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At least 1,045 records · Page 58
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

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

The global asymptotic nonlinear behavior of 11 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.↗
NASA NTRS1998

Turbulent Compressible Convection with Rotation: Mean Flows and Differential Rotation - 2

The effects of rotation on turbulent, compressible convection within stellar envelopes are studied through three-dimensional numerical simulations conducted within a local f-plane model. This work seeks to understand the types of differential rotation that can be established in convective envelopes of stars like the Sun, for which recent helioseismic observations suggest an angular velocity profile with depth and latitude at variance with many theoretical predictions. This paper analyzes the mechanisms that are responsible for the mean (horizontally averaged) zonal and meridional flows that are produced by convection influenced by Coriolis forces. The compressible convection is considered for a range of Rayleigh, Taylor, and Prandtl (and thus Rossby) numbers encompassing both laminar and turbulent flow conditions under weak and strong rotational constraints. When the nonlinearities are moderate, the effects of rotation on the resulting laminar cellular convection leads to distinctive tilts of the cell boundaries away from the vertical. These yield correlations between vertical and horizontal motions that generate Reynolds stresses that can drive mean flows, interpretable as differential rotation and meridional circulations. Under more vigorous forcing, the resulting turbulent convection involves complicated and contorted fluid particle trajectories, with few clear correlations between vertical and horizontal motions, punctuated by an evolving and intricate downflow network that can extend over much of the depth of the layer. Within such networks are some coherent structures of vortical downflow that tend to align with the rotation axis. These yield a novel turbulent alignment mechanism, distinct from the laminar tilting of cellular boundaries, that can provide the principal correlated motions and thus Reynolds stresses and subsequently mean flows. The emergence of such coherent structures that can persist amidst more random motions is a characteristic of turbulence with symmetries broken by rotation and stratification. Such structure is here found to play a crucial role in defining the mean zonal and meridional flows that coexist with the convection. Though they are subject to strong inertial oscillations, the strength and type of the mean flows are determined by a combination of the laminar tilting and the turbulent alignment mechanisms. Varying the parameters produces a wide range of mean motions. Among these, some turbulent solutions exhibit a mean zonal velocity profile that is nearly constant with depth, much as deduced by helioseismology at midlatitudes within the Sun. The solutions exhibit a definite handedness, with the direction of the persistent mean flows often prescribing a spiral with depth near the boundaries, also in accord with helioseismic deductions. The mean helicity has a profile that is positive in the upper portion of the domain and negative in the lower portion, a property bearing on magnetic dynamo processes that may be realized within such rotating layers of turbulent convection.

Brummell, Nicholas H.↗
NASA NTRS1997

Low Differential Pressure Generator

A method and apparatus for evaluating low differential pressure transducers includes a pressure generator in the form of a piston-cylinder assembly having a piston that may be manually positioned precisely within the cylinder to change the volume and thus the pressure at respective sides of the piston. At one side of the piston the cylinder communicates with a first chamber and at the other side of the piston the cylinder communicates with a second chamber, the first and second chambers being formed within a common tank by a partition wall. The chambers each communicate with the transducer to be evaluated and a standard pre-calibrated transducer the transducers being connected fluidly in parallel so that a pressure differential between air in the two chambers resulting from movement of the piston within the cylinder is communicated to both the transducer to be evaluated and the standard transducer, and the outputs of the transducers is observed and recorded.

Stout, Stephen J.↗
NASA NTRS1996

Atmospheric Pre-Corrected Differential Absorption Techniques to Retrieve Columnar Water Vapor: Theory and Simulations

Two different approaches exist to retrieve columnar water vapor from imaging spectrometer data: (1) Differential absorption techniques based on: (a) Narrow-Wide (N/W) ratio between overlapping spectrally wide and narrow channels; (b) Continuum Interpolated Band Ratio (CIBR) between a measurement channel and the weighted sum of two reference channels. (2) Non-linear fitting techniques which are based on spectral radiative transfer calculations. The advantage of the first approach is computational speed and of the second, improved retrieval accuracy. Our goal was to improve the accuracy of the first technique using physics based on radiative transfer. Using a modified version of the Duntley equation, we derived an "Atmospheric Pre-corrected Differential Absorption" (APDA) technique and described an iterative scheme to retrieve water vapor on a pixel-by-pixel basis. Next we compared both, the CIBR and the APDA using the Duntley equation for MODTRAN3 computed irradiances, transmissions and path radiance (using the DISORT option). This simulation showed that the CIBR is very sensitive to reflectance effects and that the APDA performs much better. An extensive data set was created with the radiative transfer code 6S over 379 different ground reflectance spectra. The calculated relative water vapor error was reduced significantly for the APDA. The APDA technique had about 8% (vs. over 35% for the CIBR) of the 379 spectra with a relative water vapor error of greater than +5%. The APDA has been applied to 1991 and 1995 AVIRIS scenes which visually demonstrate the improvement over the CIBR technique.

