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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 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Symbolic generation of constitutive equations

The use of the symbolic manipulation program MACSYMA for the automatic generation of constitutive equations describing the thermomechanical behavior of complex materials such as metal-matrix composites is demonstrated. Problem-specific algorithms are developed; e.g., for partial differentiation by the chain rule, automatic generation of tree structures, special tensor analysis, and the simplification of expressions. The resulting subprogram package, SDICE, is shown to be fully applicable to both isotropic and anisotropic materials; its potential usefulness as a basis for FEM analyses is indicated.

Tan, H. Q.↗
NASA NTRS1989

Auroral excitation of the N2 2P(0,0) and VK(0,9) bands

The low-energy secondary electron flux caused by auroral electron precipitation is examined using data from the Atmosphere Explorer C satellite. An energetic electron transport algorithm is used to compute the differential electron flux produced by measured primaries. Emissions of N2 in the 2P(0,0) band at 337 nm and the VK(0,9) band at 335 nm predicted by the model are compared with photometric observation of their combined volume emission rate altitude profile made by the visible airglow experiment. Reasonable correspondence between model and measurement is obtained. Ratios of emissions at 337 nm and 630 nm to the N2(+) 1N(0,0) band at 428 nm are also studied. It is concluded that the 337/428 nm ratio responds to changes in the characteristic energy of primary auroral electrons only insofar as part of the 337 nm brightness is due to N2 VK(0,9) emission. The 630/428 nm ratio, which is strongly dependent on characteristic energy, also varies significantly with changes in atomic oxygen density.

Solomon, Stanley C.↗
NASA NTRS1992

Systematic Disturbance Of Optimal Rotational Trajectory

Algorithm introduces systematic disturbance into otherwise optimal rotation of body from prescribed initial to prescribed final orientation. Disturbance introduced as deviation of actual axis of rotation from optimal one, like wobble of top. Algorithm effects rotational transformations and solves differential equations necessary to compute disturbed trajectory. Devised for use with motion-control program and three-dimensional computer-graphical display to study ability of observers to distinguish between optimal and suboptimal rotational trajectories.

Grunwald, Arthur J.↗
NASA NTRS1994

Semigroup approximation and robust stabilization of distributed parameter systems

Theoretical results that enable rigorous statements of convergence and exponential stability of Galerkin approximations of LQR controls for infinite dimensional, or distributed parameter, systems have proliferated over the past ten years. In addition, extensive progress has been made over the same time period in the derivation of robust control design strategies for finite dimensional systems. However, the study of the convergence of robust finite dimensional controllers to robust controllers for infinite dimensional systems remains an active area of research. We consider a class of soft-constrained differential games evolving in a Hilbert space. Under certain conditions, a saddle point control can be given in feedback form in terms of a solution to a Riccati equation. By considering a related LQR problem, we can show a convergence result for finite dimensional approximations of this differential game. This yields a computational algorithm for the feedback gain that can be derived from similar strategies employed in infinite dimensional LQR control design problems. The approach described in this paper also inherits the additional properties of stability robustness common to game theoretic methods in finite dimensional analysis. These theoretical convergence and stability results are verified in several numerical experiments.

Kurdila, A. J.↗
NASA NTRS1995

FORTRAN program for analyzing ground-based radar data: Usage and derivations, version 6.2

A postflight FORTRAN program called 'radar' reads and analyzes ground-based radar data. The output includes position, velocity, and acceleration parameters. Air data parameters are also provided if atmospheric characteristics are input. This program can read data from any radar in three formats. Geocentric Cartesian position can also be used as input, which may be from an inertial navigation or Global Positioning System. Options include spike removal, data filtering, and atmospheric refraction corrections. Atmospheric refraction can be corrected using the quick White Sands method or the gradient refraction method, which allows accurate analysis of very low elevation angle and long-range data. Refraction properties are extrapolated from surface conditions, or a measured profile may be input. Velocity is determined by differentiating position. Accelerations are determined by differentiating velocity. This paper describes the algorithms used, gives the operational details, and discusses the limitations and errors of the program. Appendices A through E contain the derivations for these algorithms. These derivations include an improvement in speed to the exact solution for geodetic altitude, an improved algorithm over earlier versions for determining scale height, a truncation algorithm for speeding up the gradient refraction method, and a refinement of the coefficients used in the White Sands method for Edwards AFB, California. Appendix G contains the nomenclature.

