SEARCH · Engineering Papers

Results for “order”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 721 records · Page 40

All sources NASA NTRS DOE OSTI

NASA NTRS1985

A fourth-order scheme for the unsteady compressible Navier-Stokes equations

A computational scheme is described which is second-order accurate in time and fourth-order accurate in space (2-4). This method is applied to study the stability of compressible boundary layers. The laminar compressible Navier-Stokes equations are solved with a time harmonic inflow superimposed on the steady state solution. This results in spatially unstable modes. It is shown that the second-order methods are inefficient for calculating the growth rates and phases of the unstable modes. In contrast the fourth-order method yields accurate results on relatively course meshes.

Bayliss, A.↗

NASA NTRS1986

Uniformly high order accurate essentially non-oscillatory schemes 3

In this paper (a third in a series) the construction and the analysis of essentially non-oscillatory shock capturing methods for the approximation of hyperbolic conservation laws are presented. Also presented is a hierarchy of high order accurate schemes which generalizes Godunov's scheme and its second order accurate MUSCL extension to arbitrary order of accuracy. The design involves an essentially non-oscillatory piecewise polynomial reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell. The reconstruction algorithm is derived from a new interpolation technique that when applied to piecewise smooth data gives high-order accuracy whenever the function is smooth but avoids a Gibbs phenomenon at discontinuities. Unlike standard finite difference methods this procedure uses an adaptive stencil of grid points and consequently the resulting schemes are highly nonlinear.

Harten, A.↗

NASA NTRS1986

Higher-order structure of rRNA

A comparative search for phylogenetically covarying basepair replacements within potential helices has been the only reliable method to determine the correct secondary structure of the 3 rRNAs, 5S, 16S, and 23S. The analysis of 16S from a wide phylogenetic spectrum, that includes various branches of the eubacteria, archaebacteria, eucaryotes, in addition to the mitochondria and chloroplast, is beginning to reveal the constraints on the secondary structures of these rRNAs. Based on the success of this analysis, and the assumption that higher order structure will also be phylogenetically conserved, a comparative search was initiated for positions that show co-variation not involved in secondary structure helices. From a list of potential higher order interactions within 16S rRNA, two higher-order interactions are presented. The first of these interactions involves positions 570 and 866. Based on the extent of phylogenetic covariation between these positions while maintaining Watson-Crick pairing, this higher-order interaction is considered proven. The other interaction involves a minimum of six positions between the 1400 and 1500 regions of the 16S rRNA. Although these patterns of covariation are not as striking as the 570/866 interaction, the fact that they all exist in an anti-parallel fashion and that experimental methods previously implicated these two regions of the molecule in tRNA function suggests that these interactions be given serious consideration.

Gutell, R. R.↗

NASA NTRS1987

Navier-Stokes simulations of blade-vortex interaction using high-order accurate upwind schemes

Conventional, spatially second-order-accurate, finite-difference schemes are much too dissipative for calculations involving vortices that travel large distances (relative to some measure of the size of the vortex). This study presents a fifth-order-accurate upwind-biased scheme that preserves vortex structure for much longer times than existing second-order-accurate central and upwind difference schemes. Vortex calculations demonstrating this aspect of the fifth-order scheme are also presented. The method is then applied to the blade-vortex interaction problem. Results for strong interactions wherein the vortex impinges directly on the airfoil or a shock associated with the airfoil are presented. None of these calculations required any modeling of the shape, size, and trajectory of the interacting vortex.

Rai, Man Mohan↗

NASA NTRS1988

Compact high order schemes for the Euler equations

An implicit approximate factorization (AF) algorithm is constructed which has the following characteistics. In 2-D: The scheme is unconditionally stable, has a 3 x 3 stencil and at steady state has a fourth order spatial accuracy. The temporal evolution is time accurate either to first or second order through choice of parameter. In 3-D: The scheme has almost the same properties as in 2-D except that it is now only conditionally stable, with the stability condition (the CFL number) being dependent on the cell aspect ratios, delta y/delta x and delta z/delta x. The stencil is still compact and fourth order accuracy at steady state is maintained. Numerical experiments on a 2-D shock-reflection problem show the expected improvement over lower order schemes, not only in accuracy (measured by the L sub 2 error) but also in the dispersion. It is also shown how the same technique is immediately extendable to Runge-Kutta type schemes resulting in improved stability in addition to the enhanced accuracy.

