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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Optimization methods, flux conserving methods for steady state Navier-Stokes equation

Navier-Stokes equation as discretized by new flux conserving method proposed by Chang and Scott results in the system: vector F(vector x) = 0, where F is a vector valued function. The Optimization method we use is based on Quasi-Newton methods: given a nonlinear function vector F(vector x) = 0, we solve, Delta(vector x) = -BF(vector x), where Delta(vector x) is the correction term and B is the inverse Jacobian of F(x). Then, iteratively, vector(x(sub (i+1))) = vector(x (sub i)) + alpha.Delta(vector x(sub i)), where alpha is a line search correction term determined by a line search routine. We use the BFCG's update the Jacobian matrix B(sub k) at each iteration. It is well known that B(sub k) approaches B(*) at the solution X(*). This algorithm has several advantages over the Newton-Raphson method. For example, we do not need to calculate the Jacobian matrix at each iteration which is computationally very expensive.

Adeyeye, John↗
NASA NTRS2005

AutoChem

AutoChem is a suite of Fortran 90 computer programs for the modeling of kinetic reaction systems. AutoChem performs automatic code generation, symbolic differentiation, analysis, and documentation. It produces a documented stand-alone system for the modeling and assimilation of atmospheric chemistry. Given databases of chemical reactions and a list of constituents defined by the user, AutoChem automatically does the following: 1. Selects the subset of reactions that involve a user-defined list of constituents and automatically prepares a document listing the reactions; 2. Constructs the ordinary differential equations (ODEs) that describe the reactions as functions of time and prepares a document containing the ODEs; 3. Symbolically differentiates the time derivatives to obtain the Jacobian and prepares a document containing the Jacobian; 4. Symbolically differentiates the Jacobian to obtain the Hessian and prepares a document containing the Hessian; and 5. Writes all the required Fortran 90 code and datafiles for a stand-alone chemical modeling and assimilation system (implementation of steps 1 through 5). Typically, the time taken for steps 1 through 5 is about 3 seconds. The modeling system includes diagnostic components that automatically analyze each ODE at run time, the relative importance of each term, time scales, and other attributes of the model.

Lary, David John↗
NASA NTRS2017

Electric Field Conjugation in the Presence of Model Uncertainty

The Wide-Field Infrared Survey Telescope (WFIRST) is a 2.4-meter-diameter space telescope NASA program. The payload will include a coronagraph instrument (CGI). The CGI designs under development use deformable mirrors (DM) to create a point spread function (PSF) with a dark region around the obscured star object. Electric field conjugation (EFC) is an iterative nonlinear optimization procedure that uses measurements of the electric field at the image to determine the DM displacements to modify the PSF to create the region of high contrast in the image. EFC requires a numerical model of the coronagraph to calculate the Jacobian of the system, which is used, along with regularization, to solve for the DM displacements for each iteration of the nonlinear optimization. Ideally, the coronagraph is aligned and calibrated, and the calibration data are used in the numerical model for calculating the Jacobian. However, calibration and alignment measurements always contain uncertainty resulting in calibration error. Therefore, the Jacobian calculated from the numerical model is not an exact representation of the physical coronagraph, and the resulting DM solution for an EFC iteration does not have the exact impact on the electric field of the coronagraph as predicted by the EFC. The result is slow convergence, and, as will be shown, drives the use of more restrictive regularization. Using Monte Carlo trials, we investigate the effect of calibration error on EFC convergence and regulatization. Comparison to results from the High Contrast Imaging Testbed Hybrid Lyot Coronagraph are also presented.

Marx, David↗
NASA NTRS2020

Version 2 Ozone Monitoring Instrument SO2 Product (OMSO2 V2): New Anthropogenic SO2 Vertical Column Density Dataset

