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 235 records · Page 13

All sources NASA NTRS DOE OSTI

NASA NTRS1993

Order-sorting filter transmittance measured with an array detector

The simultaneous measurement of the spectrally and spatially variant transmittance of a linear variable order-sorting filter in a manner that closely resembles its conditions of actual use is described. The transmittance of a prototype order-sorting filter was measured in the 400- to 880-nm wavelength region by illuminating it with the output beam of a spectrophotometer while the filter was attached to the front of a 30 x 32 pixel silicon array detector. The filter was designed to be used in the output beam of a grating spectrometer to prevent the dispersal of higher diffracted orders onto an array detector. Areas of the filter that were spatially matched to the corresponding detector pixel column had measured peak transmittances of about 90 percent that were uniform to within +/- 1.5 percent along a given column. Transmittances for incident wavelengths shorter than the desired bandpass, corresponding to the order overlap region, were measured in the 0.003 range. Line spread function measurements made with the array detector indicated no significant beam spreading caused by inserting the filter into the beam.

Heaney, James B.↗

NASA NTRS1993

High order accurate solutions of viscous problems

We consider a fourth order extension to MacCormack's scheme. The original extension was fourth order only for the inviscid terms but was second order for the viscous terms. We show how to modify the viscous terms so that the scheme is uniformly fourth order in the spatial derivatives. Applications are given to some boundary layer flows. In addition, for applications to shear flows the effect of the outflow boundary conditions are very important. We compare the accuracy of several of these different boundary conditions for both boundary layer and shear flows. Stretching at the outflow usually increases the oscillations in the numerical solution but the addition of a filtered sponge layer (with or without stretching) reduces such oscillations. The oscillations are generated by insufficient resolution of the shear layer. When the shear layer is sufficiently resolved then oscillations are not generated and there is less of a need for a nonreflecting boundary condition.

Hayder, M. Ehtesham↗

NASA NTRS1993

Ordered organic thin films self-assembled from the vapor phase

Organic films self-assembled from a liquid phase, as in Langmuir-Blodgett or adsorption from solution, have received much attention in the past decade as techniques to achieve highly oriented-ordered polymeric thin films. Many organic compounds including some of the same fatty acids have been vapor deposited as well. However, organic pigments and dyes comprise a major class of important materials which have very low solubilities yet excellent thermal stabilities, making them ideally suited for film deposition from the vapor phase. Surprisingly, such molecular systems exhibit a significant propensity to self order, a high sensitivity to deposition parameters, and a range of microstructural forms that cannot be duplicated by the less energetic mechanisms associated with solution adsorption processes. Molecular solids such as heterocyclic polynuclear aromatics are excellent candidates for film formation by vacuum deposition means. Over the past decade, our work and that of others investigating a wide variety of perylene and phthalocyanine derivatives identified five deposition parameters that can significantly affect film morphology, physical microstructure, and type and extent of ordering developed in vacuum and vapor transport grown films. These parameters are substrate temperature, deposition rate, substrate chemistry and epitaxy, ambient gas convective flows, and post deposition annealing. Examples of how each of these conditions manifest themselves in the film structure and ordering, most frequently revealed by scanning electron microscopy, reflection absorption infrared spectroscopy (RAIR), and grazing incidence x-ray diffraction (GIX), are presented.

Debe, M. K.↗

NASA NTRS1994

Weighted graph based ordering techniques for preconditioned conjugate gradient methods

We describe the basis of a matrix ordering heuristic for improving the incomplete factorization used in preconditioned conjugate gradient techniques applied to anisotropic PDE's. Several new matrix ordering techniques, derived from well-known algorithms in combinatorial graph theory, which attempt to implement this heuristic, are described. These ordering techniques are tested against a number of matrices arising from linear anisotropic PDE's, and compared with other matrix ordering techniques. A variation of RCM is shown to generally improve the quality of incomplete factorization preconditioners.

