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NASA NTRS1992

An efficient solution procedure for the thermoelastic analysis of truss space structures

A solution procedure is proposed for the thermal and thermoelastic analysis of truss space structures in periodic motion. In this method, the spatial domain is first descretized using a consistent finite element formulation. Then the resulting semi-discrete equations in time are solved analytically by using Fourier decomposition. Geometrical symmetry is taken advantage of completely. An algorithm is presented for the calculation of heat flux distribution. The method is demonstrated via a numerical example of a cylindrically shaped space structure.

Givoli, D.↗

NASA NTRS1998

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

Several stabilized demoralization procedures for conservation law equations on triangulated domains will be considered. Specifically, numerical schemes based on upwind finite volume, fluctuation splitting, Galerkin least-squares, and space discontinuous Galerkin demoralization will be considered in detail. A standard energy analysis for several of these methods will be given via entropy symmetrization. Next, we will present some relatively new theoretical results concerning congruence relationships for left or right symmetrized equations. These results suggest new variants of existing FV, DG, GLS, and FS methods which are computationally more efficient while retaining the pleasant theoretical properties achieved by entropy symmetrization. In addition, the task of Jacobean linearization of these schemes for use in Newton's method is greatly simplified owing to exploitation of exact symmetries which exist in the system. The FV, FS and DG schemes also permit discrete maximum principle analysis and enforcement which greatly adds to the robustness of the methods. Discrete maximum principle theory will be presented for general finite volume approximations on unstructured meshes. Next, we consider embedding these nonlinear space discretizations into exact and inexact Newton solvers which are preconditioned using a nonoverlapping (Schur complement) domain decomposition technique. Elements of nonoverlapping domain decomposition for elliptic problems will be reviewed followed by the present extension to hyperbolic and elliptic-hyperbolic problems. Other issues of practical relevance such the meshing of geometries, code implementation, turbulence modeling, global convergence, etc, will. be addressed as needed.

Barth, Timothy J.↗

NASA NTRS1977

Photoabsorption in formaldehyde

Theoretical studies of the vertical electronic dipole excitation and ionization spectra in molecular formaldehyde are reported. The investigations relied on configuration-interaction calculations and moment-theory techniques. A double-zeta basis of contracted Gaussian-lobe functions supplemented with appropriate polarization and bond functions was used to construct Fock spectra in C(2 nu) symmetry for certain states near the ground state equilibrium geometry. The ionization energies, discrete vertical transition frequencies, and oscillator strengths for occupied and vertical Fock orbitals are in general accord with experimental determinations and other theoretical calculations. Stieltjes and Chebyshev vertical electronic photoionization profiles were calculated and found to be in good agreement with appropriately averaged photoionization-mass spectrometric measurements of the cross section for parent H2CO(+) ion production.

Langhoff, P. W.↗

NASA NTRS2014

A Multiscale Progressive Failure Modeling Methodology for Composites that Includes Fiber Strength Stochastics

A multiscale modeling methodology was developed for continuous fiber composites that incorporates a statistical distribution of fiber strengths into coupled multiscale micromechanics/finite element (FE) analyses. A modified two-parameter Weibull cumulative distribution function, which accounts for the effect of fiber length on the probability of failure, was used to characterize the statistical distribution of fiber strengths. A parametric study using the NASA Micromechanics Analysis Code with the Generalized Method of Cells (MAC/GMC) was performed to assess the effect of variable fiber strengths on local composite failure within a repeating unit cell (RUC) and subsequent global failure. The NASA code FEAMAC and the ABAQUS finite element solver were used to analyze the progressive failure of a unidirectional SCS-6/TIMETAL 21S metal matrix composite tensile dogbone specimen at 650 degC. Multiscale progressive failure analyses were performed to quantify the effect of spatially varying fiber strengths on the RUC-averaged and global stress-strain responses and failure. The ultimate composite strengths and distribution of failure locations (predominately within the gage section) reasonably matched the experimentally observed failure behavior. The predicted composite failure behavior suggests that use of macroscale models that exploit global geometric symmetries are inappropriate for cases where the actual distribution of local fiber strengths displays no such symmetries. This issue has not received much attention in the literature. Moreover, the model discretization at a specific length scale can have a profound effect on the computational costs associated with multiscale simulations.models that yield accurate yet tractable results.

