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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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Computed spectra resemble von Karman spectra of frequencies of interest. Numerical technique yields simulated atmospheric-turbulence spectra that closely approximates von Karman spectra within frequency ranges of interest for aircraft response. Suitable for computation in that they represent stable systems and roll off as f-2 at high frequencies outside range of interest.
An abstract mixed problem and its approximation are studied; both are well-posed if and only if several inf-sup conditions are satisfied. These results are applied to a spectral Galerkin method for the Stokes problem in a square, when it is formulated in Chebyshev weighted Sobolev spaces. Finally, a collocation method for the Navier-Stokes equations at Chebyshev nodes is analyzed.
The conservation and convergence properties of spectral Fourier methods for the numerical approximation of the Korteweg-de Vries equation are analyzed. It is proved that the (aliased) collocation pseudospectral method enjoys the same convergence properties as the spectral Galerkin method, which is less effective from the computational point of view. This result provides a precise mathematical answer to a question raised by several authors in recent years.
A method is proposed for the spectral element simulation of incompressible flow. This method constitutes in a well-posed optimal approximation of the steady Stokes problem with no spurious modes in the pressure. The resulting method is analyzed, and numerical results are presented for a model problem.
Physical band models that use simplifying assumptions about the structure of the CO2 15-micron band are described and compared with the accurate line-by-line model of Fels and Schwarzkopf (1981). The methods have application to the models of the atmospheres of Venus, earth, and Mars. The narrow-band methods include a general random model and techniques employing the Malkmus (1967) line-strength distribution, and the accuracy of these models at low pressure is found to be sensitive to the line-strength distribution and the line shape. When combined with a simple Voigt parameterization, the more efficient approximate methods represented by an exponential wideband model are found to be almost as accurate as the expensive narrow-band models. Empirical logarithmic wideband models used in climate-modeling studies are found to be very efficient, but of limited range of validity.
This paper states a conjecture which relates Lax-Richmyer stability to the algebraic test of the stability theory of Gustafsson, Kreiss, and Sundstrom (1972), developed for difference approximations to initial boundary value problems where the matrix size J increases linearly with n as n goes to infinity. This corresponds to mesh refinement in both space and time for t = n x delta t = constant.
An approximate semianalytical method for determination of interlaminar shear stress distribution through the thickness of an arbitrarily laminated thick plate has been presented. The method is based on the assumptions of transverse inextensibility and layerwise constant shear angle theory (LCST) and utilizes an assumed quadratic displacement potential energy based finite element method (FEM). Centroid of the triangular surface has been proved from a rigorous mathematical point of view (Aubin-Nitsche theory), to be the point of exceptional accuracy for the interlaminar shear stresses. Numerical results indicate close agreement with the available three-dimensional elasticity theory solutions. A comparison between the present theory and that due to an assumed stress hybrid FEM suggest that the (normal) traction-free-edge condition is not satisfied in the latter approach. Furthermore, the present paper is the first to present the results for interlaminar shear stresses in a two-layer thick square plate of balanced unsymmetric angle-ply construction. A comparison with the recently proposed Equilibrium Method (EM) indicates the superiority of the present method, because the latter assures faster convergence as well as simultaneous vanishing of the transverse shear stresses on both of the exposed surfaces of the laminate. Superiority of the present method over the EM, in the case of a symmetric laminate, is limited to faster convergence alone. It has also been demonstrated that the combination of the present method and the reduced (quadratic order) numerical integration scheme yields convergence of the interlaminar shear stresses almost as rapidly as that of the nodal displacements, in the case of a thin plate.
An analytical technique is developed to estimate (with second-order accuracy) the curvature of a sufficiently smooth plane curve defined in finite form. The derivation of the approximations from local information is explained in detail; the continuity and invariance of the estimates under translation and rotation are demonstrated; and examples, error estimates, and a broken-line extension are presented. The suitability of the present technique for computer implementation is indicated.
Report provides approximate equations for capacitances and ratios of maximum electrostatic field strengths to potentials of variously shaped electrodes in vicinity of ground planes. Maximum-field-strength/potential ratio of given electrode used in conjunction with measured or estimated potential to determine whether discharge is likely. Capacitance and potential give measure of maximum energy release and maximum damage done by discharge.