Haering, Edward A., Jr.↗
NASA NTRS1995

Algorithm For Computation Of Chemically Reacting Flow

Efficient algorithm developed for use in solving differential equations of transient, chemically reacting flows at all speeds from zero to high mach numbers. Mathematical models represent coupling of thermal, chemical, and dynamical effects. Original intended application is numerical simulation of flows in rocket engines; also applicable to other complex flows affected by finite-rate chemistry - for example, flows in turbines and in internal-combustion engines.

Chen, Yen-Sen↗
NASA NTRS2003

In-Flight MTF Analysis of ADAR 5500 Aircraft Sensor

The Modulation Transfer Function (MTF) of an imaging system is one parameter that can be used to describe the spatial resolution or the image quality of an imaging system. MTF is the system's frequency response to an input. The MTF at a specific frequency normally ranges from 0-1, where 0 indicates no frequency response and 1 indicates perfect frequency response. The MTF value at Nyquist frequency is calculated because the Nyquist frequency is the maximum sampling frequency of the system. MTF analysis was performed on data acquired with an ADAR 5500 flown by Positive Systems on September 13-14, 2000 over Brookings, SD. Four edges from ground targets were used as inputs to the system. The system's MTF was calculated using a Matlab-based algorithm, which applied edge detection, numerical differentiation, and Fourier transformation methods to the target images.

Zanoni, Vicki↗
NASA NTRS1997

Aerodynamic Shape Sensitivity Analysis and Design Optimization of Complex Configurations Using Unstructured Grids

A three-dimensional unstructured grid approach to aerodynamic shape sensitivity analysis and design optimization has been developed and is extended to model geometrically complex configurations. The advantage of unstructured grids (when compared with a structured-grid approach) is their inherent ability to discretize irregularly shaped domains with greater efficiency and less effort. Hence, this approach is ideally suited for geometrically complex configurations of practical interest. In this work the nonlinear Euler equations are solved using an upwind, cell-centered, finite-volume scheme. The discrete, linearized systems which result from this scheme are solved iteratively by a preconditioned conjugate-gradient-like algorithm known as GMRES for the two-dimensional geometry and a Gauss-Seidel algorithm for the three-dimensional; similar procedures are used to solve the accompanying linear aerodynamic sensitivity equations in incremental iterative form. As shown, this particular form of the sensitivity equation makes large-scale gradient-based aerodynamic optimization possible by taking advantage of memory efficient methods to construct exact Jacobian matrix-vector products. Simple parameterization techniques are utilized for demonstrative purposes. Once the surface has been deformed, the unstructured grid is adapted by considering the mesh as a system of interconnected springs. Grid sensitivities are obtained by differentiating the surface parameterization and the grid adaptation algorithms with ADIFOR (which is an advanced automatic-differentiation software tool). To demonstrate the ability of this procedure to analyze and design complex configurations of practical interest, the sensitivity analysis and shape optimization has been performed for a two-dimensional high-lift multielement airfoil and for a three-dimensional Boeing 747-200 aircraft.

