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NASA NTRS1986

Upwind relaxation algorithms for Euler/Navier-Stokes equations

A description of and results from a solution algorithm for the compressible Navier-Stokes equations are presented. The main features of the algorithm are second or third order accurate upwind discretization of the convection and pressure derivatives and a relaxation scheme for the unfactored implicit backward Euler time method, implemented in a finite-volume formulation. Upwind methods were successfully used to obtain solutions to the Euler equations for flows with strong shock waves. The particular upwind method being used is based on the flux vector splitting technique developed by Van Leer and both second and third order accurate discretizations were developed. Currently, the most widely used implicit solution technique for the Navier-Stokes equations use approximate factorization (AF) methods to treat multidimensional problems. The time integration scheme being used in the present algorithm corresponds to a line Gauss-Seidel relaxation method. This method produces good convergence rates for steady-state flows, and most of the algorithm was vectorized on the NASA Langley VPS 32 computer. The Navier-Stokes algorithm was tested for several two-dimensional flow problems. Solutions for the problems gave excellent results. The presented effort is directed toward the extension of the scheme to the full three-dimensional Navier-Stokes equations.

Thomas, J. L.↗

NASA NTRS2022

A NASA-Air Force Precipitation Analysis for Near-Real-Time Operations

This article describes a new precipitation analysis algorithm developed by NASA for time-sensitive operations at the United States Air Force. Implemented as part of the Land Information System—a land modeling and data assimilation software framework—this NASA–Air Force Precipitation Analysis (NAFPA) combines numerical weather prediction model outputs with rain gauge measurements and satellite estimates to produce global, gridded 3-h accumulated precipitation fields at approximately 10-km resolution. Input observations are subjected to quality control checks before being used by the Bratseth analysis algorithm that converges to optimal interpolation. NAFPA assimilates up to 3.5 million observations without artificial data thinning or selection. To evaluate this new approach, a multiyear reanalysis is generated and intercompared with eight alternative precipitation products across the contiguous United States, Africa, and the monsoon region of eastern Asia. NAFPA yields superior accuracy and correlation over low-latency (up to 14 h) alternatives (numerical weather prediction and satellite retrievals), and often outperforms high-latency (up to 3.5 months) products, although the details for the latter vary by region and product. The development of NAFPA offers a high-quality, near-real-time product for use in meteorological, land surface, and hydrological research and applications.

Africa↗

NASA NTRS2004

Computationally-Efficient Minimum-Time Aircraft Routes in the Presence of Winds

A computationally efficient algorithm for minimizing the flight time of an aircraft in a variable wind field has been invented. The algorithm, referred to as Neighboring Optimal Wind Routing (NOWR), is based upon neighboring-optimal-control (NOC) concepts and achieves minimum-time paths by adjusting aircraft heading according to wind conditions at an arbitrary number of wind measurement points along the flight route. The NOWR algorithm may either be used in a fast-time mode to compute minimum- time routes prior to flight, or may be used in a feedback mode to adjust aircraft heading in real-time. By traveling minimum-time routes instead of direct great-circle (direct) routes, flights across the United States can save an average of about 7 minutes, and as much as one hour of flight time during periods of strong jet-stream winds. The neighboring optimal routes computed via the NOWR technique have been shown to be within 1.5 percent of the absolute minimum-time routes for flights across the continental United States. On a typical 450-MHz Sun Ultra workstation, the NOWR algorithm produces complete minimum-time routes in less than 40 milliseconds. This corresponds to a rate of 25 optimal routes per second. The closest comparable optimization technique runs approximately 10 times slower. Airlines currently use various trial-and-error search techniques to determine which of a set of commonly traveled routes will minimize flight time. These algorithms are too computationally expensive for use in real-time systems, or in systems where many optimal routes need to be computed in a short amount of time. Instead of operating in real-time, airlines will typically plan a trajectory several hours in advance using wind forecasts. If winds change significantly from forecasts, the resulting flights will no longer be minimum-time. The need for a computationally efficient wind-optimal routing algorithm is even greater in the case of new air-traffic-control automation concepts. For air-traffic-control automation, thousands of wind-optimal routes may need to be computed and checked for conflicts in just a few minutes. These factors motivated the need for a more efficient wind-optimal routing algorithm.

Jardin, Matthew R.↗

NASA NTRS1994

The formation of small grains in shocks in the ISM

Carbonaceous and silicate grains swept up, and betatron accelerated, by supernova-generated shock waves in the interstellar medium are exposed to grain destructive processing. The degree of grain destruction is determined by the differential gas-grain and grain-grain velocities, which lead to sputtering of the grain surface and grain core disruption (deformation, vaporization and shattering), respectively. The threshold pressure for grain shattering in grain-grain collisions (100 k bar) is considerably lower than that for vaporization (approximately 5 M bar). Therefore, collisions between grains shatter large grains into smaller fragments (i.e., small grains and PAH's). Using a new algorithms for the destructive processes, it was possible to model the formation fo small grain fragments in grain-grain collisions in the warm phase of the interstellar medium. It was found that in one cycle through the warm medium (approximately 3 x 10(sup 6) years) of order 1-2% of the total grain mass is shattered into particles with radii of less than 50 A.