Clift, Simon S.↗

NASA NTRS1994

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 NTRS1994

Effects of spatial order of accuracy on the computation of vortical flowfields

The objective of the present investigation is to assess the effect of the spatial order of accuracy used for the evaluation of the inviscid fluxes on the resolution of higher order quantitites, such as velocity gradients. The viscous terms are computed as second-order accurate with central difference formulas, even though for the explicit part of the algorithm higher order approximations may be used. A viscous/inviscid method is used, and the outer part of the flowfield is computed with the inviscid flow equations. The viscous boundary-layer type flow region close to the body surface is computed with an algebraic eddy viscosity model. Results obtained with the conservative and nonconservative formulations and the viscous/inviscid approach are compared with available experimental data. The effect of grid refinement on the accuracy of the solution is also presented.

Ekaterinaris, J. A.↗

NASA NTRS1996

Chaos in a Fractional Order Chua System

This report studies the effects of fractional dynamics in chaotic systems. In particular, Chua's system is modified to include fractional order elements. Varying the total system order incrementally from 2.6 to 3.7 demonstrates that systems of 'order' less than three can exhibit chaos as well as other nonlinear behavior. This effectively forces a clarification of the definition of order which can no longer be considered only by the total number of differentiations or by the highest power of the Laplace variable.

Lorenzo, Carl F.↗

NASA NTRS1998

Algorithms for Efficient Computation of Transfer Functions for Large Order Flexible Systems

An efficient and robust computational scheme is given for the calculation of the frequency response function of a large order, flexible system implemented with a linear, time invariant control system. Advantage is taken of the highly structured sparsity of the system matrix of the plant based on a model of the structure using normal mode coordinates. The computational time per frequency point of the new computational scheme is a linear function of system size, a significant improvement over traditional, still-matrix techniques whose computational times per frequency point range from quadratic to cubic functions of system size. This permits the practical frequency domain analysis of systems of much larger order than by traditional, full-matrix techniques. Formulations are given for both open- and closed-loop systems. Numerical examples are presented showing the advantages of the present formulation over traditional approaches, both in speed and in accuracy. Using a model with 703 structural modes, the present method was up to two orders of magnitude faster than a traditional method. The present method generally showed good to excellent accuracy throughout the range of test frequencies, while traditional methods gave adequate accuracy for lower frequencies, but generally deteriorated in performance at higher frequencies with worst case errors being many orders of magnitude times the correct values.

Maghami, Peiman G.↗

NASA NTRS1998

Performance of Low Dissipative High Order Shock-Capturing Schemes for Shock-Turbulence Interactions

Accurate and efficient direct numerical simulation of turbulence in the presence of shock waves represents a significant challenge for numerical methods. The objective of this paper is to evaluate the performance of high order compact and non-compact central spatial differencing employing total variation diminishing (TVD) shock-capturing dissipations as characteristic based filters for two model problems combining shock wave and shear layer phenomena. A vortex pairing model evaluates the ability of the schemes to cope with shear layer instability and eddy shock waves, while a shock wave impingement on a spatially-evolving mixing layer model studies the accuracy of computation of vortices passing through a sequence of shock and expansion waves. A drastic increase in accuracy is observed if a suitable artificial compression formulation is applied to the TVD dissipations. With this modification to the filter step the fourth-order non-compact scheme shows improved results in comparison to second-order methods, while retaining the good shock resolution of the basic TVD scheme. For this characteristic based filter approach, however, the benefits of compact schemes or schemes with higher than fourth order are not sufficient to justify the higher complexity near the boundary and/or the additional computational cost.

Sandham, N. D.↗

NASA NTRS1998

Performance of Low Dissipative High Order Shock-Capturing Schemes for Shock-Turbulence Interactions

Abstract Accurate and efficient direct numerical simulation of turbulence in the presence of shock waves represents a significant challenge for numerical methods. The objective of this paper is to evaluate the performance of high order compact and non-compact central spatial differencing employing total variation diminishing (TVD) shock-capturing dissipations as characteristic based filters for two model problems combining shock wave and shear layer phenomena. A vortex pairing model evaluates the ability of the schemes to cope with shear layer instability and eddy shock waves, while a shock wave impingement on a spatially-evolving mixing layer model studies the accuracy of computation of vortices passing through a sequence of shock and expansion waves. A drastic increase in accuracy is observed if a suitable artificial compression formulation is applied to the TVD dissipations. With this modification to the filter step the fourth-order non-compact scheme shows improved results in comparison to second-order methods, while retaining the good shock resolution of the basic TVD scheme. For this characteristic based filter approach, however, the benefits of compact schemes or schemes with higher than fourth order are not sufficient to justify the higher complexity near the boundary and/or the additional computational cost.

