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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.

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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Numerical recovery of material parameters in Euler-Bernoulli beam models

A fully Sinc-Galerkin method for recovering the spatially varying stiffness parameter in fourth-order time-dependence problems with fixed and cantilever boundary conditions is presented. The forward problems are discretized with a sinc basis in both the spatial and temporal domains. This yields an approximation solution which converges exponentially and is valid on the infinite time interval. When the forward methods are applied to parameter recovery problems, the resulting inverse problems are ill-posed. Tikhonov regularization is applied and the resulting minimization problems are solved via a quasi-Newton/trust region algorithm. The L-curve method is used to determine an appropriate value of the regularization parameter. Numerical results which highlight the method are given for problems with both fixed and cantilever boundary conditions.

Smith, R. C.↗
NASA NTRS1991

Accurate monotone cubic interpolation

Monotone piecewise cubic interpolants are simple and effective. They are generally third-order accurate, except near strict local extrema where accuracy degenerates to second-order due to the monotonicity constraint. Algorithms for piecewise cubic interpolants, which preserve monotonicity as well as uniform third and fourth-order accuracy are presented. The gain of accuracy is obtained by relaxing the monotonicity constraint in a geometric framework in which the median function plays a crucial role.

Huynh, Hung T.↗
NASA NTRS1990

Analysis of spectral projectors in one-dimensional domains

A class of projection operators with values in a subspace of polynomials is analyzed. These projection operators are related to the Hilbert spaces involved in the numerical analysis of spectral methods. They are, in the first part of the paper, the standard Sobolev spaces and, in the second part, some weighted Sobolev spaces, the weight of which is related to the orthoronality relation satisfied by the Chebyshev polynomials. These results are used to study the approximation of a model fourth-order problem.

Maday, Y.↗
NASA NTRS1990

An improved fully stressed design algorithm for plate/shell structures

The stress-ratio algorithm associated with fully stressed design philosophy has been used as a convenient tool to achieve minimum weight design of strength-limited structures. The algorithm is effective and converges quickly for many cases. However, it presents extremely slow oscillatory iteration histories for plate-thickness design problems that involve transverse bending loads. Modification of the basic algorithm presented in this paper provides an effective remedy to this problem when both membrane and bending loads are present. The modified resizing algorithm requires numerical solutions of a fourth-order algebraic equation. No additional data, beyond the ordinary static analysis results, are required.

Miura, H.↗
NASA NTRS1991

Shedding patterns of the near-wake vortices behind a circular cylinder

The unsteady incompressible Navier-Stokes equations have been accurately solved for the laminar flow past a circular cylinder in the Reynolds number range 50-200. A direct elliptic solver called the SEVP is used to rapidly advance the streamfunction in time, facilitating the overall convergence to the fully periodic or quasi-steady state. A new integral-series method is developed for the far-field streamfunction condition on a finite two-dimensional computational domain. The use of fourth-order Hermitain relations for the convection terms in the conservation-form vorticity transport equation has also contributed to the good comparison of the present results with the earlier experimental data. The vortex-shedding patterns visualized by the experimentalist are numerically reproduced here in the given Reynolds number range. Discussions that may be helpful in interpreting the behavior of the shedding frequency are presented in the main text.

Sa, Jong-Youb↗
NASA NTRS1990

Curvature-squared cosmology in the first-order formalism

Variation of the R + alpha-R-squared action with respect to independent metric and connection fields is shown to be equivalent to the metric-compatible fourth-order gravity coupled to a vector defined as a function of the trace of the energy-momentum tensor. The field equations are second order. The Friedmann cosmology based on this model is studied and it is shown to include nonsingular solutions at t = 0.

Shahid-Saless, Bahman↗
NASA NTRS1991

Resonant behaviour of MHD waves on magnetic flux tubes. I - Connection formulae at the resonant surfaces. II - Absorption of sound waves by sunspots

The present method of addressing the resonance problems that emerge in such MHD phenomena as the resonant absorption of waves at the Alfven resonance point avoids solving the fourth-order differential equation of dissipative MHD by recourse to connection formulae across the dissipation layer. In the second part of this investigation, the absorption of solar 5-min oscillations by sunspots is interpreted as the resonant absorption of sounds by a magnetic cylinder. The absorption coefficient is interpreted (1) analytically, under certain simplifying assumptions, and numerically, under more general conditions. The observed absorption coefficient magnitude is explained over suitable parameter ranges.