The Ozone Monitoring Instrument (OMI) has been providing global observations of SO2 pollution since 2004. Here we introduce the new anthropogenic SO2 vertical column density (VCD) dataset in the version 2 OMI SO2 product (OMSO2 V2). As with the previous version (OMSO2 V1.3), the new dataset is generated with an algorithm based on principal component analysis of OMI radiances, but features several updates. The most important among those is the use of expanded lookup tables and model a priori profiles to estimate SO2 Jacobians for individual OMI pixels, in order to better characterize pixel-to-pixel variations in SO2 sensitivity, including over snow and ice. Additionally, new data screening and spectral fitting schemes have been implemented to improve the quality of the spectral fit. As compared with the planetary boundary layer SO2 dataset in OMSO2 V1.3, the new dataset has substantially better data quality, especially over areas that are relatively clean or affected by the south Atlantic anomaly. The updated retrievals over snow/ice yield more realistic seasonal changes in SO2 at high latitudes and offer enhanced sensitivity to sources during wintertime. An error analysis has been conducted to assess uncertainties in SO2 VCDs from both the spectral fit and Jacobian calculations. The uncertainties from spectral fitting are reflected in SO2 slant column densities (SCDs) and largely depend on the signal-to-noise ratio of the measured radiances, as implied by the generally smaller SCD uncertainties over clouds or for smaller solar zenith angles. The SCD uncertainties for individual pixels are estimated to be~0.15-0.3 DU (Dobson Units) between ~40°S and ~40°N and to be~0.2-0.5 DU at higher latitudes. The uncertainties from the Jacobians are approximately ~50-100% over polluted areas, and primarily attributed to errors in SO2 a priori profiles and cloud pressures, as well as the lack of explicit treatment for aerosols. Finally, the daily mean and median SCDs over the presumably SO2-free equatorial East Pacific have increased by only~0.0035 DU and ~0.003 DU respectively over the entire 15-year OMI record; while the standard deviation of SCDs has grown by only~0.02 DU or ~10%. Such remarkable long-term stability makes the new dataset particularly suitable for detecting regional changes in SO2 pollution.

OMI, SO2, Remote Sensing↗
NASA NTRS2018

An Algorithm for Trajectory Generation in Redundant Manipulators with Joint Transmission Accommodation

Trajectory generation for manipulators involves generating incremental updates of joint variables to achieve a desired end–effector motion. The Jacobian matrix maps incremental joint motion to incremental end–effector motion in a linear fashion and is typically used in manipulator trajectory generation algorithms. In the case of a redundant manipulator, the Jacobian matrix is not square or invertible and therefore algorithms based on pseudoinverses and their variations are commonly used for trajectory generation. These methods either are computationally not efficient or do not utilize all the joints in motion generation and therefore do not completely exploit the redundancy of the manipulator. The method presented in this paper is a simple method that maximizes transmission of all joint variables onto a desired end–effector motion trajectory. The method is based on aligning the null–space of an augmented Jacobian matrix with the path of the desired end–effector motion, from which a linear combination of joints that projects fully onto the desired end–effector trajectory is obtained. In this manner, all joints of the redundant manipulator are used to generate the end–effector trajectory accommodating the ability of each joint in terms of its motion transmission.

Ravani, Bahram↗
NASA NTRS2023

The Community Radiative Transfer Model (CRTM): Community-Focused Collaborative Model Development Accelerating Research to Operations

The Joint Center for Satellite Data Assimilation (JCSDA) Community Radiative Transfer Model (CRTM) is a fast, 1-D radiative transfer model used in numerical weather prediction, calibration/validation, etc. across multiple federal agencies and universities. The key benefit of the CRTM is that it is a satellite simulator. It provides a highly accurate representation of satellite radiances by using the specific sensor response functions convolved with a line-by-line radiative transfer model (LBLRTM). CRTM covers the spectral ranges consistent with all present operational and most research satellites, from visible to microwave. The capability to simulate ultraviolet radiances and support space-based radar sensors is being added over the next two years in CRTM Version 3.0. In addition to simulated radiances, the CRTM also provides Jacobian outputs needed to interpret satellite observations for numerical weather prediction. The Jacobian estimates how changes in geophysical parameters affect simulated measurements from satellite sensors. Using the Jacobian in modeling and weather prediction improves the accuracy and efficiency of data analysis, leading to better weather predictions. The CRTM model's success and growth depend on community contributions and evaluation. To facilitate this, we have made the CRTM highly accessible through modular programming, clear documentation and tutorials, public domain licensing, unfettered public access via Github, and a clear path to operational implementation for innovative research. We encourage and welcome contributions from the community to help us continue to improve the CRTM.