Taylor, Arthur C., III↗
NASA NTRS2015

Construction of Polarimetric Radar-Based Reference Rain Maps for the Iowa Flood Studies Campaign

The Global Precipitation Measurement (GPM) Mission Iowa Flood Studies (IFloodS) campaign was conducted in central and northeastern Iowa during the months of April-June, 2013. Specific science objectives for IFloodS included quantification of uncertainties in satellite and ground-based estimates of precipitation, 4-D characterization of precipitation physical processes and associated parameters (e.g., size distributions, water contents, types, structure etc.), assessment of the impact of precipitation estimation uncertainty and physical processes on hydrologic predictive skill, and refinement of field observations and data analysis approaches as they pertain to future GPM integrated hydrologic validation and related field studies. In addition to field campaign archival of raw and processed satellite data (including precipitation products), key ground-based platforms such as the NASA NPOL S-band and D3R Ka/Ku-band dual-polarimetric radars, University of Iowa X-band dual-polarimetric radars, a large network of paired rain gauge platforms, and a large network of 2D Video and Parsivel disdrometers were deployed. In something of a canonical approach, the radar (NPOL in particular), gauge and disdrometer observational assets were deployed to create a consistent high-quality distributed (time and space sampling) radar-based ground "reference" rainfall dataset, with known uncertainties, that could be used for assessing the satellite-based precipitation products at a range of space/time scales. Subsequently, the impact of uncertainties in the satellite products could be evaluated relative to the ground-benchmark in coupled weather, land-surface and distributed hydrologic modeling frameworks as related to flood prediction. Relative to establishing the ground-based "benchmark", numerous avenues were pursued in the making and verification of IFloodS "reference" dual-polarimetric radar-based rain maps, and this study documents the process and results as they pertain specifically to efforts using the NPOL radar dataset. The initial portions of the "process" involved dual-polarimetric quality control procedures which employed standard phase and correlation-based approaches to removal of clutter and non-meteorological echo. Calculation of a scale-adaptive KDP was accomplished using the method of Wang and Chandrasekar (2009; J. Atmos. Oceanic Tech.). A dual-polarimetric blockage algorithm based on Lang et al. (2009; J. Atmos. Oceanic Tech.) was then implemented to correct radar reflectivity and differential reflectivity at low elevation angles. Next, hydrometeor identification algorithms were run to identify liquid and ice hydrometeors. After the quality control and data preparation steps were completed several different dual-polarimetric rain estimation algorithms were employed to estimate rainfall rates using rainfall scans collected approximately every two to three minutes throughout the campaign. These algorithms included a polarimetrically-tuned Z-R algorithm that adjusts for drop oscillations (via Bringi et al., 2004, J. Atmos. Oceanic Tech.), and several different hybrid polarimetric variable approaches, including one that made use of parameters tuned to IFloodS 2D Video Disdrometer measurements. Finally, a hybrid scan algorithm was designed to merge the rain rate estimates from multiple low level elevation angle scans (where blockages could not be appropriately corrected) in order to create individual low-level rain maps. Individual rain maps at each time step were subsequently accumulated over multiple time scales for comparison to gauge network data. The comparison results and overall error character depended strongly on rain event type, polarimetric estimator applied, and range from the radar. We will present the outcome of these comparisons and their impact on constructing composited "reference" rainfall maps at select time and space scales.

Radar↗
DOE OSTI2025

Preserving nonlinear constraints in variational flow filtering data assimilation

Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems of interest obey nonlinear physical constraints, and the corresponding dynamics is confined to a certain sub-manifold of the state space. Standard data assimilation techniques applied to such systems yield posterior states lying outside the manifold, violating the physical constraints. This work focuses on particle flow filters which use stochastic differential equations to evolve state samples from a prior distribution to samples from an observation-informed posterior distribution. The variational Fokker-Planck (VFP)—a generic particle flow filtering framework—is extended to incorporate non-linear, equality state constraints in the analysis. To this end, two algorithmic approaches that modify the VFP stochastic differential equation are discussed: (i) VFPSTAB, to inexactly preserve constraints with the addition of a stabilizing drift term, and (ii) VFPDAE, to exactly preserve constraints by treating the VFP dynamics as a stochastic differential-algebraic equation (SDAE). Additionally, an implicit-explicit time integrator is developed to evolve the VFPDAE dynamics. The strength of the proposed approach for constraint preservation in data assimilation is demonstrated on three test problems: the double pendulum, Korteweg-de-Vries, and the incompressible Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

