Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “higher-order calculations”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Polynominal Interpolation Methods for Viscous Flow Calculations

Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and by Hermitian (Taylor series) finite-difference discretization. The similarities and special features of these different developments are discussed. The governing systems apply for both uniform and variable meshes. Hybrid schemes resulting from two different polynomial approximations for the first and second derivatives lead to a nonuniform mesh extension of the so-called compact or Pad? difference technique (Hermite 4). A variety of fourth-order methods are described and the Hermitian approach is extended to sixth-order (Hermite 6). The appropriate spline boundary conditions are derived for all procedures. For central finite differences, this leads to a two-point, second-order accurate generalization of the commonly used three-point end-difference formula. Solutions with several spline and Hermite procedures are presented for the boundary layer equations, with and without mass transfer, and for the incompressible viscous flow in a driven cavity. Divergence and nondivergence equations are considered for the cavity. Among the fourth-order techniques, it is shown that spline 4 has the smallest truncation error. The spline 4 procedure generally requires one-quarter the number of mesh points in a given coordinate direction as a central finite-difference calculation of equal accuracy. The Hermite 6 procedure leads to remarkably accurate boundary layer solutions.

Rubin, S. G.↗
NASA NTRS1974

Development of a second order closure model for computation of turbulent diffusion flames

A typical eddy box model for the second-order closure of turbulent, multispecies, reacting flows developed. The model structure was quite general and was valid for an arbitrary number of species. For the case of a reaction involving three species, the nine model parameters were determined from equations for nine independent first- and second-order correlations. The model enabled calculation of any higher-order correlation involving mass fractions, temperatures, and reaction rates in terms of first- and second-order correlations. Model predictions for the reaction rate were in very good agreement with exact solutions of the reaction rate equations for a number of assumed flow distributions.

Varma, A. K.↗
NASA NTRS1973

Intermediate energy nucleon-deuteron elastic scattering

The adequacy of a multiple scattering description of nucleon-deuteron scattering at intermediate energy is examined. Although the multiple-scattering series is expected to converge slowly, model calculations indicate that the higher-order multiple-scattering terms contribute only to the low-order partial waves. The first two terms, nucleon exchange and single scattering, are assumed to describe the high-order partial waves completely. It is assumed that the deuteron is coupled only to the nucleon channel and that the internal structure is adequately defined by a nonrelativistic wave function.

Wilson, J. W.↗
NASA NTRS1975

Propagation of sound in elliptic ducts

The paper studies the propagation of sound in an elliptic duct, which is of considerable interest in the field of jet-engine noise reduction. The cutoff frequencies of the higher-order circumferential modes in an elliptic duct are calculated for various duct eccentricities. The results indicate that, if equal inlet area is retained, even major deformations of the inlet shape will have virtually no influence on the cutoff conditions of the radiated sound.

Lowson, M. V.↗
NASA NTRS1995

Analysis of developing laminar flows in circular pipes using a higher-order finite-difference technique

A higher-order finite-difference technique is developed to calculate the developing-flow field of steady incompressible laminar flows in the entrance regions of circular pipes. Navier-Stokes equations governing the motion of such a flow field are solved by using this new finite-difference scheme. This new technique can increase the accuracy of the finite-difference approximation, while also providing the option of using unevenly spaced clustered nodes for computation such that relatively fine grids can be adopted for regions with large velocity gradients. The velocity profile at the entrance of the pipe is assumed to be uniform for the computation. The velocity distribution and the surface pressure drop of the developing flow then are calculated and compared to existing experimental measurements reported in the literature. Computational results obtained are found to be in good agreement with existing experimental correlations and therefore, the reliability of the new technique has been successfully tested.

Gladden, Herbert J.↗
NASA NTRS1974

Improved solution for potential flow about arbitrary axisymmetric bodies by the use of a higher-order surface source method. Part 1. Theory and results

The surface-source method of calculating potential flow is improved by refining the underlying numerical analysis. The analysis uses parabolic elements and linearly-varying source density. The result is a large increase in computing speed and accuracy. The theory is described, and the effectiveness of the modification is illustrated.

Hess, J. L.↗
NASA NTRS1974

Improved solution for potential flow about arbitrary axisymmetric bodies by the use of a higher-order surface source method. Part 2. User's manual for computer program

The surface-source method of calculating potential flow is improved by refining the underlying numerical analysis. The present analysis uses parabolic elements and linearly-varying source density which results in a large increase in computing speed and accuracy. The computer program including all relevant input and output is described.

