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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

A wavelet-optimized, very high order adaptive grid and order numerical method

Differencing operators of arbitrarily high order can be constructed by interpolating a polynomial through a set of data followed by differentiation of this polynomial and finally evaluation of the polynomial at the point where a derivative approximation is desired. Furthermore, the interpolating polynomial can be constructed from algebraic, trigonometric, or, perhaps exponential polynomials. This paper begins with a comparison of such differencing operator construction. Next, the issue of proper grids for high order polynomials is addressed. Finally, an adaptive numerical method is introduced which adapts the numerical grid and the order of the differencing operator depending on the data. The numerical grid adaptation is performed on a Chebyshev grid. That is, at each level of refinement the grid is a Chebvshev grid and this grid is refined locally based on wavelet analysis.

Jameson, Leland↗
NASA NTRS1996

First-Order System Least-Squares for Second-Order Elliptic Problems with Discontinuous Coefficients

The first-order system least-squares methodology represents an alternative to standard mixed finite element methods. Among its advantages is the fact that the finite element spaces approximating the pressure and flux variables are not restricted by the inf-sup condition and that the least-squares functional itself serves as an appropriate error measure. This paper studies the first-order system least-squares approach for scalar second-order elliptic boundary value problems with discontinuous coefficients. Ellipticity of an appropriately scaled least-squares bilinear form of the size of the jumps in the coefficients leading to adequate finite element approximation results. The occurrence of singularities at interface corners and cross-points is discussed. and a weighted least-squares functional is introduced to handle such cases. Numerical experiments are presented for two test problems to illustrate the performance of this approach.

Manteuffel, Thomas A.↗
NASA NTRS2000

A Low Order and a High Order Solution for a Converging-Diverging Nozzle Problem

The Computational Aeroacoustics Workshops on Benchmark problems are conducted in order to generate solutions with a variety of methods for problems that are chosen both to be representative of significant and relevant acoustic phenomena. It is generally recognized that CAA applications require the resolution in time and in space of solution details over a significantly broader range of scales than typical computational fluid dynamics applications. These requirements are forcing the development of new methodologies for CAA applications. This paper presents numerical results from a third and a seventh order algorithm for the propagation of an acoustic signal through a converging-diverging nozzle. These two algorithms are members of a new family of high accuracy methods that have the same order accuracy in both space and time, and are an extension of previous work for linearized Euler equations to fully nonlinear time dependent problems. The simulations are all with the fully nonlinear quasi-1D Euler equations for the total solution, which includes both the fluid dynamics and the acoustics. The acoustic solution is obtained from the time dependent nonlinear solution by subtracting the steady solution.

Goodrich, John W.↗
NASA NTRS1973

Classical eighth- and lower-order Runge-Kutta-Nystroem formulas with a new stepsize control procedure for special second-order differential equations

New Runge-Kutta-Nystrom formulas of the eighth, seventh, sixth, and fifth order are derived for the special second-order (vector) differential equation x = f (t,x). In contrast to Runge-Kutta-Nystrom formulas of an earlier NASA report, these formulas provide a stepsize control procedure based on the leading term of the local truncation error in x. This new procedure is more accurate than the earlier Runge-Kutta-Nystrom procedure (with stepsize control based on the leading term of the local truncation error in x) when integrating close to singularities. Two central orbits are presented as examples. For these orbits, the accuracy and speed of the formulas of this report are compared with those of Runge-Kutta-Nystrom and Runge-Kutta formulas of earlier NASA reports.

Fehlberg, E.↗
NASA NTRS1977

Comparisons among second-order, fourth-order, and pseudospectral advection techniques in a mesoscale numerical model

The reported investigation is concerned with mesoscale squall-line simulation utilizing numerical techniques. Particular attention is given to fourth-order results and their implications for the dynamical evolution of mesoscale squall-line systems which contain severe local storms. An adiabatic inviscid set of prognostic equations is utilized in a z coordinate system for the fundamental experiment. The fourth-order advection is employed for all time-dependent equations. The Euler-backward time marching scheme is utilized with a 60 second time step. The horizontal mesh length is 42 km. Horizontal diffusion is accomplished by utilizing a smoother-desmoother. Lateral boundary conditions are designed to reduce the development of strong gradients in dependent variables near the boundaries by bringing interior values from the grid to the boundaries.

Kaplan, M.↗
NASA NTRS1992

Partially coherent scattering in stellar chromospheres. II - The first-order escape probability method. III - A second-order escape probability method

Approximate analytic expressions are derived for resonance-line wing diagnostics, accounting for frequency redistribution effects, for homogeneous slabs, and slabs with a constant Planck function gradient. Resonance-line emission profiles from a simplified conceptual standpoint are described in order to elucidate the basic physical parameters of the line-forming layers prior to the performance of detailed numerical calculations. An approximate analytic expression is derived for the dependence on stellar surface gravity of the location of the Ca II and Mg II resonance-line profile peaks. An approximate radiative transfer equation using generalized second-order escape probabilities, applicable even in the presence of nearly coherent scattering in the damping wings of resonance lines, is derived. Approximate analytic solutions that can be applied in special regimes and achieve good agreement with accurate numerical results are found.