Choice of velocity variables for complex flow computation

The issue of adopting the velocity components as dependent velocity variables for the Navier-Stokes flow computations is investigated. The viewpoint advocated is that a numerical algorithm should preferably honor both the physical conservation law in differential form and the geometric conservation law in discrete form. With the use of Cartesian velocity vector, the momentum equations in curvilinear coordinates can retain the full conservation-law form and satisfy the physical conservation laws. With the curvilinear velocity components, source terms appear in differential equations and hence the full conservation law form can not be retained. In discrete expressions, algorithms based on the Cartesian components can satisfy the geometric conservation-law form for convection terms but not for viscous terms; those based on the curvilinear components, on the other hand, cannot satisfy the geometric conservation-law form for either convection or viscous terms. Several flow solutions for domain with 90 and 360 degree turnings are presented to illustrate the issues of using the Cartesian velocity components and the staggered grid arrangement.

Shyy, W.↗
NASA NTRS2000

Any Two Learning Algorithms Are (Almost) Exactly Identical

This paper shows that if one is provided with a loss function, it can be used in a natural way to specify a distance measure quantifying the similarity of any two supervised learning algorithms, even non-parametric algorithms. Intuitively, this measure gives the fraction of targets and training sets for which the expected performance of the two algorithms differs significantly. Bounds on the value of this distance are calculated for the case of binary outputs and 0-1 loss, indicating that any two learning algorithms are almost exactly identical for such scenarios. As an example, for any two algorithms A and B, even for small input spaces and training sets, for less than 2e(-50) of all targets will the difference between A's and B's generalization performance of exceed 1%. In particular, this is true if B is bagging applied to A, or boosting applied to A. These bounds can be viewed alternatively as telling us, for example, that the simple English phrase 'I expect that algorithm A will generalize from the training set with an accuracy of at least 75% on the rest of the target' conveys 20,000 bytes of information concerning the target. The paper ends by discussing some of the subtleties of extending the distance measure to give a full (non-parametric) differential geometry of the manifold of learning algorithms.

Wolpert, David H.↗
DOE OSTI2023

Quantum algorithm for the linear Vlasov equation with collisions

The Vlasov equation is a nonlinear partial differential equation that provides a first-principles description of the dynamics of plasmas. Its linear limit is routinely used in plasma physics to investigate plasma oscillations and stability. In this paper, we present a quantum algorithm that simulates the linearized Vlasov equation with and without collisions, in the one-dimensional electrostatic limit. Rather than solving this equation in its native spatial and velocity phase space, we adopt an efficient representation in the dual space yielded by a Fourier-Hermite expansion. For a given simulation time, the Fourier-Hermite representation is exponentially more compact, thus yielding a classical algorithm that can match the performance of a previously proposed quantum algorithm for this problem. Further, this representation results in a system of linear ordinary differential equations (ODEs) which can be solved with well-developed quantum algorithms: a Hamiltonian simulation in the collisionless case, and quantum ODE solvers in the collisional case. In particular, we demonstrate that a quadratic speedup in system size is attainable.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1991

Distributed Minimal Residual (DMR) method for acceleration of iterative algorithms

A new method for enhancing the convergence rate of iterative algorithms for the numerical integration of systems of partial differential equations was developed. It is termed the Distributed Minimal Residual (DMR) method and it is based on general Krylov subspace methods. The DMR method differs from the Krylov subspace methods by the fact that the iterative acceleration factors are different from equation to equation in the system. At the same time, the DMR method can be viewed as an incomplete Newton iteration method. The DMR method was applied to Euler equations of gas dynamics and incompressible Navier-Stokes equations. All numerical test cases were obtained using either explicit four stage Runge-Kutta or Euler implicit time integration. The formulation for the DMR method is general in nature and can be applied to explicit and implicit iterative algorithms for arbitrary systems of partial differential equations.