Sakurai, Takashi↗
NASA NTRS1991

Numerical analysis of a nuclear fuel element for nuclear thermal propulsion

A computational fluid dynamics model with porosity and permeability formulations in the transport equations has been developed to study the concept of nuclear thermal propulsion through the analysis of a pulsed irradiation of a particle bed element (PIPE). The numerical model is a time-accurate pressure-based formulation. An adaptive upwind scheme is employed for spatial discretization. The upwind scheme is based on second- and fourth-order central differencing with adaptive artificial dissipation. Multiblocked porosity regions have been formulated to model the cold frit, particle bed, and hot frit. Multiblocked permeability regions have been formulated to describe the flow shaping effect from the thickness-varying cold frit. Computational results for several zero-power density PIPEs and an elevated-particle-temperature PIPE are presented. The implications of the computational results are discussed.

Wang, Ten-See↗
NASA NTRS1992

Improved Depiction Of Computed Unsteady Flows

PLOT4D and STREAKER programs increase ease of production and utility of animated depictions of unsteady flows simulated numerically by advanced computational fluid dynamics. Programs developed to maximize information displayed while minimizing amount stored. PLOT4D, an extended version of PLOT3D, used to depict steady three-dimensional flows, incorporates features making it more computationally efficient than to visualize unsteady flow as succession of steady flows, animating frame by frame. PLOT4D postprocesses numerical output of fluid-dynamical computation into maps of flow quantities on two-coordinate surfaces depicting cut through flow field or conform to body surface. STREAKER generates streaklines, close approximations of patterns traced by streams of dye or smoke released into simulated flows. Streaklines defined via spatial succession of endpoints of pathlines of massless particles released into flow. STREAKER computes endpoints by fourth-order Runge-Kutta integration of velocity vectors.

Smith, Merritt H.↗
NASA NTRS1991

An iterative implicit diagonally-dominant factorization algorithm for solving the Navier-Stokes equations

Presented here is an algorithm for solving the multidimensional unsteady Navier-Stokes equations for compressible flows. It is based on a diagonally-dominant approximate factorization procedure. The factorization error and the timewise linearization error associated with this procedure are reduced by performing Newton-type inner iterations at each time step. The inviscid fluxes are evaluated by the fourth-order central differencing scheme amended with a numerical dissipation directly proportional to the entire dissipative part of the truncation error intrinsic to the third order biased upwind scheme. The important features of the proposed solution are elucidated by the numerical results of the convection of a vortex and the backward-facing step flows.

Chen, Shu-Cheng↗
NASA NTRS1991

Palatini variation of curvature-squared action and gravitational collapse

It is shown that Palatini variation of a class of gravitational actions based on a quadratic generalization of the Einstein-Hilbert action results in a metric-incompatible theory of gravity but one that satisfies Birkhoff's theorem. The usual fourth-order field equations are replaced by two second-order equations. Application of the field equations to a model of freely falling dust are discussed.

Shahid-Saless, Bahman↗
NASA NTRS1991

Diffraction image formation in optical systems with polarization aberrations. II - Amplitude response matrices for rotationally symmetric systems

In the previous paper in this series (McGuire and Chipman, 1990), a formulation was established for the calculation and analysis of diffraction image quality in polarizing optical systems illuminated with partially polarized, partially coherent light. In the present paper, the effect of second- and fourth-order polarization aberrations on the image plane diffraction patterns are examined. The amplitude response matrix is calculated for optical systems with small numerical apertures. Numerical results are presented for optical systems with circular apertures for three of the aberration types.

