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At least 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

On the comparison of numerical theories of orbital motion

The requirements for the independent numerical replication of an ephemeris generated by numerical integration are examined and an investigation concerned with the duplication of the ephemeris of the numerical theory reported by Oesterwinter and Cohen (1972) is discussed. Discrepancies between the results of the investigation and the data reported by Oesterwinter and Cohen are considered. It was found very difficult to determine the cause for the discrepancies. Proposals are, therefore, made to provide together with the results of a numerical calculation sufficient information concerning the theoretical and computational basis on which the data were obtained.

Mulholland, J. D.↗
NASA NTRS1976

Numerical simulation of small perturbation transonic flows

The results of a systematic study of small perturbation transonic flows are presented. Both the flow over thin airfoils and the flow over wedges were investigated. Various numerical schemes were employed in the study. The prime goal of the research was to determine the efficiency of various numerical procedures by accurately evaluating the wave drag, both by computing the pressure integral around the body and by integrating the momentum loss across the shock. Numerical errors involved in the computations that affect the accuracy of drag evaluations were analyzed. The factors that effect numerical stability and the rate of convergence of the iterative schemes were also systematically studied.

Seebass, A. R.↗
NASA NTRS1977

Numerical comparison of Kalman filter algorithms - Orbit determination case study

Numerical characteristics of various Kalman filter algorithms are illustrated with a realistic orbit determination study. The case study of this paper highlights the numerical deficiencies of the conventional and stabilized Kalman algorithms. Computational errors associated with these algorithms are found to be so large as to obscure important mismodeling effects and thus cause misleading estimates of filter accuracy. The positive result of this study is that the U-D covariance factorization algorithm has excellent numerical properties and is computationally efficient, having CPU costs that differ negligibly from the conventional Kalman costs. Accuracies of the U-D filter using single precision arithmetic consistently match the double precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity to variations in the a priori statistics.

Bierman, G. J.↗
NASA NTRS1976

Numerical comparison of discrete Kalman filter algorithms - Orbit determination case study

Numerical characteristics of various Kalman filter algorithms are illustrated with a realistic orbit determination study. The case study of this paper highlights the numerical deficiencies of the conventional and stabilized Kalman algorithms. Computational errors associated with these algorithms are found to be so large as to obscure important mismodeling effects and thus cause misleading estimates of filter accuracy. The positive result of this study is that the U-D covariance factorization algorithm has excellent numerical properties and is computationally efficient, having CPU costs that differ negligibly from the conventional Kalman costs. Accuracies of the U-D filter using single precision arithmetic consistently match the double precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity to variations in the a priori statistics.

Bierman, G. J.↗
NASA NTRS1977

Numerical solution of three-dimensional free turbulent shear flows

Numerical results are presented for three-dimensional compressible turbulent jet and wake flows. An alternating direction implicit numerical procedure is used to solve the finite-difference form of the parabolic elliptic Navier-Stokes equations. A coordinate transformation maps the boundaries at infinity into a finite computational domain in order to properly specify infinity boundary conditions as well as contain the downstream growth of the viscous flow field in a fixed computational grid. Turbulence closure is achieved through an algebraic mixing length eddy viscosity model. Numerical results for supersonic flow are presented for an axisymmetric jet, an elliptical jet, an elliptical wake, and two interacting rectangular jets. Experimental data were not available for comparison with the numerical results. However, the results compare well with empirical results for free shear flows.

Oh, Y. H.↗
NASA NTRS1977

Efficient numerical treatment of periodic systems with application to stability problems

Two efficient numerical methods for dealing with the stability of linear periodic systems are presented. Both methods combine the use of multivariable Floquet-Liapunov theory with an efficient numerical scheme for computing the transition matrix at the end of one period. The numerical properties of these methods are illustrated by applying them to the simple parametric excitation problem of a fixed end column. The practical value of these methods is shown by applying them to some helicopter rotor blade aeroelastic and structural dynamics problems. It is concluded that these methods are numerically efficient, general and practical for dealing with the stability of large periodic systems.

Friedmann, P.↗
NASA NTRS1978

Numerical solution of a class of integral equations arising in two-dimensional aerodynamics

We consider the numerical solution of a class of integral equations arising in the determination of the compressible flow about a thin airfoil in a ventilated wind tunnel. The integral equations are of the first kind with kernels having a Cauchy singularity. Using appropriately chosen Hilbert spaces, it is shown that the kernel gives rise to a mapping which is the sum of a unitary operator and a compact operator. This allows the problem to be studied in terms of an equivalent integral equation of the second kind. A convergent numerical algorithm for its solution is derived by using Galerkin's method. It is shown that this algorithm is numerically equivalent to Bland's collocation method, which is then used as the method of computation. Extensive numerical calculations are presented establishing the validity of the theory.