Jones, Anthony P.↗

NASA NTRS2017

Downlink Receiver Algorithms for Deep Space Optical Communications

The goal of the Deep Space Optical Communications project at the Jet Propulsion Laboratory is to demonstrate laser communication links at ranges out to approximately 3 AU. In this paper, we discuss a downlink receiver concept capable of demodulating optical pulse-position modulated (PPM) waveforms with data rates varying from approximately 50 kbps up to 265 Mbps, using a range of PPM orders, slot widths, and code rates. The receiver operates on recorded timestamps corresponding to the times-of-arrival of photons detected by a photon-counting detector array followed by a commercial time-tagger. Algorithms are presented for slot, symbol, and frame synchronization as well as parameter estimation. Estimates of link performance are evaluated through Monte- Carlo simulation for an optical channel that includes optical losses, detector blocking, signal clock dynamics, and pointing-induced downlink fades. Based upon these simulation results, it is expected that link closure may be achieved with at least 3 dB of margin under a variety of relevant conditions.

Tkacenko, Andre↗

NASA NTRS1979

Preliminary test results of a flight management algorithm for fuel conservative descents in a time based metered traffic environment

A flight management algorithm designed to improve the accuracy of delivering the airplane fuel efficiently to a metering fix at a time designated by air traffic control is discussed. The algorithm provides a 3-D path with time control (4-D) for a test B 737 airplane to make an idle thrust, clean configured descent to arrive at the metering fix at a predetermined time, altitude, and airspeed. The descent path is calculated for a constant Mach/airspeed schedule from linear approximations of airplane performance with considerations given for gross weight, wind, and nonstandard pressure and temperature effects. The flight management descent algorithms and the results of the flight tests are discussed.

Knox, C. E.↗

NASA NTRS2005

Solar Modulation of Inner Trapped Belt Radiation Flux as a Function of Atmospheric Density

Lodhi, M. A. K.↗

NASA NTRS2005

Simplified Solar Modulation Model of Inner Trapped Belt Proton Flux As a Function of Atmospheric Density

No simple algorithm seems to exist for calculating proton fluxes and lifetimes in the Earth's inner, trapped radiation belt throughout the solar cycle. Most models of the inner trapped belt in use depend upon AP8 which only describes the radiation environment at solar maximum and solar minimum in Cycle 20. One exception is NOAAPRO which incorporates flight data from the TIROS/NOAA polar orbiting spacecraft. The present study discloses yet another, simple formulation for approximating proton fluxes at any time in a given solar cycle, in particular between solar maximum and solar minimum. It is derived from AP8 using a regression algorithm technique from nuclear physics. From flux and its time integral fluence, one can then approximate dose rate and its time integral dose. It has already been published in this journal that the absorbed dose rate, D, in the trapped belts exhibits a power law relationship, D = A(rho)(sup -n), where A is a constant, rho is the atmospheric density, and the index n is weakly dependent upon shielding. However, that method does not work for flux and fluence. Instead, we extend this idea by showing that the power law approximation for flux J is actually bivariant in energy E as well as density rho. The resulting relation is J(E,rho)approx.(sum of)A(E(sup n))rho(sup -n), with A itself a power law in E. This provides another method for calculating approximate proton flux and lifetime at any time in the solar cycle. These in turn can be used to predict the associated dose and dose rate.

Wilson, Thomas L.↗

NASA NTRS1977

The separated turbulent boundary layer over a wavy wall

A study and application of the fourth order spline collocation procedure, numerical solution of boundary layer like differential equations, is presented. A simple inversion algorithm for the simultaneous solution of the resulting difference equations is given. Particular attention is focused on the boundary condition representation for the spline second derivative approximations. Solutions using the spline procedure, as well as the three point finite difference method, are presented for several model problems in order to assess and improve the spline numerical scheme. Application of the resulting algorithm to the incompressible laminar self similar boundary layer equations is presented.

Polak, A.↗

NASA NTRS1975

Diagonalization and simultaneous symmetrization of the gas-dynamic matrices

The hyperbolic nature of the unsteady, inviscid, gas-dynamic equations implies the existence of a similarity transformation for diagonalizing an arbitrary linear combination of coefficient matrices. It is shown that the individual matrices are simultaneously symmetrized by the similarity transformation. The transformations and their norms can be applied to the well-posedness of the Cauchy problem, linear stability theory for finite-difference approximations, and simplification of block-tridiagonal systems that arise in implicit time-split algorithms.

Warming, R. F.↗

NASA NTRS1981

Shape determination and control for large space structures

An integral operator approach is used to derive solutions to static shape determination and control problems associated with large space structures. Problem assumptions include a linear self-adjoint system model, observations and control forces at discrete points, and performance criteria for the comparison of estimates or control forms. Results are illustrated by simulations in the one dimensional case with a flexible beam model, and in the multidimensional case with a finite model of a large space antenna. Modal expansions for terms in the solution algorithms are presented, using modes from the static or associated dynamic mode. These expansions provide approximated solutions in the event that a used form analytical solution to the system boundary value problem is not available.

