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At least 415 records · Page 23

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NASA NTRS1982

Numerical generation of composite three dimensional grids by quasilinear elliptic systems

A three-dimensional grid generation technique designed to numerically construct a boundary-conforming grid within a three-dimensional region bounded by a closed surface is described. The boundary values are generated numerically by a modified elliptic system and are used to compute grid control parameters that are contained in the elliptic systems. The interior grid distribution is governed by the distribution of points on the boundary as well as by the boundary's geometric shape. The composite three-dimensional grid remains both continuous and smooth across the surface of juncture between any two adjoining subregions. The details of the method and its implementation are presented, displaying numerical results for three-dimensional composite grid for a wing-body combination and surface grids.

Thomas, P. D.↗

NASA NTRS1984

The well-posedness of the Kuramoto-Sivashinsky equation

The Kuramoto-Sivashinsky equation arises in a variety of applications, among which are modeling reaction diffusion systems, flame propagation and viscous flow problems. It is considered here, as a prototype to the larger class of generalized Burgers equations: those consist of a quadratic nonlinearity and an arbitrary linear parabolic part. It is shown that such equations are well posed, thus admitting a unique smooth solution, continuously dependent on its initial data. As an attractive alternative to standard energy methods, existence and stability are derived in this case, by patching in the large short time solutions without loss of derivatives.

Tadmor, E.↗

NASA NTRS1986

The well-posedness of the Kuramoto-Sivashinsky equation

Tadmor, E.↗

NASA NTRS1989

Monte Carlo calculation of dynamical properties of the two-dimensional Hubbard model

A new method is introduced for analytically continuing imaginary-time data from quantum Monte Carlo calculations to the real-frequency axis. The method is based on a least-squares-fitting procedure with constraints of positivity and smoothness on the real-frequency quantities. Results are shown for the single-particle spectral-weight function and density of states for the half-filled, two-dimensional Hubbard model.

White, S. R.↗

NASA NTRS1991

High order filtering methods for approximating hyperbolic systems of conservation laws

The essentially nonoscillatory (ENO) schemes, while potentially useful in the computation of discontinuous solutions of hyperbolic conservation-law systems, are computationally costly relative to simple central-difference methods. A filtering technique is presented which employs central differencing of arbitrarily high-order accuracy except where a local test detects the presence of spurious oscillations and calls upon the full ENO apparatus to remove them. A factor-of-three speedup is thus obtained over the full-ENO method for a wide range of problems, with high-order accuracy in regions of smooth flow.

Lafon, F.↗

NASA NTRS1992

Data reduction using cubic rational B-splines

A geometric method is proposed for fitting rational cubic B-spline curves to data that represent smooth curves including intersection or silhouette lines. The algorithm is based on the convex hull and the variation diminishing properties of Bezier/B-spline curves. The algorithm has the following structure: it tries to fit one Bezier segment to the entire data set and if it is impossible it subdivides the data set and reconsiders the subset. After accepting the subset the algorithm tries to find the longest run of points within a tolerance and then approximates this set with a Bezier cubic segment. The algorithm uses this procedure repeatedly to the rest of the data points until all points are fitted. It is concluded that the algorithm delivers fitting curves which approximate the data with high accuracy even in cases with large tolerances.

Chou, Jin J.↗

NASA NTRS1991

A three dimensional multigrid multiblock multistage time stepping scheme for the Navier-Stokes equations

A general multiblock method for the solution of the three-dimensional, unsteady, compressible, thin-layer Navier-Stokes equations has been developed. The convective and pressure terms are spatially discretized using Roe's flux differencing technique while the viscous terms are centrally differenced. An explicit Runge-Kutta method is used to advance the solution in time. Local time stepping, adaptive implicit residual smoothing, and the Full Approximation Storage (FAS) multigrid scheme are added to the explicit time stepping scheme to accelerate convergence to steady state. Results for three-dimensional test cases are presented and discussed.

Elmiligui, Alaa↗

NASA NTRS1996

Quadrature-Free Implementation of the Discontinuous Galerkin Method for Hyperbolic Equations

A discontinuous Galerkin formulation that avoids the use of discrete quadrature formulas is described and applied to linear and nonlinear test problems in one and two space dimensions. This approach requires less computational time and storage than conventional implementations but preserves the compactness and robustness inherent to the discontinuous Galerkin method. Test problems include both linear and nonlinear one-dimensional scalar advection of botH smooth and discontinuous initial value problems, two-dimensional scalar advection of smooth initial value problems discretized by using unstructured grids with varying degrees of smoothness and regularity, and two-dimensional linear Euler solutions on unstructured grids.