Benjamin T Johnson↗
NASA NTRS1973

The cometary and asteroidal origins of meteors

A quantitative examination of the gravitational and nongravitational changes of orbits shows that for larger interplanetary bodies the perturbations by Jupiter strongly predominate over all other effects, which include perturbations by other planets, splitting of comet nuclei and jet effects of cometary ejections. The structure of meteor streams, indicates that the mutual compensation of the changes in individual elements entering the Jacobian integral, which is characteristic for the comets, does not work among the meteoroids. It appears that additional forces of a different kind must exert appreciable influence on the motion of interplanetary particles of meteoroid size. Nevertheless, the distribution of the Jacobian constant in various samples of meteor orbits furnishes some information on the type of their parent bodies and on the relative contribution of individual sources.

Kresak, L.↗
NASA NTRS1976

Linearized blade row compression component model. Stability and frequency response analysis of a J85-3 compressor

NASA developed stability and frequency response analysis techniques were applied to a dynamic blade row compression component stability model to provide a more economic approach to surge line and frequency response determination than that provided by time-dependent methods. This blade row model was linearized and the Jacobian matrix was formed. The clean-inlet-flow stability characteristics of the compressors of two J85-13 engines were predicted by applying the alternate Routh-Hurwitz stability criterion to the Jacobian matrix. The predicted surge line agreed with the clean-inlet-flow surge line predicted by the time-dependent method to a high degree except for one engine at 94% corrected speed. No satisfactory explanation of this discrepancy was found. The frequency response of the linearized system was determined by evaluating its Laplace transfer function. The results of the linearized-frequency-response analysis agree with the time-dependent results when the time-dependent inlet total-pressure and exit-flow function amplitude boundary conditions are less than 1 percent and 3 percent, respectively. The stability analysis technique was extended to a two-sector parallel compressor model with and without interstage crossflow and predictions were carried out for total-pressure distortion extents of 180 deg, 90 deg, 60 deg, and 30 deg.

Tesch, W. A.↗
NASA NTRS1981

Approximations of satellite stability

Modifications and corrections are presented to relations obtained in an investigation conducted by Szebehely (1978), who has discussed the problem of Hill's (1878) stability of satellites in the restricted problem of three bodies. Attention is given to an approximation of the Jacobian constant for the satellite, the critical value of the Jacobian constant, and approximate solutions.

Markellos, V. V.↗
NASA NTRS1983

Flux-based acceleration of the Euler equations

A new coarse grid acceleration scheme for the Euler equations is presented. This flux based scheme eliminates the need, exhibited by previous accelerators, for computing flux vector Jacobian matrices. The method is derived and implemented in a two dimensional flow algorithm. Numerical results are presented for both subcritical and shocked, supercritical flow. These results demonstrate that the flux based accelerator is more efficient than its Jacobian based counterpart. Generalization to three dimensions is immediate. Construction of flux based accelerators for the Navier-Stokes equations is also discussed.

Johnson, G. M.↗
NASA NTRS1983

Flux vector splitting and approximate Newton methods

In the present investigation, the basic approach is employed to view an iterative scheme as Newton's method or as a modified Newton's method. Attention is given to various modified Newton methods which can arise from differencing schemes for the Euler equations. Flux vector splitting is considered as the basic spatial differencing technique. This technique is based on the partition of a flux vector into groups which have certain properties. The Euler equations fluxes can be split into two groups, the first group having a flux Jacobian with all positive eigenvalues, and the second group having a flux Jacobian with all negative eigenvalues. Flux vector splitting based on a velocity-sound speed split is considered along with the use of numerical techniques to analyze nonlinear systems, and the steady Euler equations for quasi-one-dimensional flow in a nozzle. Results are given for steady flows with shocks.

Jespersen, D. C.↗
NASA NTRS1984

Numerical modeling of D-mappings with applications to chemical kinetics

Numerical modeling of D-mappings was studied and applied to solving nonlinear stiff systems. These mappings were locally linearized for convergence analysis, and some applications were made to chemical kinetics. The technique avoids using multistep implicit codes that require inversion of Jacobian matrices, but depends on the Jacobians for its convergence analysis.

Dey, S. K.↗
NASA NTRS1983

A mathematical model for efficient estimation of aircraft motions

In the usual formulation of the aircraft state-estimation problem, motions along a flight trajectory are represented by a plant consisting of nonlinear state and measurement models. Problem solution using this formulation requires that both state- and measurement-dependent Jacobian matrices be evaluated along any trajectory. In this paper it is shown that a set of state variables can be chosen to realize a linear state model of very simple form, such that all nonlinearities appear in the measurement model. The potential advantage of the new formulation is computational: the Jacobian matrix corresponding to a linear state model is constant, a feature that should outweigh the fact that the measurement model is more complicated than in the conventinal formulation. To compare the modeling methods, aircraft motions from typical flight-test and accident data were estimated, using each formulation with the same off-line (smoothing) algorithm. The results of these experiments, reported in the paper, demonstrate clearly the computational superiority of the linear state-variable formulation. The procedure advocated here may be extended to other nonlinear estimation problems, including on-line (filtering) applications.