Borel, Christoph C.↗
NASA NTRS1996

Atmospheric Pre-Corrected Differential Absorption Techniques to Retrieve Columnar Water Vapor: Application to AVIRIS 91/95 Data

Water vapor is one of the main forces for weather development as well as for mesoscale air transport processes. The monitoring of water vapor is therefore an important aim in remote sensing of the atmosphere. Current operational systems for water vapor detection use primarily the emission in the thermal infrared (AVHRR, GOES, ATSR, Meteosat) or in the microwave radiation bands (DMSP). The disadvantage of current satellite systems is either a coarse spatial (horizontal) resolution ranging from one to tens of kilometers or a limited insight into the lower atmosphere. Imaging spectrometry on the other hand measures total column water vapor contents at a high spatial horizontal resolution and has therefore the potential of filling these gaps. The sensors of the AVIRIS instrument are capable of acquiring hyperspectral data in 224 bands located in the visible and near infrared at 10 nm resolution. This data includes the information on constituents of the earth's surface as well as of the atmosphere. The optical measurement of water vapor can be performed using sensor channels located in bands or lines of the absorption spectrum. The AVIRIS sensor has been used to retrieve water vapor and with less accuracy carbon dioxide, oxygen and ozone. To retrieve the water vapor amount, the so called differential absorption technique has been applied. The goal of this technique is to eliminate background factors by taking a ratio between channels within the absorption band and others besides the band. Various ratioing methods on the basis of different channels and calculation techniques were developed. The influence of a trace gas of interest on the radiance at the sensor level is usually simulated by using radiative transfer codes. In this study, the spectral transmittance and radiance are calculated by MODTRAN3 simulations with the new DISORT option. The objective of this work is to test the best performing differential absorption techniques for imaging spectrometry of tropospheric water vapor.

Schlaepfer, Daniel↗
NASA NTRS1997

Runge-Kutta Methods for Linear Ordinary Differential Equations

Three new Runge-Kutta methods are presented for numerical integration of systems of linear inhomogeneous ordinary differential equations (ODES) with constant coefficients. Such ODEs arise in the numerical solution of the partial differential equations governing linear wave phenomena. The restriction to linear ODEs with constant coefficients reduces the number of conditions which the coefficients of the Runge-Kutta method must satisfy. This freedom is used to develop methods which are more efficient than conventional Runge-Kutta methods. A fourth-order method is presented which uses only two memory locations per dependent variable, while the classical fourth-order Runge-Kutta method uses three. This method is an excellent choice for simulations of linear wave phenomena if memory is a primary concern. In addition, fifth- and sixth-order methods are presented which require five and six stages, respectively, one fewer than their conventional counterparts, and are therefore more efficient. These methods are an excellent option for use with high-order spatial discretizations.

Zingg, David W.↗
NASA NTRS1998

First- and Second-Order Sensitivity Analysis of a P-Version Finite Element Equation Via Automatic Differentiation

Sensitivity analysis is a technique for determining derivatives of system responses with respect to design parameters. Among many methods available for sensitivity analysis, automatic differentiation has been proven through many applications in fluid dynamics and structural mechanics to be an accurate and easy method for obtaining derivatives. Nevertheless, the method can be computational expensive and can require a high memory space. This project will apply an automatic differentiation tool, ADIFOR, to a p-version finite element code to obtain first- and second- order then-nal derivatives, respectively. The focus of the study is on the implementation process and the performance of the ADIFOR-enhanced codes for sensitivity analysis in terms of memory requirement, computational efficiency, and accuracy.

Hou, Gene↗
NASA NTRS1998

Robust Real-Time Wide-Area Differential GPS Navigation

The present invention provides a method and a device for providing superior differential GPS positioning data. The system includes a group of GPS receiving ground stations covering a wide area of the Earth's surface. Unlike other differential GPS systems wherein the known position of each ground station is used to geometrically compute an ephemeris for each GPS satellite. the present system utilizes real-time computation of satellite orbits based on GPS data received from fixed ground stations through a Kalman-type filter/smoother whose output adjusts a real-time orbital model. ne orbital model produces and outputs orbital corrections allowing satellite ephemerides to be known with considerable greater accuracy than from die GPS system broadcasts. The modeled orbits are propagated ahead in time and differenced with actual pseudorange data to compute clock offsets at rapid intervals to compensate for SA clock dither. The orbital and dock calculations are based on dual frequency GPS data which allow computation of estimated signal delay at each ionospheric point. These delay data are used in real-time to construct and update an ionospheric shell map of total electron content which is output as part of the orbital correction data. thereby allowing single frequency users to estimate ionospheric delay with an accuracy approaching that of dual frequency users.