Sandham, N. D.↗

NASA NTRS1998

A {3,2}-Order Bending Theory for Laminated Composite and Sandwich Beams

A higher-order bending theory is derived for laminated composite and sandwich beams thus extending the recent {1,2}-order theory to include third-order axial effect without introducing additional kinematic variables. The present theory is of order {3,2} and includes both transverse shear and transverse normal deformations. A closed-form solution to the cylindrical bending problem is derived and compared with the corresponding exact elasticity solution. The numerical comparisons are focused on the most challenging material systems and beam aspect ratios which include moderate-to-thick unsymmetric composite and sandwich laminates. Advantages and limitations of the theory are discussed.

Cook, Geoffrey M.↗

NASA NTRS1979

Finite-field Calculations of Molecular Polarizabilities Using Field-Induced Polarization Functions: Second- and Third-order Perturbation Correlation Corrections to the Coupled Hartree-Fock Polarizability of H2O

Ordinary Rayleigh-Schroudinger perturbation theory with Moller-Plesset (RSMP) partitioning is used to calculate second- and third-order correlation corrections to the CHF polarizability and dipole moment of the water molecule by a finite-field procedure. Pade approximants are found to be useful in accelerating the convergence of the property perturbation expansions. Field-induced polarization functions suitable for polarizability calculations are determined. The average polarizability calculated, neglecting vibrational averaging, with Dunning's (9s5p/4s-4s2p/2s) contracted GTO basis set augmented by field-induced lslp2d/lp polarization functions is within 3 per cent of the experimental result. Correlation corrections to the dipole moment and polarizability of the water molecule calculated by the finite-field RSMP and single + double excitation CI(SDCI) methods for the same basis set are found to be in close agreement. The RSMP approach has the advantages of being size-consistent and of being capable of greater efficiency than the SCDI method. Comparative calculations carried out using Epstein-Nesbet partitioning show that through third order RSEN correlation perturbation expansions for the dipole moment and polarizability are less rapidly convergent than RSMP expansions. However, reasonable accord with RSMP results can be achieved by using Pade approximants to accelerate the convergence of RSEN energy perturbation expansions. The convergence of RSMP property correlation expansions based on the zeroth-order uncoupled-Hartree-Fock (UCHF) and coupled-Hartree-Fock (CHF) approximations are compared through third order. Whereas the CHF + RSMP expansions are for practical purposes fully converged, the UCHF + RSMP expansions are not adequately converged.

Langhoff, S. R.↗

NASA NTRS1999

Fractional System Identification: An Approach Using Continuous Order-Distributions

This paper discusses the identification of fractional- and integer-order systems using the concept of continuous order-distribution. Based on the ability to define systems using continuous order-distributions, it is shown that frequency domain system identification can be performed using least squares techniques after discretizing the order-distribution.

Hartley, Tom T.↗

NASA NTRS2000

A Very High Order, Adaptable MESA Implementation for Aeroacoustic Computations

Since computational efficiency and wave resolution scale with accuracy, the ideal would be infinitely high accuracy for problems with widely varying wavelength scales. Currently, many of the computational aeroacoustics methods are limited to 4th order accurate Runge-Kutta methods in time which limits their resolution and efficiency. However, a new procedure for implementing the Modified Expansion Solution Approximation (MESA) schemes, based upon Hermitian divided differences, is presented which extends the effective accuracy of the MESA schemes to 57th order in space and time when using 128 bit floating point precision. This new approach has the advantages of reducing round-off error, being easy to program. and is more computationally efficient when compared to previous approaches. Its accuracy is limited only by the floating point hardware. The advantages of this new approach are demonstrated by solving the linearized Euler equations in an open bi-periodic domain. A 500th order MESA scheme can now be created in seconds, making these schemes ideally suited for the next generation of high performance 256-bit (double quadruple) or higher precision computers. This ease of creation makes it possible to adapt the algorithm to the mesh in time instead of its converse: this is ideal for resolving varying wavelength scales which occur in noise generation simulations. And finally, the sources of round-off error which effect the very high order methods are examined and remedies provided that effectively increase the accuracy of the MESA schemes while using current computer technology.

