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At least 721 records · Page 40
All sourcesNASA NTRSDOE OSTI
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.↗
NASA NTRS1992

Polarimetric signatures of a canopy of dielectric cylinders based on first and second order vector radiative transfer theory

Complete polarimetric signatures of a canopy of dielectric cylinders overlying a homogeneous half space are studied with the first and second order solutions of the vector radiative transfer theory. The vector radiative transfer equations contain a general nondiagonal extinction matrix and a phase matrix. The energy conservation issue is addressed by calculating the elements of the extinction matrix and the elements of the phase matrix in a manner that is consistent with energy conservation. Two methods are used. In the first method, the surface fields and the internal fields of the dielectric cylinder are calculated by using the fields of an infinite cylinder. The phase matrix is calculated and the extinction matrix is calculated by summing the absorption and scattering to ensure energy conservation. In the second method, the method of moments is used to calculate the elements of the extinction and phase matrices. The Mueller matrix based on the first order and second order multiple scattering solutions of the vector radiative transfer equation are calculated. Results from the two methods are compared. The vector radiative transfer equations, combined with the solution based on method of moments, obey both energy conservation and reciprocity. The polarimetric signatures, copolarized and depolarized return, degree of polarization, and phase differences are studied as a function of the orientation, sizes, and dielectric properties of the cylinders. It is shown that second order scattering is generally important for vegetation canopy at C band and can be important at L band for some cases.

Tsang, Leung↗
NASA NTRS1992

Second order closure modeling of turbulent buoyant wall plumes

Non-intrusive measurements of scalar and momentum transport in turbulent wall plumes, using a combined technique of laser Doppler anemometry and laser-induced fluorescence, has shown some interesting features not present in the free jet or plumes. First, buoyancy-generation of turbulence is shown to be important throughout the flow field. Combined with low-Reynolds-number turbulence and near-wall effect, this may raise the anisotropic turbulence structure beyond the prediction of eddy-viscosity models. Second, the transverse scalar fluxes do not correspond only to the mean scalar gradients, as would be expected from gradient-diffusion modeling. Third, higher-order velocity-scalar correlations which describe turbulent transport phenomena could not be predicted using simple turbulence models. A second-order closure simulation of turbulent adiabatic wall plumes, taking into account the recent progress in scalar transport, near-wall effect and buoyancy, is reported in the current study to compare with the non-intrusive measurements. In spite of the small velocity scale of the wall plumes, the results showed that low-Reynolds-number correction is not critically important to predict the adiabatic cases tested and cannot be applied beyond the maximum velocity location. The mean and turbulent velocity profiles are very closely predicted by the second-order closure models. but the scalar field is less satisfactory, with the scalar fluctuation level underpredicted. Strong intermittency of the low-Reynolds-number flow field is suspected of these discrepancies. The trends in second- and third-order velocity-scalar correlations, which describe turbulent transport phenomena, are also predicted in general, with the cross-streamwise correlations better than the streamwise one. Buoyancy terms modeling the pressure-correlation are shown to improve the prediction slightly. The effects of equilibrium time-scale ratio and boundary condition are also discussed.

Zhu, Gang↗
NASA NTRS1990

Navier-Stokes computation of compressible turbulent flows with a second order closure, part 1

A second order closure turbulence model for compressible flows is developed and implemented in a 2D Reynolds-averaged Navier-Stokes solver. From the beginning where a kappa-epsilon turbulence model was implemented in the bidiagonal implicit method of MACCORMACK (referred to as the MAC3 code) to the final stage of implementing a full second order closure in the efficient line Gauss-Seidel algorithm, numerous work was done, individually and collectively. Besides the collaboration itself, the final product of this work is a second order closure derived from the Launder, Reece, and Rodi model to account for near wall effects, which has been called FRAME model, which stands for FRench-AMerican-Effort. During the reporting period, two different problems were worked out. The first was to provide Ames researchers with a reliable compressible boundary layer code including a wide collection of turbulence models for quick testing of new terms, both in two equations and in second order closure (LRR and FRAME). The second topic was to complete the implementation of the FRAME model in the MAC5 code. The work related to these two different contributions is reported. dilatation in presence of stron shocks. This work, which has been conducted during a work at the Center for Turbulence Research with Zeman aimed also to cros-check earlier assumptions by Rubesin and Vandromme.

Haminh, Hieu↗
NASA NTRS1992

Protostellar hydrodynamics: Constructing and testing a spatially and temporally second-order-accurate method. I - Spherical coordinates

Two related numerical schemes for calculating the 3D collapse of protostellar clouds are defined, developed, and checked on a wide variety of test problems in spherical symmetry and multiple dimensions. One scheme is first-order accurate in time (code S), and the other second-order accurate in time (code ST). Through convergence testing, the codes are shown to be second-order accurate in spatial differences. Compared with the previous 3D code, the combination of reduced numerical dissipation through second-order accuracy and of removing the systematic bias toward central concentrations implies that the tendency for fragmentation into binary or multiple protostars should increase. A reinvestigation of fragmentation as a mechanism for forming binary stars is expected to yield an even more favorable evaluation.

Boss, Alan P.↗