Yunck, Thomas P.↗
NASA NTRS1998

Differential Absorption Lidar (DIAL) Measurements from Air and Space

Differential absorption lidar (DIAL) systems have been used for the measurement of ozone, water vapor, and aerosols from aircraft platforms for over 18 years, yielding new insights into atmospheric chemistry, composition, and dynamics in large-scale field experiments conducted all over the world. The successful deployment of the lidar in-space technology experiment (LITE) in September 1994 demonstrated that space-based lidars can also collect valuable information on the global atmosphere. This paper reviews some of the contributions of the NASA Langley Research Center's airborne ozone and water vapor DIAL systems and space-based LITE system to the understanding of the atmosphere and discusses the feasibility and advantages of putting DIAL systems in space for routine atmospheric measurements of ozone and/or water vapor and aerosols and clouds. The technology and applications of the differential absorption lidar (DIAL) technique have progressed significantly since the first DIAL measurements of Schotland, and airborne DIAL measurements of ozone and water vapor are frequently being made in a wide range of field experiments. In addition, plans are underway to develop DIAL systems for use on satellites for continuous global measurements. This paper will highlight the history of airborne lidar and DIAL systems, summarize the major accomplishments of the NASA Langley DIAL program, and discuss specifications and goals for DIAL systems in space.

Browell, E. V.↗
NASA NTRS1999

Numerical Study of Buoyancy and Differential Diffusion Effects on the Structure and Dynamics of Triple Flames

Triple flames arise in a number of practical configurations where fuel and oxidizer are partially premixed, such as in the base of a lifted jet flame. Past experimental studies, theoretical analyses, and numerical modeling of triple flames suggested the potential role of triple flames in stabilizing turbulent flames and in promoting flame propagation. From recent numerical simulations of laminar triple flames, a strong influence of differential diffusion among species and heat on the triple flame structure has been gradually appreciated. This paper reports preliminary numerical results on the influence of gravity and differential diffusion effects on the structure and dynamics of triple flames with a one-step global irreversible chemistry model.

Chen, J. -Y.↗
NASA NTRS2000

A Real Time Differential GPS Tracking System for NASA Sounding Rockets

Sounding rockets are suborbital launch vehicles capable of carrying scientific payloads to several hundred miles in altitude. These missions return a variety of scientific data including: chemical makeup and physical processes taking place in the atmosphere, natural radiation surrounding the Earth, data on the Sun, stars, galaxies and many other phenomena. In addition, sounding rockets provide a reasonably economical means of conducting engineering tests for instruments and devices to be used on satellites and other spacecraft prior to their use in these more expensive missions. Typically around thirty of these rockets are launched each year, from established ranges at Wallops Island, Virginia; Poker Flat Research Range, Alaska; White Sands Missile Range, New Mexico and from a number of ranges outside the United States. Many times launches are conducted from temporary launch ranges in remote parts of the world requiring considerable expense to transport and operate tracking radars. In order to support these missions, an inverse differential GPS system has been developed. The flight system consists of a small, inexpensive receiver, a preamplifier and a wrap-around antenna. A rugged, compact, portable ground station extracts GPS data from the raw payload telemetry stream, performs a real time differential solution and graphically displays the rocket's path relative to a predicted trajectory plot. In addition to generating a real time navigation solution, the system has been used for payload recovery, timing, data timetagging, precise tracking of multiple payloads and slaving of optical tracking systems for over the horizon acquisition. This paper discusses, in detail, the flight and ground hardware, as well as data processing and operational aspects of the system, and provides evidence of the system accuracy.