Dydson, Roger W.↗

NASA NTRS2000

Parallel Conjugate Gradient: Effects of Ordering Strategies, Programming Paradigms, and Architectural Platforms

The Conjugate Gradient (CG) algorithm is perhaps the best-known iterative technique to solve sparse linear systems that are symmetric and positive definite. A sparse matrix-vector multiply (SPMV) usually accounts for most of the floating-point operations within a CG iteration. In this paper, we investigate the effects of various ordering and partitioning strategies on the performance of parallel CG and SPMV using different programming paradigms and architectures. Results show that for this class of applications, ordering significantly improves overall performance, that cache reuse may be more important than reducing communication, and that it is possible to achieve message passing performance using shared memory constructs through careful data ordering and distribution. However, a multi-threaded implementation of CG on the Tera MTA does not require special ordering or partitioning to obtain high efficiency and scalability.

Oliker, Leonid↗

NASA NTRS2000

An Automated Approach to Very High Order Aeroacoustic Computations in Complex Geometries

Computational aeroacoustics requires efficient, high-resolution simulation tools. And for smooth problems, this is best accomplished with very high order in space and time methods on small stencils. But the complexity of highly accurate numerical methods can inhibit their practical application, especially in irregular geometries. This complexity is reduced by using a special form of Hermite divided-difference spatial interpolation on Cartesian grids, and a Cauchy-Kowalewslci recursion procedure for time advancement. In addition, a stencil constraint tree reduces the complexity of interpolating grid points that are located near wall boundaries. These procedures are used to automatically develop and implement very high order methods (>15) for solving the linearized Euler equations that can achieve less than one grid point per wavelength resolution away from boundaries by including spatial derivatives of the primitive variables at each grid point. The accuracy of stable surface treatments is currently limited to 11th order for grid aligned boundaries and to 2nd order for irregular boundaries.

Dyson, Rodger W.↗

NASA NTRS2001

Automated Approach to Very High-Order Aeroacoustic Computations

Computational aeroacoustics requires efficient, high-resolution simulation tools. For smooth problems, this is best accomplished with very high-order in space and time methods on small stencils. However, the complexity of highly accurate numerical methods can inhibit their practical application, especially in irregular geometries. This complexity is reduced by using a special form of Hermite divided-difference spatial interpolation on Cartesian grids, and a Cauchy-Kowalewski recursion procedure for time advancement. In addition, a stencil constraint tree reduces the complexity of interpolating grid points that am located near wall boundaries. These procedures are used to develop automatically and to implement very high-order methods (> 15) for solving the linearized Euler equations that can achieve less than one grid point per wavelength resolution away from boundaries by including spatial derivatives of the primitive variables at each grid point. The accuracy of stable surface treatments is currently limited to 11th order for grid aligned boundaries and to 2nd order for irregular boundaries.

Dyson, Rodger W.↗

NASA NTRS2001

Reduced-Order Modeling: Cooperative Research and Development at the NASA Langley Research Center

Cooperative research and development activities at the NASA Langley Research Center (LaRC) involving reduced-order modeling (ROM) techniques are presented. Emphasis is given to reduced-order methods and analyses based on Volterra series representations, although some recent results using Proper Orthogonal Deco in position (POD) are discussed as well. Results are reported for a variety of computational and experimental nonlinear systems to provide clear examples of the use of reduced-order models, particularly within the field of computational aeroelasticity. The need for and the relative performance (speed, accuracy, and robustness) of reduced-order modeling strategies is documented. The development of unsteady aerodynamic state-space models directly from computational fluid dynamics analyses is presented in addition to analytical and experimental identifications of Volterra kernels. Finally, future directions for this research activity are summarized.

Silva, Walter A.↗