Abarbanel, Saul↗

NASA NTRS1988

Electron Diffraction Evidence for the Ordering of Excess Nickel Atoms by Relation to Stoichiometry in Nickel-Rich Beta'-Nial Formation of a Nickel-Aluminum (Ni2al) Superlattices

In electron diffraction patterns of nickel-rich beta-NiAl alloys, many anomalies are observed. One of these is the appearance of diffuse intensity maxima between the reflexions of the B2 structure. This is explained by the short-range ordering of the excess nickel atoms on the simple cubic sublattice occupied only by aluminum atoms in the stoichiometric, perfectly ordered NiAl alloy. After annealing Ni 37.5 atomic percent Al and Ni 37.75 atomic percent Al for 1 week at 300 and 400 C, the diffuse intensity maxima transformed into sharp superstructure reflexions. These reflexions are explained by the formation of the four possible variants of an ordered hexagonal superstructure corresponding to the Ni2Al composition. This structure is closely related to the Ni2Al3 structure (same space group) formed by the ordering of vacancies on the nickel sublattice in aluminum-rich beta-NiAl alloys.

Reynaud, F.↗

NASA NTRS1988

A new class of natural magnetic materials - The ordering alloys

It is shown that tetrataenite (approximately FeNi), found in many meteorites, and Josephinite (approximately FeNi3), found in many serpentinized peridotites and possibly in Allende, are atomically ordered alloys. Data are presented, showing magnetic hysteresis loops, coercivity-temperature behavior at cryogenic temperatures, and thermomagnetic curves, that show that these ordered magnetic materials have unique magnetic properties and do not fit the conventional rock magnetism paradigms represented by Fe3O4 serpentinites. The ordered state is characterized by induced magnetic anisotropy, reaching the extreme for the tetragonal truly uniaxial anisotropy in FeNi. It is suggested that these ordered magnetic alloys should be considered a new class of natural magnetic materials.

Wasilewski, Peter↗

NASA NTRS1988

An approximation technique for computing optimal fixed-order controllers for infinite-dimensional systems

The finite-dimensional approximation of the infinite-dimensional Bernstein/Hyland optimal projection theory is investigated analytically. The approach yields fixed-finite-order controllers which are optimal with respect to high-order approximating finite-dimensional plant models. The technique is illustrated by computing a sequence of first-order controllers for a one-dimensional SISO parabolic (heat/diffusion) system using a spline-based Ritz-Galerkin finite-element approximation. The numerical studies indicate convergence of the feedback gains with less than 2-percent performance degradation over full-order LQG controllers.

Bernstein, Dennis S.↗

NASA NTRS1989

Orthogonal canonical forms for second-order systems

The authors prove that a linear second-order system with arbitrary damping cannot be reduced to Hessenberg-triangular form by means of orthogonal transformations, while this reduction is always possible for the modal damping commonly assumed for models of flexible structures. The type of canonical form obtainable by means of orthogonal transformations acting on a second-order system is heavily dependent on the type of damping considered. If the damping matrix is merely positive semi-definite symmetric, it is generally not possible to obtain a reduction to Hessenberg-triangular form, while this reduction is trivial for zero or Rayleigh damping. If damping is modal, however, as is commonly assumed in structural models, the reduction exists and is nontrivial. Furthermore, reduction to triangular second-order Schur form is always possible for such damping: this canonical form appears likely to have applications to second-order system theory.

Williams, Trevor↗

NASA NTRS1989

Minimum-variance reduced-order estimation algorithms from Pontrygin's minimum principle

A uniform derivation of minimum-variance reduced-order (MVRO) filter-smoother algorithms from Pontrygin's Minimum Principle is presented. An appropriate performance index for a general class of reduced order estimation problem is formulated herein to yield optimal results over the entire time interval of estimation. These results provide quantitative criteria for measuring the performance of certain classes of heuristically designed, suboptimal reduced-order estimators as well as explicit guidance to the suboptimal filter design process with both continuous and discrete filter-smoother algorithms being considered. By the duality principle, the algorithms of reduced-order estimation can be easily extended to the deterministic problems of optimal control (i.e., the regulator and linear tracking problem).

Ebrahimi, Yaghoob S.↗

NASA NTRS1989

A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations

A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.

Ho, Lee-Wing↗

NASA NTRS1989

Part A: Nonprincipal-plane scattering from flat plates: Second-order and corner diffractions

Two models of a flat plate for nonprincipal-plane scattering are explored. The first is a revised version of the Physical Optics/Physical Theory of Diffraction (PO/PTD) model with second-order PTD equivalent currents included to account for second-order interactions among the plate edges. The second model uses a heurisitcally derived corner diffraction coefficient to account for the corner scattering mechanism. The patterns obtained using the newer models were compared to the data of previously reported models, the Moment Method (MM), and experimental results. Near normal incidence, all the models agreed; however, near grazing incidence a need for higher-order and corner diffraction mechanisms was noted. In many instances the second-order and corner-scattered fields which were formulated improved the results.