Bull, Barton↗
NASA NTRS2000

Emergency Multiengine Aircraft System for Lateral Control Using Differential Thrust Control of Wing Engines

Development of an emergency flight control system is disclosed for lateral control using only differential engine thrust modulation of multiengine aircraft is currently underway. The multiengine has at least two engines laterally displaced to the left and right from the axis of the aircraft. In response to a heading angle command psi(sub c) is to be tracked. By continually sensing the heading angle psi of the aircraft and computing a heading error signal psi(sub e) as a function of the difference between the heading angle command psi(sub c) and the sensed heading angle psi, a track control signal is developed with compensation as a function of sensed bank angle phi. Bank angle rate phi, or roll rate p, yaw rate tau, and true velocity produce an aircraft thrust control signal ATC(sub psi(L,R)). The thrust control signal is differentially applied to the left and right engines, with equal amplitude and opposite sign, such that a negative sign is applied to the control signal on the side of the aircraft. A turn is required to reduce the error signal until the heading feedback reduces the error to zero.

Burken, John J.↗
NASA NTRS2000

Los Angeles: The Most Differentiated Basaltic Martian Meteorite

Los Angeles is a new martian meteorite that expands the compositional range of basaltic shergottites. Compared to Shergotty, Zagami, QUE94201, and EET79001-B, Los Angeles is more differentiated, with higher concentrations of incompatible elements (e.g., La) and a higher abundance of late-stage phases such as phosphates and K-rich feldspathic glass. The pyroxene crystallization trend starts at compositions more ferroan than in other martian basaits. Trace elements indicate a greater similarity to Shergotty and Zagami than to QUE94201 or EET79001-B, but the Mg/Fe ratio is low even compared to postulated parent melts of Shergotty and Zagami. Pyroxene in Los Angeles has 0.7-4-microns-thick exsolution lamellae, approx. 10 times thicker than those in Shergotty and Zaganii. Opaque oxide compositions suggest a low equilibration temperature at an oxygen fugacity near the fayafite-magnetitequartz buffer. Los Angeles cooled more slowly than Shergotty and Zagami. Slow cooling, coupled with the ferroan bulk composition, produced abundant fine-grained intergrowths of fayalite, hedenbergite, and silica, by the breakdown of pyroxferroite. Shock effects in Los Angeles include maskelynitized plagioclase, pyroxene with mosaic extinction, and rare fault zones. One such fault ruptured a previously decomposed zone of pyroxferroite. Although highly differentiated, the bulk composition of Los Angeles is not close to the low-Ca/Si composition or the globally wind-stirred soil of Mars.

Rubin, Alan E.↗
NASA NTRS2002

Reliable Real-Time Solution of Parametrized Partial Differential Equations: Reduced-Basis Output Bound Methods

We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced basis approximations, Galerkin projection onto a space W(sub N) spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation, relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures, methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage, in which, given a new parameter value, we calculate the output of interest and associated error bound, depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control.

Prudhomme, C.↗
NASA NTRS2002

Multiobjective Optimization Using a Pareto Differential Evolution Approach

Differential Evolution is a simple, fast, and robust evolutionary algorithm that has proven effective in determining the global optimum for several difficult single-objective optimization problems. In this paper, the Differential Evolution algorithm is extended to multiobjective optimization problems by using a Pareto-based approach. The algorithm performs well when applied to several test optimization problems from the literature.

Madavan, Nateri K.↗
NASA NTRS2002

Turbomachinery Airfoil Design Optimization Using Differential Evolution

An aerodynamic design optimization procedure that is based on a evolutionary algorithm known at Differential Evolution is described. Differential Evolution is a simple, fast, and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems, including highly nonlinear systems with discontinuities and multiple local optima. The method is combined with a Navier-Stokes solver that evaluates the various intermediate designs and provides inputs to the optimization procedure. An efficient constraint handling mechanism is also incorporated. Results are presented for the inverse design of a turbine airfoil from a modern jet engine and compared to earlier methods. The capability of the method to search large design spaces and obtain the optimal airfoils in an automatic fashion is demonstrated. Substantial reductions in the overall computing time requirements are achieved by using the algorithm in conjunction with neural networks.

Madavan, Nateri K.↗
NASA NTRS2002

Turbomachinery Airfoil Design Optimization Using Differential Evolution

An aerodynamic design optimization procedure that is based on a evolutionary algorithm known at Differential Evolution is described. Differential Evolution is a simple, fast, and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems, including highly nonlinear systems with discontinuities and multiple local optima. The method is combined with a Navier-Stokes solver that evaluates the various intermediate designs and provides inputs to the optimization procedure. An efficient constraint handling mechanism is also incorporated. Results are presented for the inverse design of a turbine airfoil from a modern jet engine. The capability of the method to search large design spaces and obtain the optimal airfoils in an automatic fashion is demonstrated. Substantial reductions in the overall computing time requirements are achieved by using the algorithm in conjunction with neural networks.

Madavan, Nateri K.↗