Gayley, K. G.↗
NASA NTRS1989

Low-order design and high-order simulation of active closed-loop control for aerospace structures under construction

Partially constructed/assembled structures in space are complicated enough but their dynamics will also be operating in closed-loop with feedback controllers. The dynamics of such structures are modeled by large-scale finite element models. The model dimension L is extremely large (approximately 10,000) while the numbers of actuators (M) and sensors (P) are small. The model parameters M(sub m) mass matrix, D(sub o) damping matrix, and K(sub o) stiffness matrix, are all symmetric and sparse (banded). Thus simulation of open-loop structure models of very large dimension can be accomplished by special integration techniques for sparse matrices. The problem of simulation of closed-loop control of such structures is complicated by the addition of controllers. Simulation of closed-loop controlled structures is an essential part of the controller design and evaluation process. Current research in the following areas is presented: high-order simulation of actively controlled aerospace structures; low-order controller design and SCI compensation for unmodeled dynamics; prediction of closed-loop stability using asymptotic eigenvalue series; and flexible robot manipulator control experiment.

Balas, Mark J.↗
NASA NTRS1997

Molecular Static Third-Order Polarizabilities of Carbon-Cage Fullerenes and their Correlation with Three Geometric Parameters: Group Order, Aromaticity, and Size

Calculations were performed on the valence contribution to the static molecular third-order polarizabilities (gamma) of thirty carbon-cage fullerenes (C60, C70, five isomers of C78, and twenty-three isomers of C84). The molecular structures were obtained from B3LYP/STO-3G calculations. The values of the tensor elements and an associated numerical uncertainty were obtained using the finite-field approach and polynomial expansions of orders four to eighteen of polarization versus static electric field data. The latter information was obtained from semiempirical calculations using the AM1 hamiltonian.

Moore, Craig E.↗
NASA NTRSDate not supplied

Updating High-Order Aeroservoelastic Models from Low-Order System Identification Results

Estimating aircraft models from test data requires several simplifying assumptions that introduce biases into the parameter estimates. In this paper, these biases are defined and a method for estimating the biases is discussed. Having an estimate of the bias allows the parameters estimated from test to be integrated into a high-order model. The Integrated Adaptive Wing Technology Maturation (IAWTM) wind tunnel model is discussed and the bias is demonstrated for one of the testing configurations. The methodology was able to estimate these biases and apply corrections to high-order aeroelastic models to improve the fit to test data. The consideration of the biases allows more meaningful comparisons and avoids the erroneous differences between pretest predictions and the fitted model.

Jeffrey Ouellette↗
NASA NTRSDate not supplied

Updating High-Order Aeroservoelastic Models from Low-Order System Identification Results

Estimating aircraft models from test data requires several simplifying assumptions that introduce biases into the parameter estimates. In this paper, these biases are defined and a method for estimating the biases is discussed. Having an estimate of the bias allows the parameters estimated from test to be integrated into a high-order model. The Integrated Adaptive Wing Technology Maturation (IAWTM) wind tunnel model is discussed and the bias is demonstrated for one of the testing configurations. The methodology was able to estimate these biases and apply corrections to high-order aeroelastic models to improve the fit to test data. The consideration of the biases allows more meaningful comparisons and avoids the erroneous differences between pretest predictions and the fitted model.

Jeffrey Ouellette↗
NASA NTRS1995

Second-order numerical solution of time-dependent, first-order hyperbolic equations

A finite difference scheme is developed to find an approximate solution of two similar hyperbolic equations, namely a first-order plane wave and spherical wave problem. Finite difference approximations are made for both the space and time derivatives. The result is a conditionally stable equation yielding an exact solution when the Courant number is set to one.

Shah, Patricia L.↗
NASA NTRS1994

On The Choice of a Zeroth-Order Hamiltonian for Second-Order Perturbation Theory with A CASSCF Reference Function

A new approach to perturbation theory based on a CASSCF reference function has been developed. The key to the approach is the definition of the zeroth order Hamiltonian, H(sub 0), which includes the full CI Hamiltonian for the active space. In the the inactive and secondary spaces, operators may be chosen which reduce to the usual Moller-Plesset or Epstein-Nesbet forms in the limit of a null active space. These operators are diagonal in the orbital indices and permit the block-diagonalization of H(sub 0). The reference is an eigenfunction of Ho without N-particle projection. H(sub 0) automatically incorporates denominator shifts in the style of those appearing in recent open-shell perturbation theories. Comparative results are presented for a few test cases.

Dyall, Kenneth G.↗
NASA NTRS1972

Classical eight- and lower-order Runge-Kutta-Nystroem formulas with stepsize control for special second-order differential equations

The formulas include a stepsize control procedure, based on a complete coverage of the leading term of the truncation error in x. The formulas require fewer evaluations per stop than other Runge-Kutta-Nystrom formulas if the latter are operated by using the standard procedure for stepsize control. An example is presented. With results being of the same accuracy, Runge-Kutta-Nystrom formulas discussed save 50 percent or more computer time compared with other Runge-Kutta-Nystrom formulas.

Fehlberg, E.↗