Generalized Method of Cells↗

NASA NTRS1993

Use of switched capacitor filters to implement the discrete wavelet transform

This paper analyzes the use of IIR switched capacitor filters to implement the discrete wavelet transform and the inverse transform, using quadrature mirror filters (QMF) which have the necessary symmetry for reconstruction of the data. This is done by examining the sensitivity of the QMF transforms to the manufacturing variance in the desired capacitances. The performance is evaluated at the outputs of the separate filter stages and the error in the reconstruction of the inverse transform is compared with the desired results.

Kaiser, Kraig E.↗

NASA NTRS2003

Fragmentation under the Scaling Symmetry and Turbulent Cascade with Intermittency

Fragmentation plays an important role in a variety of physical, chemical, and geological processes. Examples include atomization in sprays, crushing of rocks, explosion and impact of solids, polymer degradation, etc. Although each individual action of fragmentation is a complex process, the number of these elementary actions is large. It is natural to abstract a simple 'effective' scenario of fragmentation and to represent its essential features. One of the models is the fragmentation under the scaling symmetry: each breakup action reduces the typical length of fragments, r (right arrow) alpha r, by an independent random multiplier alpha (0 < alpha < 1), which is governed by the fragmentation intensity spectrum q(alpha), integral(sup 1)(sub 0) q(alpha)d alpha = 1. This scenario has been proposed by Kolmogorov (1941), when he considered the breakup of solid carbon particle. Describing the breakup as a random discrete process, Kolmogorov stated that at latest times, such a process leads to the log-normal distribution. In Gorokhovski & Saveliev, the fragmentation under the scaling symmetry has been reviewed as a continuous evolution process with new features established. The objective of this paper is twofold. First, the paper synthesizes and completes theoretical part of Gorokhovski & Saveliev. Second, the paper shows a new application of the fragmentation theory under the scale invariance. This application concerns the turbulent cascade with intermittency. We formulate here a model describing the evolution of the velocity increment distribution along the progressively decreasing length scale. The model shows that when the turbulent length scale gets smaller, the velocity increment distribution has central growing peak and develops stretched tails. The intermittency in turbulence is manifested in the same way: large fluctuations of velocity provoke highest strain in narrow (dissipative) regions of flow.

Gorokhovski, M.↗

NASA NTRS1987

Tectonic domains in the Eastern Hemisphere of Mars

The definition of boundaries of discrete structural provinces on the surface of Mars has previously been made by the assumptions of circular or radial symmetry (in the case of the Tharsis olateau), by artificial quadrangle boundaries for regional studies, or simply by regional geographical features. Much of the planetary structural mapping has been presented in a line or spot format in existing consortium data. Methods are being generated to convert the detailed maps of tectonic features to a format that can be used with standard image processing techniques. In this manner such data can be more readily compared to age and other attributes deduced from geological mapping, gravity results, and topography. The 24 photomosaics covering the Eastern Hemisphere of Mars have already been examined for four types of structural features: erosional remnants, ridges, graben, and scarps. When digitized, each feature was flagged according to feature type, azimuth and length. These values were stored as text files on a quad-by-quad basis for each quad studied.

Maxwell, Ted A.↗

NASA NTRS1991

Comparison of four stable numerical methods for Abel's integral equation

The 3-D image reconstruction from cone-beam projections in computerized tomography leads naturally, in the case of radial symmetry, to the study of Abel-type integral equations. If the experimental information is obtained from measured data, on a discrete set of points, special methods are needed in order to restore continuity with respect to the data. A new combined Regularized-Adjoint-Conjugate Gradient algorithm, together with two different implementations of the Mollification Method (one based on a data filtering technique and the other on the mollification of the kernal function) and a regularization by truncation method (initially proposed for 2-D ray sample schemes and more recently extended to 3-D cone-beam image reconstruction) are extensively tested and compared for accuracy and numerical stability as functions of the level of noise in the data.