Atkins, H. L.↗

NASA NTRS1997

Method for Ultrasonic Imaging and Device for Performing the Method

A method for ultrasonic imaging of interior structures and flaws in a test specimen with a smooth or irregular contact surfaces, in which an ultrasonic transducer is coupled acoustically to the contact surface via a plurality of ultrasonic wave guides with equal delay times. The wave guides are thin and bendable, so they adapt to variations in the distance between the transducer and different parts of the contact surface by bending more or less. All parts of the irregular contact surface accordingly receive sound waves that are in phase, even when the contact surface is irregular, so a coherent sound wave is infused in the test specimen. The wave guides can be arranged in the form of an ultrasonic brush, with a flat head for coupling to a flat transducer, and free bristles that can be pressed against the test specimen. By bevelling the bristle ends at a suitable angle, shear mode waves can be infused into the test specimen from a longitudinal mode transducer.

Madaras, Eric I.↗

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 NTRS1997

Extension of a Kolmogorov Atmospheric Turbulence Model for Time-Based Simulation Implementation

The development of any super/hypersonic aircraft requires the interaction of a wide variety of technical disciplines to maximize vehicle performance. For flight and engine control system design and development on this class of vehicle, realistic mathematical simulation models of atmospheric turbulence, including winds and the varying thermodynamic properties of the atmosphere, are needed. A model which has been tentatively selected by a government/industry group of flight and engine/inlet controls representatives working on the High Speed Civil Transport is one based on the Kolmogorov spectrum function. This report compares the Dryden and Kolmogorov turbulence forms, and describes enhancements that add functionality to the selected Kolmogorov model. These added features are: an altitude variation of the eddy dissipation rate based on Dryden data, the mapping of the eddy dissipation rate database onto a regular latitude and longitude grid, a method to account for flight at large vehicle attitude angles, and a procedure for transitioning smoothly across turbulence segments.

McMinn, John D.↗

NASA NTRS2007

Forecast of the Amplitude of Solar Cycle 24 Based on the Disturbed Days Precursor

R. J. Thompson (1993, Solar Physics 148, 383) exhibited a significant linear relationship between the number of geomagnetically disturbed days (those that exceed some threshold value of the Ap or nu index) in a solar cycle and the sum of the peak sunspot number in that cycle and the next cycle. Thus, the number of disturbed days during a full cycle, together with the peak sunspot number in that cycle, is a predictor of the amplitude of the next cycle. The work reported here applies Thompson's method to the current cycle. Linear relationships as described above are derived both for the pure aa record (1868-2006) and for a composite of aa (1868-1931) and Ap (1932-2006). For the composite record, the relationship between aa and Ap is determined cycle-by-cycle during the period of overlap. The method is tested for sensitivity to the adopted Ap (or equivalent aa) threshold. The highest smoothed monthly sunspot number for Cycle 24 is forecasted to be R(sub z) = 115 plus or minus 30, where the uncertainty is conservatively based on the full spread of the data around the fitted line in the sunspot number direction. In terms of smoothed monthly 10.7-cm radio flux, the forecast is F10.7 = 164 plus or minus 28.

Rabin, Douglas M.↗

NASA NTRS2018

Topological Control of Polystyrene-Silica Core-Shell Microspheres

Controllable surface morphology is requisite across a gamut of processes, industries, and applications. The surface morphology of silica-coated polystyrene microspheres was controllably modified to enable generation of both smooth and bumpy, or raspberry-like, surfaces. Although smooth and raspberry-like silica shells on polystyrene templates have been demonstrated extensively, the method described here used readily available materials to produce radical changes in surface morphology from a single polystyrene template coated in silica through a facile sol-gel reaction processes. Silica shells were deposited via a sol-gel process (using tetraethyl orthosilicate as the silica precursor) onto 1 to 2 m diameter anionic polystyrene spheres, fabricated by emulsifier-free polymerization. By varying of the concentration of silica precursor and ammonium hydroxide catalyst and altering the electrostatic surface interactions via addition of a cationic polymeric brush, an array of surface topologies was generated. The resulting silica shells ranged from 100 to 200 nm in thickness, as measured by calcination of the polystyrene template. Empirical relations between reaction conditions and the resulting silica colloid diameter were utilized to understand the resultant silica shell topology. These results may serve as a guide to generate a versatile platform for research in the multitude of applications where polystyrene-silica core-shell particles are utilized.