Bach, R. E., Jr.↗
NASA NTRS1985

Errors in reduction methods

A mathematical basis is given for comparing the relative merits of various techniques used to reduce the order of large linear and nonlinear dynamics problems during their numerical integration. In such techniques as Guyan-Irons, path derivatives, selected eigenvectors, Ritz vectors, etc., the nth order initial value problem of /y(dot) = f(y) for t greater than 0, y(0) given/ is typically reduced to the mth order (m is much less than n) problem of /z(dot) = g(z) for t greater than 0, z(0) given/ by the transformation y = Pz where P changes from technique to technique. This paper gives an explicit approximate expression for the reduction error e-i in terms of P and the Jacobian of f. It is shown that: (a) reduction techniques are more accurate when the time rate of change of the response y is relatively small; (b) the change in response between two successive stations contributes to the errors at future stations after the change in response is transformed by a filtering matrix H, defined in terms of P; (c) the error committed at a station propagates to future stations by a mixing and scaling matrix G, defined in terms of P, Jacobian and of f, and time increment h. The paper discusses the conditions under which the reduction errors may be minimized and gives guidelines for selecting the reduction basis vector, i.e., the columns of P.

Utku, S.↗
NASA NTRS1986

The effects of various implicit operators on a flux vector splitting method

Three different implicit operators in a numerical method for solving the two-dimensional steady Euler equations using flux vector splitting are investigated. These include the implementation of the true Jacobian matrices in the implicit part, the use of their splitting approximate form, and a modification of the implicit part of the scheme that uses the scalar form of the implicit part based on the spectral radii of the split Jacobian matrices. The three versions of the basic algorithm are compared with the results given by two common numerical methods using several two-dimensional test cases. Special attention is paid to the quality of results as well as computational efficiency and convergence properties.

Von Lavante, E.↗
NASA NTRS1987

A computational procedure for automated flutter analysis

A direct solution procedure for computing the flutter Mach number and the flutter frequency is applied to the aeroelastic analysis of propfans using a finite element structural model and an unsteady aerodynamic model based on a three-dimensional subsonic compressible lifting surface theory. An approximation to the Jacobian matrix that improves the efficiency of the iterative process is presented. The Jacobian matrix is indirectly approximated from approximate derivatives of the flutter matrix. Examples are used to illustrate the convergence properties. The direct solution procedure facilitates the automated flutter analysis in addition to contributing to the efficient use of computer time as well as the analyst's time.

Murthy, Durbha V.↗
NASA NTRS1987

Chemistry-split techniques for viscous reactive blunt body flow computations

The weak-coupling structure between the fluid and species equations has been exploited and resulted in three, closely related, time-iterative implicit techniques. While the primitive variables are solved in two separated groups and each by an Alternating Direction Implicit (ADI) factorization scheme, the rate-species Jacobian can be treated in either full or diagonal matrix form, or simply ignored. The latter two versions render the split technique to solving for species as scalar rather than vector variables. The solution is completed at the end of each iteration after determining temperature and pressure from the flow density, energy and species concentrations. Numerical experimentation has shown that the split scalar technique, using partial rate Jacobian, yields the best overall stability and consistency. Satisfactory viscous solutions were obtained for an ellipsoidal body of axis ratio 3:1 at Mach 35 and an angle of attack of 20 degrees.

Li, C. P.↗
NASA NTRS1988

A computational procedure for automated flutter analysis

A direct solution procedure for computing the flutter Mach number and the flutter frequency is applied to the aeroelastic analysis of propfans using an unsteady aerodynamic model based on a three-dimensional subsonic compressible lifting surface theory. An approximation to the Jacobian matrix that improves the efficiency of the iterative process is presented. The Jacobian matrix is indirectly approximated from approximate derivatives of the flutter matrix. Examples are used to illustrate the convergence properties. The direct solution procedure facilitates the automated flutter analysis in addition to contributing to the efficient use of computer time as well as the analyst's time.

Murthy, Durbha V.↗