Mcguire, James P., Jr.↗
NASA NTRS1992

A GCM case study on the maintenance of short-term subtropical wind maxima in the summer hemisphere during SOP-1, FGGE

In order to substantiate earlier findings of pronounced short-term deviations in Southern Hemisphere tropical convection during the first Special Observing Period (SOP-1) of FGGE, the hypothesis that the observed summertime subtropical wind maxima were strengthened by episodes of enhanced tropical divergence is numerically tested using a fourth-order GCM. FGGE observational data for January 6-20, 1979 suggested that strong convection over the South Pacific helped to maintain a nearby subtropical jet. The dominant term in the zonal momentum budget was the Coriolis force applied to the diabatically driven meridional circulation. The present GCM study simulates these processes to a reasonable degree of accuracy. Experimental reduction of the latent energy supplied to the GCM is used to substantiate that summertime subtropical westerly maxima are largely forced by divergent outflow from the tropics.

Hurrell, James W.↗
NASA NTRS1992

Effect of spatial resolution on apparent sensitivity to initial conditions of a decaying flow as it becomes turbulent

In order to check for spurious chaos and obtain superior solutions for decaying Navier-Stokes flows, an investigation is conducted of the effect of spatial resolution on numerical results. The fourth-order finite difference method results obtained with grids of 32-cubed and 64-cubed points, and those of a pseudospectral method for 128-cubed points, indicate that the sensitivity of initially neighboring solutions to small changes in initial conditions increases with improving spatial resolution.

Deissler, Robert G.↗
NASA NTRS1992

A comparison of the impact of two time-differencing schemes on the NASA-GLAS climate model

Evidence is presented of the sensitivity of a GCM to the time-differencing scheme employed when the physical parameterizations and space discretization are not changed. Two-time marching schemes, the leapfrog and the Matsuno schemes, are analyzed and tested on the NASA-Goddard Laboratory for Atmospheric Studies fourth-order GCM in terms of the behavior and stability of two-month-averaged fields. Linear analysis indicates that Rossby waves are slightly accelerated and slightly damped when the Matsuno scheme is utilized and that these effects are scale selective, being smallest for the longest waves.

Pfeffer, Richard L.↗
NASA NTRS1992

Runge-Kutta methods combined with compact difference schemes for the unsteady Euler equations

Recent development using compact difference schemes to solve the Navier-Stokes equations show spectral-like accuracy. A study was made of the numerical characteristics of various combinations of the Runge-Kutta (RK) methods and compact difference schemes to calculate the unsteady Euler equations. The accuracy of finite difference schemes is assessed based on the evaluations of dissipative error. The objectives are reducing the numerical damping and, at the same time, preserving numerical stability. While this approach has tremendous success solving steady flows, numerical characteristics of unsteady calculations remain largely unclear. For unsteady flows, in addition to the dissipative errors, phase velocity and harmonic content of the numerical results are of concern. As a result of the discretization procedure, the simulated unsteady flow motions actually propagate in a dispersive numerical medium. Consequently, the dispersion characteristics of the numerical schemes which relate the phase velocity and wave number may greatly impact the numerical accuracy. The aim is to assess the numerical accuracy of the simulated results. To this end, the Fourier analysis is to provide the dispersive correlations of various numerical schemes. First, a detailed investigation of the existing RK methods is carried out. A generalized form of an N-step RK method is derived. With this generalized form, the criteria are derived for the three and four-step RK methods to be third and fourth-order time accurate for the non-linear equations, e.g., flow equations. These criteria are then applied to commonly used RK methods such as Jameson's 3-step and 4-step schemes and Wray's algorithm to identify the accuracy of the methods. For the spatial discretization, compact difference schemes are presented. The schemes are formulated in the operator-type to render themselves suitable for the Fourier analyses. The performance of the numerical methods is shown by numerical examples. These examples are detailed. described. The third case is a two-dimensional simulation of a Lamb vortex in an uniform flow. This calculation provides a realistic assessment of various finite difference schemes in terms of the conservation of the vortex strength and the harmonic content after travelling a substantial distance. The numerical implementation of Giles' non-refelctive equations coupled with the characteristic equations as the boundary condition is discussed in detail. Finally, the single vortex calculation is extended to simulate vortex pairing. For the distance between two vortices less than a threshold value, numerical results show crisp resolution of the vortex merging.

Yu, Sheng-Tao↗
NASA NTRS1991

Current status of conformal Weyl gravity

The status of fourth-order conformal Weyl gravity theory as an alternative theory of gravity to standard second-order Einstein theory is briefly reviewed. The questions remaining open are addressed.

Mannheim, Philip D.↗