Fromme, J.↗
NASA NTRS1980

Symbolic-numeric interface: A review

A survey of the use of a combination of symbolic and numerical calculations is presented. Symbolic calculations primarily refer to the computer processing of procedures from classical algebra, analysis, and calculus. Numerical calculations refer to both numerical mathematics research and scientific computation. This survey is intended to point out a large number of problem areas where a cooperation of symbolic and numerical methods is likely to bear many fruits. These areas include such classical operations as differentiation and integration, such diverse activities as function approximations and qualitative analysis, and such contemporary topics as finite element calculations and computation complexity. It is contended that other less obvious topics such as the fast Fourier transform, linear algebra, nonlinear analysis and error analysis would also benefit from a synergistic approach.

Ng, E. W.↗
NASA NTRS1980

Numerical method for predicting flow characteristics and performance of nonaxisymmetric nozzles. Part 2: Applications

A computer implemented numerical method for predicting the flow in and about an isolated three dimensional jet exhaust nozzle is summarized. The approach is based on an implicit numerical method to solve the unsteady Navier-Stokes equations in a boundary conforming curvilinear coordinate system. Recent improvements to the original numerical algorithm are summarized. Equations are given for evaluating nozzle thrust and discharge coefficient in terms of computed flowfield data. The final formulation of models that are used to simulate flow turbulence effect is presented. Results are presented from numerical experiments to explore the effect of various quantities on the rate of convergence to steady state and on the final flowfield solution. Detailed flowfield predictions for several two and three dimensional nozzle configurations are presented and compared with wind tunnel experimental data.

Thomas, P. D.↗
NASA NTRS1981

Finite-analytic numerical solution of heat transfer in two-dimensional cavity flow

Heat transfer in cavity flow is numerically analyzed by a new numerical method called the finite-analytic method. The basic idea of the finite-analytic method is the incorporation of local analytic solutions in the numerical solutions of linear or nonlinear partial differential equations. In the present investigation, the local analytic solutions for temperature, stream function, and vorticity distributions are derived. When the local analytic solution is evaluated at a given nodal point, it gives an algebraic relationship between a nodal value in a subregion and its neighboring nodal points. A system of algebraic equations is solved to provide the numerical solution of the problem. The finite-analytic method is used to solve heat transfer in the cavity flow at high Reynolds number (1000) for Prandtl numbers of 0.1, 1, and 10.

Chen, C.-J.↗
NASA NTRS1981

The Numerical Studies Program for the Atmospheric General Circulation Experiment (AGCE) for Spacelab Flights

The atmospheric general circulation experiment (AGCE) numerical design for Spacelab flights was studied. A spherical baroclinic flow experiment which models the large scale circulations of the Earth's atmosphere was proposed. Gravity is simulated by a radial dielectric body force. The major objective of the AGCE is to study nonlinear baroclinic wave flows in spherical geometry. Numerical models must be developed which accurately predict the basic axisymmetric states and the stability of nonlinear baroclinic wave flows. A three dimensional, fully nonlinear, numerical model and the AGCE based on the complete set of equations is required. Progress in the AGCE numerical design studies program is reported.

Fowlis, W. W.↗
NASA NTRS1982

Numerical analysis and FORTRAN program for the computation of the turbulent wakes of turbomachinery rotor blades, isolated airfoils and cascade of airfoils

Turbulent wakes of turbomachinery rotor blades, isolated airfoils, and a cascade of airfoils were investigated both numerically and experimentally. Low subsonic and incompressible wake flows were examined. A finite difference procedure was employed in the numerical analysis utilizing the continuity, momentum, and turbulence closure equations in the rotating, curvilinear, and nonorthogonal coordinate system. A nonorthogonal curvilinear coordinate system was developed to improve the accuracy and efficiency of the numerical calculation. Three turbulence models were employed to obtain closure of the governing equations. The first model was comprised to transport equations for the turbulent kinetic energy and the rate of energy dissipation, and the second and third models were comprised of equations for the rate of turbulent kinetic energy dissipation and Reynolds stresses, respectively. The second model handles the convection and diffusion terms in the Reynolds stress transport equation collectively, while the third model handles them individually. The numerical results demonstrate that the second and third models provide accurate predictions, but the computer time and memory storage can be considerably saved with the second model.