Murio, Diego A.↗

NASA NTRS1992

Analysis of rotationally symmetric arrays of apertures on conducting spherical surfaces

Rotationally symmetric arrays of circular waveguide fed apertures on conducting spherical surfaces have been analyzed. Representation of the outside electromagnetic fields in terms of spherical transmission line modes permit the array analysis to be viewed as a spherical waveguide junction discontinuity problem. The apertures, in general, carry dual polarized circular waveguide TE11 modes. Two independent formulations - the unit cell method and the eigenexcitation method that take rotational symmetry into account - are developed and are checked against each other numerically for computational accuracy. These two formulations are analytically linked as discrete Fourier series pairs. It is seen that mutual coupling along the array decays more rapidly when the polarization of excitation is perpendicular to the array plane than when it is parallel to it. This analysis has been applied in the performance analysis of the Dome Lens phased array radar antenna.

Bondyopadhyay, Probir K.↗

NASA NTRS1997

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

Several stabilized discretization procedures for conservation law equations on triangulated domains will be considered. Specifically, numerical schemes based on upwind finite volume, fluctuation splitting, Galerkin least-squares, and space discontinuous Galerkin discretization will be considered in detail. A standard energy analysis for several of these methods will be given via entropy symmetrization. Next, we will present some relatively new theoretical results concerning congruence relationships for left or right symmetrized equations. These results suggest new variants of existing FV, DG, GLS and FS methods which are computationally more efficient while retaining the pleasant theoretical properties achieved by entropy symmetrization. In addition, the task of Jacobian linearization of these schemes for use in Newton's method is greatly simplified owing to exploitation of exact symmetries which exist in the system. These variants have been implemented in the "ELF" library for which example calculations will be shown. The FV, FS and DG schemes also permit discrete maximum principle analysis and enforcement which greatly adds to the robustness of the methods. Some prevalent limiting strategies will be reviewed. Next, we consider embedding these nonlinear space discretizations into exact and inexact Newton solvers which are preconditioned using a nonoverlapping (Schur complement) domain decomposition technique. Elements of nonoverlapping domain decomposition for elliptic problems will be reviewed followed by the present extension to hyperbolic and elliptic-hyperbolic problems. Other issues of practical relevance such the meshing of geometries, code implementation, turbulence modeling, global convergence, etc. will be addressed as needed.

Barth, Timothy↗

NASA NTRS1979

Design of a 24-channel transmultiplexer

The design of a transmultiplexer capable of performing the bilateral conversion between one 1544 kbit/s digital signal (which represents 24 PCM coded voice channels) and two analog group signals (each one containing 12 voice channels in the 60-108 kHz band) is investigated. It is shown that an FIR filter bank required as part of such a transmultiplexer can be realized efficiently by cascading a discrete cosine transform processor and a weighting network. Fast convolution algorithms are derived for evaluating the cosine transform. A method of using the symmetry conditions to reduce the computation rate in the weighting network and an elegant hardware configuration for implementing it are also discussed.

Narasimha, M. J.↗

NASA NTRS1974

Efficient stream distributions in radiative transfer theory

This paper discusses a new, computationally-efficient method for approximating the integro-differential equation of radiative transfer with a finite set of coupled differential equations for discrete streams. The method uses recommended spatial distributions of streams that are quite different from those typically used in that they are based on the symmetry of several regular Platonic solids. To facilitate the use of such distributions, an explicit, one-parameter relationship between the physical radiance and the abstract stream is formulated. The parameter is used to determine the minimum number of streams required in the radiative transfer model. Accuracy and computational efficiency are shown to be served best by choosing a stream distribution that is invariant to a large number of three space rotations. For various values of the above-mentioned parameter, the resulting recommended stream distribution is shown to be more computationally efficient than more conventional stream distributions. Finally, the incorporation of polarization in the stream definition is described.

Whitney, C.↗

NASA NTRS1983

Symmetric linear systems - An application of algebraic systems theory

Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.