Lee, Seungsoo↗
NASA NTRS1974

Finite element solution algorithm for incompressible fluid dynamics

A finite element solution algorithm is established for the two-dimensional Navier-Stokes equations governing the transient motion of a viscous incompressible fluid, i.e., hydrodynamics. Dependent variable transformation renders the differential equation description uniformly elliptic. The finite element algorithm is established using the Galerkin criterion on a local basis within the Method of Weighted Residuals. It is unconstrained with respect to system linearity, computational mesh uniformity or solution domain closure regularity. The finite element matrices are established using a linear 'natural coordinate function' description. Computational solutions using the COMOC computer program illustrate the various features of the algorithm including recirculating flows.

Baker, A. J.↗
DOE OSTI2016

Non-gray gas radiation effect on mixed convection in lid driven square cavity

A numerical study is performed to investigate the effect of non-gray radiation on mixed convection in a vertical two sided lid driven square cavity filled with air-H{sub 2}O-CO{sub 2} gas mixture. The vertical moving walls of the enclosure are maintained at two different but uniform temperatures. The horizontal walls are thermally insulated and considered as adiabatic walls. The governing differential equations are solved by a finite-volume method and the SIMPLE algorithm was adopted to solve the pressure–velocity coupling. The radiative transfer equation (RTE) is solved by the discrete ordinates method (DOM). The spectral line weighted sum of gray gases model (SLW) is used to account for non-gray radiation properties. Simulations are performed in configurations where thermal and shear forces induce cooperating buoyancy forces. Streamlines, isotherms, and Nusselt number are analyzed for three different values of Richardson’s number (from 0.1 to 10) and by considering three different medium (transparent medium, gray medium using the Planck mean absorption coefficient, and non-gray medium assumption).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1983

Adaptive grids generated by elliptic systems

It is pointed out that a finite difference grid which moves with the solution of the partial differential equation being solved can improve the accuracy and efficiency of a numerical algorithm. This technique is particularly advantageous in the solution of problems involving boundary layers or shocks where a poorly chosen grid may give a numerical solution which is useless because of poor resolution or extreme oscillations. The present investigation is concerned with the development of a scheme which does not excessively distort the grid. The grid generation algorithm is based on the numerical solution of a system of elliptic differential equations. Holst and Brown (1981) have used a preliminary solution to move points on the boundary of the physical region and then resolved the problem on a new grid generated by an elliptic system. In the current investigation, the grid movement and the solution will develop simultaneously. The solution is used to modify the generating equations, thereby controlling the grid point distributions.

Mastin, C. W.↗
NASA NTRS1980

An interaction algorithm for prediction of mean and fluctuating velocities in two-dimensional aerodynamic wake flows

A theoretical analysis is presented yielding sets of partial differential equations for determination of turbulent aerodynamic flowfields in the vicinity of an airfoil trailing edge. A four phase interaction algorithm is derived to complete the analysis. Following input, the first computational phase is an elementary viscous corrected two dimensional potential flow solution yielding an estimate of the inviscid-flow induced pressure distribution. Phase C involves solution of the turbulent two dimensional boundary layer equations over the trailing edge, with transition to a two dimensional parabolic Navier-Stokes equation system describing the near-wake merging of the upper and lower surface boundary layers. An iteration provides refinement of the potential flow induced pressure coupling to the viscous flow solutions. The final phase is a complete two dimensional Navier-Stokes analysis of the wake flow in the vicinity of a blunt-bases airfoil. A finite element numerical algorithm is presented which is applicable to solution of all partial differential equation sets of inviscid-viscous aerodynamic interaction algorithm. Numerical results are discussed.

Baker, A. J.↗