Balanis, Constantine A.↗

NASA NTRS1989

Multivariable frequency weighted model order reduction for control synthesis

Quantitative criteria are presented for model simplification, or order reduction, such that the reduced order model may be used to synthesize and evaluate a control law, and the stability robustness obtained using the reduced order model will be preserved when controlling the full-order system. The error introduced due to model simplification is treated as modeling uncertainty, and some of the results from multivariate robustness theory are brought to bear on the model simplification problem. A numerical procedure developed previously is shown to lead to results that meet the necessary criteria. The procedure is applied to reduce the model of a flexible aircraft. Also, the importance of the control law itself, in meeting the modeling criteria, is underscored. An example is included that demonstrates that an apparently robust control law actually amplifies modest modeling errors in the critical frequency region, and leads to undesirable results. The cause of this problem is associated with the canceling of lightly damped transmission zeroes in the plant. An attempt is made to expand on some of the earlier results and to further clarify the theoretical basis behind the proposed methodology.

Schmidt, David K.↗

NASA NTRS1990

TE scattering by a two-dimensional groove in a ground plane using higher order boundary conditions

Higher order boundary conditions involve derivatives of the fields beyond the first and were recently shown to be more effective than traditional first order conditions in modeling dielectric coatings and layers. In this report an application of a third order generalized boundary condition to scattering by a filled rectangular groove is presented. Deficiencies of such higher-order boundary conditions are addressed and a correction is proposed for the present case. As part of the process of examining and correcting the accuracy of the proposed generalized boundary conditions, an exact solution is developed and a comparison is provided with a solution based on the standard impedance boundary condition.

Barkeshli, Kasra↗

NASA NTRS1991

Bond-orientational order in liquid Si

Bond-orientational order in liquid Si via Monte Carlo simulation in conjuncation with empirical two- and three-body potentials of the form proposed by Stillinger and Weber are studied. Bond-orientational order (BOO) is described in terms of combinations of spherical harmonic functions. Liquid Si is found to have pronounced short-range BOO corresponding to l = 3, as expected for a structure with local tetrahedral order. No long-range BOO is found either in the equilibrium or the supercooled liquid. When the three-body potential is artificially removed, the tetrahedral bond-orientation order disappears and the liquid assumes a close-packed structure.

Wang, Z. Q.↗

NASA NTRS1991

Design of optimal second-order state estimators

The present consideration of the design of online computation-saving second-order state estimators for second-order vector-matrix differential systems proposes a class of such estimators which is proven to possess guaranteed convergence. A class of optimal second-order estimators is then obtained, and the conditions required for optimality are identified. The estimator proposed offers high performance in conjunction with online computation reductions sufficiently great to allow the estimation of the large number of state variables associated with control of large, flexible space structures represented by high-dimensional second-order systems.

Joshi, Suresh M.↗

NASA NTRS1991

Higher-order neural network software for distortion invariant object recognition

The state-of-the-art in pattern recognition for such applications as automatic target recognition and industrial robotic vision relies on digital image processing. We present a higher-order neural network model and software which performs the complete feature extraction-pattern classification paradigm required for automatic pattern recognition. Using a third-order neural network, we demonstrate complete, 100 percent accurate invariance to distortions of scale, position, and in-plate rotation. In a higher-order neural network, feature extraction is built into the network, and does not have to be learned. Only the relatively simple classification step must be learned. This is key to achieving very rapid training. The training set is much smaller than with standard neural network software because the higher-order network only has to be shown one view of each object to be learned, not every possible view. The software and graphical user interface run on any Sun workstation. Results of the use of the neural software in autonomous robotic vision systems are presented. Such a system could have extensive application in robotic manufacturing.

Reid, Max B.↗

NASA NTRS1992

A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow

High order essentially non-oscillatory (ENO) schemes, originally designed for compressible flow and in general for hyperbolic conservation laws, are applied to incompressible Euler and Navier-Stokes equations with periodic boundary conditions. The projection to divergence-free velocity fields is achieved by fourth order central differences through Fast Fourier Transforms (FFT) and a mild high-order filtering. The objective of this work is to assess the resolution of ENO schemes for large scale features of the flow when a coarse grid is used and small scale features of the flow, such as shears and roll-ups, are not fully resolved. It is found that high-order ENO schemes remain stable under such situations and quantities related to large-scale features, such as the total circulation around the roll-up region, are adequately resolved.

Weinan, E.↗