Convergence properties of controls, trajectories, and feedback kernels analyzed. Report discusses use of factorization techniques to approximate optimal feedback gains in finite-time, linear-regulator/quadratic-cost-function problem of system governed by retarded-functional-difference equations RFDE's with control delays. Presents approach to factorization based on discretization of state penalty leading to simple structure for feedback control law.
The least-squares transformation of a discrete-time multivariable linear system into a desired one by convolving the first with a polynomial system yields optimal polynomial solutions to the problems of system compensation, inversion, and approximation. The polynomial coefficients are obtained from the solution to a so-called normal linear matrix equation, whose coefficients are shown to be the weighting patterns of certain linear systems. These, in turn, can be used in the recursive solution of the normal equation.
A theoretical framework is presented that can be used to treat approximation techniques for very general classes of parameter estimation problems involving distributed systems that are either first or second order in time. Using the approach developed, one can obtain both convergence and stability (continuous dependence of parameter estimates with respect to the observations) under very weak regularity and compactness assumptions on the set of admissible parameters. This unified theory can be used for many problems found in the recent literature and in many cases offers significant improvements to existing results.
An approximate method to compute the maximum deformation and permanent set of a beam subjected to shock wave laoding in vacuo and in water was investigated. The method equates the maximum kinetic energy of the beam (and water) to the elastic plastic work done by a static uniform load applied to a beam. Results for the water case indicate that the plastic deformation is controlled by the kinetic energy of the water. The simplified approach can result in significant savings in computer time or it can expediently be used as a check of results from a more rigorous approach. The accuracy of the method is demonstrated by various examples of beams with simple support and clamped support boundary conditions.
The Mechanics of Materials Model (MOMM) is one of a series of new stand-alone three dimensional nonlinear structural analysis codes. Incorporation of a general purpose finite element computer code into the hot section design process was severely limited by the high costs involved. MOMM is a stiffness method finite element code that uses an internally generated network of beams to characterize hot section component behavior. The method was proposed as a fast, easy to use, computationally efficient tool for approximate analyses. MOMM incorporates a wide variety of analysis capabilities, material models, and load type specifiers instrumental for the analysis of hot section components.
Utilizing a one-dimensional transport theory for heavy ion propagation, evaluations of typical energy-dependent transport coefficient approximations are made by comparing theoretical depth-dose predictions to published experimental values for incident 670 MeV/nucleon Ne-20 beams in water. Results are presented for cases where the input nuclear absorption cross sections, or input fragmentation parameters, or both, are fixed. The lack of fragment charge and mass concentration resulting from the use of Silberberg-Tsao fragmentation parameters continues to be the main source of disagreement between theory and experiment.
In this paper, an approximate extension of the deHoffmann-Teller (1950) theorem for electrons within layers possessing a normal mass flux is derived. It is shown that the deHoffmann-Teller frame electron bulk velocity is nearly parallel to the magnetic field everywhere through those one-dimensional time-stationary layers which possess a normal mass flux, even though electric field perpendicular to the magnetic field exists throughout such layers. Examples of layers of this class are the fast and slow shocks as well as rotational discontinuities.
A method is proposed for treating steady-state, thermally driven convection using the full direct interaction approximation to treat the nonlinear energy transfer and a prescribed instability function to model the eenrgy input. The instability function used is the growth rate of the mechanism generating the turbulence. This methodology can be easily generalized and applied to other driving mechanisms. The 1/3 power law form of the N vs. R relation for water is duplicated here and the coefficient is computed, using a two-point closure, to be less than about 0.08.
A new algorithm for solving the duals of separable convex optimization problems is presented. The algorithm is based on an active set strategy in conjunction with a variable metric method. This first order algorithm is more reliable than Newton's method used in DUAL-2 because it does not break down when the Hessian matrix becomes singular or nearly singular. A perturbation technique is introduced in order to remove the nondifferentiability of the dual function which arises when linear constraints are present in the approximate problem.