Hazewinkel, M.↗

NASA NTRS1987

Computational and experimental investigation of cavity flowfields

This paper presents a computational and experimental investigation of supersonic flow past a cavity in a flat plate. The source of the particular interest in this problem is the ongoing study of the aerodynamic interference effects between a separating store and its bay in the parent body. An upwind relaxation scheme, utilizing flux vector splitting and line-Gauss-Seidel iterations, is used to solve Reynolds-averaged Navier-Stokes equations. Spatial discretizations of this two-dimensional analysis are based on implicit and finite-volume methods. Turbulence is modeled and shocks are captured. The flowfield of the symmetry plane at the half-width is computationally visualized and all flow properties are computed. Experimental tests are conducted in the Langley Unitary Plan Wind Tunnel to measure wall pressures and to capture schlieren photographs. Qualitative as well as quantitative data of computations and experiments agree very well. These two vehicles of investigation are merged to show open, closed and transitional cavity flow behaviors.

Baysal, O.↗

NASA NTRS1981

Cross-bispectrum computation and variance estimation

A method for the estimation of cross-bispectra of discrete real time series is developed. The asymptotic variance properties of the bispectrum are reviewed, and a method for the direct estimation of bispectral variance is given. The symmetry properties are described which minimize the computations necessary to obtain a complete estimate of the cross-bispectrum in the right-half-plane. A procedure is given for computing the cross-bispectrum by subdividing the domain into rectangular averaging regions which help reduce the variance of the estimates and allow easy application of the symmetry relationships to minimize the computational effort. As an example of the procedure, the cross-bispectrum of a numerically generated, exponentially distributed time series is computed and compared with theory.

Lii, K. S.↗

NASA NTRS1980

Hamiltonian indices and rational spectral densities

Several (global) topological properties of various spaces of linear systems, particularly symmetric, lossless, and Hamiltonian systems, and multivariable spectral densities of fixed McMillan degree are announced. The study is motivated by a result asserting that on a connected but not simply connected manifold, it is not possible to find a vector field having a sink as its only critical point. In the scalar case, this is illustrated by showing that only on the space of McMillan degree = /Cauchy index/ = n, scalar transfer functions can one define a globally convergent vector field. This result holds both in discrete-time and for the nonautonomous case. With these motivations in mind, theorems of Bochner and Fogarty are used in showing that spaces of transfer functions defined by symmetry conditions are, in fact, smooth algebraic manifolds.

Byrnes, C. I.↗

NASA NTRS1987

High temperature transport properties of air

A general computer code was developed to allow calculation of atom-atom and ion-atom transport collision integrals from accurate potential energy curves described by a set of discrete data points for a broad range of scattering conditions. This code is based upon semiclassical approximations that properly account for quantum mechanical behavior such as tunneling effects near a barrier maximum, resonance charge exchange, and nuclear symmetry effects. Transport collision integrals were determined for N-N, O-O, N(+)-N, and O(+)-O interactions from complete sets of accurate potential functions derived from combined experimental and ab initio structure calculations. For the O-O case, this includes results for excited states. The calculated values of the N(+)-N and O(+)-O resonance charge exchange cross section Q(ex) agree well with measurements from beam experiment that are available at high energies where the diffusion cross section Q(d) satisfies Q(d) approximately equal to 2Q(ex).

Levin, E.↗

NASA NTRS2010

Modeling Optical Properties of Mineral Aerosol Particles by Using Nonsymmetric Hexahedra

We explore the use of nonsymmetric geometries to simulate the single-scattering properties of airborne dust particles with complicated morphologies. Specifically, the shapes of irregular dust particles are assumed to be nonsymmetric hexahedra defined by using the Monte Carlo method. A combination of the discrete dipole approximation method and an improved geometric optics method is employed to compute the single-scattering properties of dust particles for size parameters ranging from 0.5 to 3000. The primary optical effect of eliminating the geometric symmetry of regular hexahedra is to smooth the scattering features in the phase function and to decrease the backscatter. The optical properties of the nonsymmetric hexahedra are used to mimic the laboratory measurements. It is demonstrated that a relatively close agreement can be achieved by using only one shape of nonsymmetric hexahedra. The agreement between the theoretical results and their measurement counterparts can be further improved by using a mixture of nonsymmetric hexahedra. It is also shown that the hexahedron model is much more appropriate than the "equivalent sphere" model for simulating the optical properties of dust particles, particularly, in the case of the elements of the phase matrix that associated with the polarization state of scattered light.

Bi, Lei↗