERN. Automatically reconstructed track lists agree with our best manual measurements to 3%. We describe the image analysis and track reconstruction techniques, and discuss the measurement and reconstruction uncertainties.

Deines-Jones, P.↗
NASA NTRS1998

Correlative Stratospheric Ozone Measurements with the Airborne UV DIAL System during TOTE/VOTE

The airborne UV differential absorption lidar (DIAL) system participated in the Tropical Ozone Transport Experiment/Vortex Ozone Transport Experiment (TOTE/VOTE) in late 1995/early 1996. This mission afforded the opportunity to compare the DIAL system's stratospheric ozone measuring capability with other remote-sensing instruments through correlative measurements over a latitude range from the tropics to the Arctic. These instruments included ground-based DIAL and space-based stratospheric instruments: HALOE; MLS; and SAGE II. The ozone profiles generally agreed within random error estimates for the various instruments in the middle of the profiles in the tropics, but regions of significant systematic differences, especially near or below the tropopause or at the higher altitudes were also found. The comparisons strongly suggest that the airborne UV DIAL system can play a valuable role as a mobile lower-stratospheric ozone validation instrument.

Grant, William B.↗
NASA NTRS1999

A Robust and Scalable Software Library for Parallel Adaptive Refinement on Unstructured Meshes

The design and implementation of Pyramid, a software library for performing parallel adaptive mesh refinement (PAMR) on unstructured meshes, is described. This software library can be easily used in a variety of unstructured parallel computational applications, including parallel finite element, parallel finite volume, and parallel visualization applications using triangular or tetrahedral meshes. The library contains a suite of well-designed and efficiently implemented modules that perform operations in a typical PAMR process. Among these are mesh quality control during successive parallel adaptive refinement (typically guided by a local-error estimator), parallel load-balancing, and parallel mesh partitioning using the ParMeTiS partitioner. The Pyramid library is implemented in Fortran 90 with an interface to the Message-Passing Interface (MPI) library, supporting code efficiency, modularity, and portability. An EM waveguide filter application, adaptively refined using the Pyramid library, is illustrated.

Lou, John Z.↗
NASA NTRS1999

Main Geomagnetic Field Models from Oersted and Magsat Data Via a Rigorous General Inverse Theory with Error Bounds

The purpose of the grant was to study how prior information about the geomagnetic field can be used to interpret surface and satellite magnetic measurements, to generate quantitative descriptions of prior information that might be so used, and to use this prior information to obtain from satellite data a model of the core field with statistically justifiable error estimates. The need for prior information in geophysical inversion has long been recognized. Data sets are finite, and faithful descriptions of aspects of the earth almost always require infinite-dimensional model spaces. By themselves, the data can confine the correct earth model only to an infinite-dimensional subset of the model space. Earth properties other than direct functions of the observed data cannot be estimated from those data without prior information about the earth. Prior information is based on what the observer already knows before the data become available. Such information can be "hard" or "soft". Hard information is a belief that the real earth must lie in some known region of model space. For example, the total ohmic dissipation in the core is probably less that the total observed geothermal heat flow out of the earth's surface. (In principle, ohmic heat in the core can be recaptured to help drive the dynamo, but this effect is probably small.) "Soft" information is a probability distribution on the model space, a distribution that the observer accepts as a quantitative description of her/his beliefs about the earth. The probability distribution can be a subjective prior in the sense of Bayes or the objective result of a statistical study of previous data or relevant theories.

Backus, George E.↗
NASA NTRS1999

A Self-Tuning Kalman Filter for Autonomous Navigation Using the Global Positioning System (GPS)

Most navigation systems currently operated by NASA are ground-based, and require extensive support to produce accurate results. Recently developed systems that use Kalman filter and GPS (Global Positioning Systems) data for orbit determination greatly reduce dependency on ground support, and have potential to provide significant economies for NASA spacecraft navigation. These systems, however, still rely on manual tuning from analysts. A sophisticated neuro-fuzzy component fully integrated with the flight navigation system can perform the self-tuning capability for the Kalman filter and help the navigation system recover from estimation errors in real time.

Truong, Son H.↗
NASA NTRS1999

A High Order Discontinuous Galerkin Method for 2D Incompressible Flows

In this paper we introduce a high order discontinuous Galerkin method for two dimensional incompressible flow in vorticity streamfunction formulation. The momentum equation is treated explicitly, utilizing the efficiency of the discontinuous Galerkin method The streamfunction is obtained by a standard Poisson solver using continuous finite elements. There is a natural matching between these two finite element spaces, since the normal component of the velocity field is continuous across element boundaries. This allows for a correct upwinding gluing in the discontinuous Galerkin framework, while still maintaining total energy conservation with no numerical dissipation and total enstrophy stability The method is suitable for inviscid or high Reynolds number flows. Optimal error estimates are proven and verified by numerical experiments.

Liu, Jia-Guo↗
NASA NTRS1999

Solving Upwind-Biased Discretizations: Multigrid Solver Using Semicoarsening - 2

This paper studies a novel multigrid approach to the solution for a second order upwind biased discretization of the convection equation in two dimensions. This approach is based on semi-coarsening and well balanced explicit correction terms added to coarse-grid operators to maintain on coarse-grid the same cross-characteristic interaction as on the target (fine) grid. Colored relaxation schemes are used on all the levels allowing a very efficient parallel implementation. The results of the numerical tests can be summarized as follows: 1) The residual asymptotic convergence rate of the proposed V(0, 2) multigrid cycle is about 3 per cycle. This convergence rate far surpasses the theoretical limit (4/3) predicted for standard multigrid algorithms using full coarsening. The reported efficiency does not deteriorate with increasing the cycle, depth (number of levels) and/or refining the target-grid mesh spacing. 2) The full multi-grid algorithm (FMG) with two V(0, 2) cycles on the target grid and just one V(0, 2) cycle on all the coarse grids always provides an approximate solution with the algebraic error less than the discretization error. Estimates of the total work in the FMG algorithm are ranged between 18 and 30 minimal work units (depending on the target (discretizatioin). Thus, the overall efficiency of the FMG solver closely approaches (if does not achieve) the goal of the textbook multigrid efficiency. 3) A novel approach to deriving a discrete solution approximating the true continuous solution with a relative accuracy given in advance is developed. An adaptive multigrid algorithm (AMA) using comparison of the solutions on two successive target grids to estimate the accuracy of the current target-grid solution is defined. A desired relative accuracy is accepted as an input parameter. The final target grid on which this accuracy can be achieved is chosen automatically in the solution process. the actual relative accuracy of the discrete solution approximation obtained by AMA is always better than the required accuracy; the computational complexity of the AMA algorithm is (nearly) optimal (comparable with the complexity of the FMG algorithm applied to solve the problem on the optimally spaced target grid).

Diskin, Boris↗