Zane A. Grady↗

NASA NTRS1986

An efficient method for solving the steady Euler equations

An efficient numerical procedure for solving a set of nonlinear partial differential equations, the steady Euler equations, using Newton's linearization procedure is presented. A theorem indicating quadratic convergence for the case of differential equations is demonstrated. A condition for the domain of quadratic convergence Omega(2) is obtained which indicates that whether an approximation lies in Omega(2) depends on the rate of change and the smoothness of the flow vectors, and hence is problem-dependent. The choice of spatial differencing, of particular importance for the present method, is discussed. The treatment of boundary conditions is addressed, and the system of equations resulting from the foregoing analysis is summarized and solution strategies are discussed. The convergence of calculated solutions is demonstrated by comparing them with exact solutions to one and two-dimensional problems.

Liou, M.-S.↗

NASA NTRS1992

Accurate upwind-monotone (nonoscillatory) methods for conservation laws

The well known MUSCL scheme of Van Leer is constructed using a piecewise linear approximation. The MUSCL scheme is second order accurate at the smooth part of the solution except at extrema where the accuracy degenerates to first order due to the monotonicity constraint. To construct accurate schemes which are free from oscillations, the author introduces the concept of upwind monotonicity. Several classes of schemes, which are upwind monotone and of uniform second or third order accuracy are then presented. Results for advection with constant speed are shown. It is also shown that the new scheme compares favorably with state of the art methods.

Huynh, Hung T.↗

NASA NTRS1975

Some estimation formulae for continuous time-invariant linear systems

In this brief paper we examine a Riccati equation decomposition due to Reid and Lainiotis and apply the result to the continuous time-invariant linear filtering problem. Exploitation of the time-invariant structure leads to integration-free covariance recursions which are of use in covariance analyses and in filter implementations. A super-linearly convergent iterative solution to the algebraic Riccati equation (ARE) is developed. The resulting algorithm, arranged in a square-root form, is thought to be numerically stable and competitive with other ARE solution methods. Certain covariance relations that are relevant to the fixed-point and fixed-lag smoothing problems are also discussed.

Bierman, G. J.↗

NASA NTRS1976

Environmental effects on aluminum fracture

The sustained load stress corrosion cracking (SCC) threshold for aluminum alloy 214 was determined using smooth (sigma sub TH) and precracked (K sub ISCC) specimens, and cyclic load growth behavior in 3.5% NaCl salt solution was studied. The relationship between K sub ISCC and sigma sub TH was also studied. The work showed that 2124-T851 aluminum alloy in plate gage has a moderately high resistance to stress corrosion attack. Experimental results showed that no SCC occurred in the longitudinal and long transverse directions in any of the tests. Some SCC was found by smooth tests in the short transverse direction, and the data were confirmed by two test methods-sigma sub TH = 275 MN/sq m (40 ksi). No SCC was found from compact specimen tests in any direction: surface flaw and center notch specimens evaluated in the short transverse direction exhibited SCC. The data indicate that stress corrosion behavior is defect, size, and stress dependent, but not entirely in accordance with a stress intensity controlled mechanism.

Schwartzberg, F. R.↗

NASA NTRS1985

HPOTP low-speed flexible rotor balancing, phase 1

A method was developed that shows promise in overcoming many balancing limitations. This method establishes one or more windows for low speed, out-of-housing balancing of flexible rotors. These windows are regions of speed and support flexibility where two conditions are simultaneously fulfilled. First, the rotor system behaves flexibly; therefore, there is separation among balance planes. Second, the response due to balance weights is large enough to reliably measure. The analytic formulation of the low-speed flexible rotor balancing method is described. The results of proof-of-principle tests conducted under the program are presented. Based on this effort, it is concluded that low speed flexible rotor balancing is a viable technology. In particular, the method can be used to balance a rotor bearing system at low speed which results in smooth operation above more than one bending critical speed. Furthermore, this balancing methodology is applicable to SSME turbopump rotors.

Giordano, J.↗