Weeks, C. J.↗

NASA NTRS1981

Static shape determination and control for a large space antenna

An integral operator approach is used to derive solutions to static shape determination and control problems associated with large space structures. Problem assumptions include a linear self-adjoint system model, observations and control forces at discrete points, and quadratic performance criteria for the comparison of estimates or control forces. Results are illustrated by simulations with a finite element model of a large space antenna. Modal expansions for terms in the solution algorithms are presented, using modes from the static or associated dynamic model. These expansions provide approximate solutions in the event that a closed form analytical solution to the system boundary value problem is not available.

Weeks, C.↗

NASA NTRS1982

The effects of seasonal differences in climatic conditions on Landsat spectral signatures and associated land cover classification

Unsupervised classification algorithms are used to analyze Landsat computer-compatible tape data for an area of approximately 840 sq km in central Oklahoma, over the period from June 12 to August 4, 1979. The results obtained show that changes in remotely sensed spectral signatures and land cover classes are associated with a period of transition from moisture availability in late spring to moisture deficit in midsummer, with the latter being marked by greater visible spectrum reflectance and greater near-IR absorption, although each surface cover type has responded differently to the seasonal change in water availability. Consideration of these results has led to the identification of important factors in the use of multidate satellite data in environmental change monitoring. Naturally induced trends in surface albedo introduce noise into studies aimed at identifying anthropogenic land cover change. Specific problems associated with prairie-forest ecotonal areas in the southern Great Plains involve the seasonally induced differences in separability of forest, bush, and grassland cover types.

Harrington, J. A., Jr.↗

NASA NTRS1988

Spectral element multigrid. Part 2: Theoretical justification

A multigrid algorithm is analyzed which is used for solving iteratively the algebraic system resulting from tha approximation of a second order problem by spectral or spectral element methods. The analysis, performed here in the one dimensional case, justifies the good smoothing properties of the Jacobi preconditioner that was presented in Part 1 of this paper.

Maday, Yvon↗

NASA NTRS1988

Spectral element miltigrid. II - Theoretical justification

A multigrid algorithm is analyzed which is used for solving iteratively the algebraic system resulting from the approximation of a second order problem by spectral or spectral element methods. The analysis, performed here in the one-dimensional case, justifies the good smoothing properties of the Jacobi preconditioner that was presented in Part 1 of this paper.

Maday, Yvon↗

NASA NTRS1992

Design of a new squaring function for the Viterbi algorithm

A new algorithm and hardware implementation of the Viterbi squaring function was developed. The use of an approximation squaring technique preserves the Viterbi performance as is demonstrated by Monte-Carlo simulations. Additionally, the 16-bit approximate squaring implementation is expected to require one-fourth the area and operate at three times the speed of the conventional squaring implementation.

Eshraghi, Aria↗

NASA NTRS1994

Multiresolution representation and numerical algorithms: A brief review

In this paper we review recent developments in techniques to represent data in terms of its local scale components. These techniques enable us to obtain data compression by eliminating scale-coefficients which are sufficiently small. This capability for data compression can be used to reduce the cost of many numerical solution algorithms by either applying it to the numerical solution operator in order to get an approximate sparse representation, or by applying it to the numerical solution itself in order to reduce the number of quantities that need to be computed.

Harten, Amiram↗

NASA NTRS2000

Cloud and Aerosol Retrieval for the 2001 GLAS Satellite Lidar Mission

The Geoscience Laser Altimeter System (GLAS) is scheduled for launch in July of 2001 aboard the Ice, Cloud and Land Elevation Satellite (ICESAT). In addition to being a precision altimeter for mapping the height of the Earth's icesheets, GLAS will be an atmospheric lidar, sensitive enough to detect gaseous, aerosol, and cloud backscatter signals, at horizontal and vertical resolutions of 175 and 75m, respectively. GLAS will be the first lidar to produce temporally continuous atmospheric backscatter profiles with nearly global coverage (94-degree orbital inclination). With a projected operational lifetime of five years, GLAS will collect approximately six billion lidar return profiles. The large volume of data dictates that operational analysis algorithms, which need to keep pace with the data yield of the instrument, must be efficient. So, we need to evaluate the ability of operational algorithms to detect atmospheric constituents that affect global climate. We have to quantify, in a statistical manner, the accuracy and precision of GLAS cloud and aerosol observations. Our poster presentation will show the results of modeling studies that are designed to reveal the effectiveness and sensitivity of GLAS in detecting various atmospheric cloud and aerosol features. The studies consist of analyzing simulated lidar returns. Simulation cases are constructed either from idealized renditions of atmospheric cloud and aerosol layers or from data obtained by the NASA ER-2 Cloud Lidar System (CLS). The fabricated renditions permit quantitative evaluations of operational algorithms to retrieve cloud and aerosol parameters. The use of observational data permits the evaluations of performance for actual atmospheric conditions. The intended outcome of the presentation is that climatology community will be able to use the results of these studies to evaluate and quantify the impact of GLAS data upon atmospheric modeling efforts.

Hart, William D.↗