Friedman, D. M.↗
NASA NTRS1975

Calculation of arbitrary-order diffraction efficiencies of thick gratings with arbitrary grating shape

A method for calculating arbitrary-order diffraction efficiencies of thick, lossless transmission gratings with arbitrary periodic grating shapes has been developed. A Fourier-series representation of the grating is employed, along with a coupled-mode theory of diffraction. For illustration, numerical values of the diffraction efficiencies at the first three Bragg angles are calculated for sinusoidal, square-wave, triangular, and saw-tooth gratings. Numerical results for the same grating shapes with the same parameters are also calculated for comparison, by extending Burckhardt's numerical method for analyzing thick sinusoidal gratings. The comparison shows that the coupled-mode theory provides results with relative computational ease and results that are in agreement with calculations obtained by extending the more-rigorous Burckhardt theory to nonsinusoidal grating shapes and to higher-order Bragg angles.

Su, S. F.↗
NASA NTRS1975

Improved solution for potential flow about arbitrary axisymmetric bodies by the use of a higher-order surface source method

An investigation is conducted of a case of axisymmetric bodies in which the application of main interest is an inlet, possibly with centerbody and ring vanes. The technique employed makes use of curved surface elements and a source density which varies over the element. Such an approach is designated a higher-order implementation. Questions of surface element geometry are discussed along with the computation of the induced velocity matrices and the organization of the calculation. The calculated results are compared with analytic solutions.

Hess, J. L.↗
NASA NTRS1974

The role of higher-multipolar and repulsive forces in the calculation of collision-broadened line-widths of linear molecules

Collision-broadened line widths in CO-CO2 and CO-O2 collisions have been calculated by incorporating interactions due to octopoles and hexadecapoles and short-range repulsive interactions into Anderson's (1949) theory. It is shown how these higher-order interactions can be manipulated to yield good agreement with experimental data. A critical evaluation of this totally empirical manipulation suggests that a thorough revision of the theory is required for all but simple dipole-dipole interactions. In the process of the evaluation, the values of the multipole moments are discussed.

Varanasi, P.↗
NASA NTRS1976

Power conservation for reflector antennas with truncated feed patterns

Reflector-antenna calculations using idealised truncated feed patterns can lead to incorrect values of total secondary radiated power. It is demonstrated that this discrepancy is due to the presence of higher-order spherical modes incident on the reflector. When a proper spherical-wave expansion of the incident field is used, in conjunction with the physical-optics technique, to determine the scattered field, the total power of the scattered field will equal the power radiated by the feed.

Rush, W. V. T.↗
NASA NTRS1974

Model of Saturn's rings that satisfies the observed phase curve for optical scattering

The effects of multiple anisotropic scattering were calculated, including the solar penumbra effect for shadowing computations. The classical model was matched to observations, including the wavelength dependence, by varying the particle albedo as a function of wavelength. A scattering diagram is also presented showing the relative amount of primary and higher-order scattering necessary to match the B ring brightness and the shape of the phase curve.

Irvine, W. M.↗
NASA NTRS1972

General method for calculating derivatives of the lattice electrostatic energy.

A method for calculating the derivatives of lattice electrostatic strain energy is proposed. It offers a computation procedure that is more general, concise, and systematic than any of the procedures previously used by Fuchs (1936), Cousins (1967), and Suzuki et al. (1968). The method can also easily be extended to fourth- and higher-order derivatives without undue difficulty.

Macdonald, D. E.↗
NASA NTRS1973

Auroral ion velocity distributions using a relaxation model.

Calculation of ion velocity distributions for a weakly-ionized plasma subjected to crossed electric and magnetic fields for application to the auroral ionosphere. By replacing the Boltzmann collision integral with a simple relaxation model, an exact solution to Boltzmann's equation could be obtained. This solution has the advantage over a series expansion in that all the higher-order velocity moments are inherent in it. The exact solution is particularly advantageous when studying large departures of the distribution from its Maxwellian form, because these departures are caused by the higher velocity moments. In general, however, a simple relaxation model can only be used to obtain qualitative information on the distribution function. Consequently, it is possible to determine when the higher-order velocity moments affect the ion velocity distribution and the nature of their effect, but it is not possible to obtain accurate quantitative results.

St-Maurice, J.-P.↗
NASA NTRS1977

A critical study of higher-order numerical methods for solving the boundary-layer equations

A fourth-order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations. The efficiency of the present method is compared with other two-point and three-point higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, and the three-point spline methods. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.

Wornom, S. F.↗