Hah, C.↗
NASA NTRS1982

Numerical solution of potential flow about arbitrary 2-dimensional multiple bodies

A procedure for the finite-difference numerical solution of the lifting potential flow about any number of arbitrarily shaped bodies is given. The solution is based on a technique of automatic numerical generation of a curvilinear coordinate system having coordinate lines coincident with the contours of all bodies in the field, regardless of their shapes and number. The effects of all numerical parameters involved are analyzed and appropriate values are recommended. Comparisons with analytic solutions for single Karman-Trefftz airfoils and a circular cylinder pair show excellent agreement. The technique of application of the boundary-fitted coordinate systems to the numerical solution of partial differential equations is illustrated.

Thompson, J. F.↗
NASA NTRS1984

Direct numerical simulation of reacting flows

The objectives of this work are: (1) to extend the technique of direct numerical simulations to turbulent, chemically reacting flows, (2) to test the validity of the method by comparing computational results with laboratory data, and (3) to use the simulations to gain a better understanding of the effects of turbulence on chemical reactions. The effects of both the large scale structure and the smaller scale turbulence on the overall reaction rates are addressed. The relationship between infinite reaction rate and finite reaction rate chemistry is compared with some of the results of calculations with existing theories and laboratory data. The direct numerical simulation method involves the numerical solution of the detailed evolution of the complex turbulent velocity and concentration fields. Using very efficient numerical methods (e.g., pseudospectral methods), the fully nonlinear (possibly low pass filtered) equations of motion are solved and no closure assumptions or turbulence models are used. Statistical data are obtained by performing spatial, temporal, and/or ensemble averages over the computed flow fields.

Riley, J. J.↗
NASA NTRS1982

Random element method for numerical modeling of diffusional processes

The random element method is a generalization of the random vortex method that was developed for the numerical modeling of momentum transport processes as expressed in terms of the Navier-Stokes equations. The method is based on the concept that random walk, as exemplified by Brownian motion, is the stochastic manifestation of diffusional processes. The algorithm based on this method is grid-free and does not require the diffusion equation to be discritized over a mesh, it is thus devoid of numerical diffusion associated with finite difference methods. Moreover, the algorithm is self-adaptive in space and explicit in time, resulting in an improved numerical resolution of gradients as well as a simple and efficient computational procedure. The method is applied here to an assortment of problems of diffusion of momentum and energy in one-dimension as well as heat conduction in two-dimensions in order to assess its validity and accuracy. The numerical solutions obtained are found to be in good agreement with exact solution except for a statistical error introduced by using a finite number of elements, the error can be reduced by increasing the number of elements or by using ensemble averaging over a number of solutions.

Ghoniem, A. F.↗
NASA NTRS1984

Hurricane Debby - Analysis and numerical forecasts using VAS soundings

The utility of VISSR Atmospheric Sounder (VAS) temperature and moisture soundings in defining the storm and its surroundings at subsynoptic scales has been examined using a numerical analysis and prognosis system. In particular, VAS temperature and moisture soundings and cloud and water vapor motion winds have been used in numerical analysis for three time periods. It is shown that the VAS temperature and moisture data which specify temperature and moisture well in cloud free regions are complemented by cloud and water vapor wind data which provide horizontal gradient information for the cloudy areas. The loss of analysis integrity due to the reduction of VAS data density in the cloudy regions associated with synoptic activity is ameliorated by using cloud and water vapor motion winds. The improvement in numerical forecasts resulting from the addition of these data to the numerical data base is also recorded.

Le Marshall, J. F.↗
NASA NTRS1985

A numerical method for approximating antenna surfaces defined by discrete surface points

A simple numerical method for the quadratic approximation of a discretely defined reflector surface is described. The numerical method was applied to interpolate the surface normal of a parabolic reflector surface from a grid of nine closest surface points to the point of incidence. After computing the surface normals, the geometrical optics and the aperture integration method using the discrete Fast Fourier Transform (FFT) were applied to compute the radiaton patterns for a symmetric and an offset antenna configurations. The computed patterns are compared to that of the analytic case and to the patterns generated from another numerical technique using the spline function approximation. In the paper, examples of computations are given. The accuracy of the numerical method is discussed.

Lee, R. Q.↗
NASA NTRS1986

A two-dimensional numerical study of the flow inside the combustion chambers of a motored rotary engine

A numerical study was performed to investigate the unsteady, multidimensional flow inside the combustion chambers of an idealized, two-dimensional, rotary engine under motored conditions. The numerical study was based on the time-dependent, two-dimensional, density-weighted, ensemble-averaged conservation equations of mass, species, momentum, and total energy valid for two-component ideal gas mixtures. The ensemble-averaged conservation equations were closed by a K-epsilon model of turbulence. This K-epsilon model of turbulence was modified to account for some of the effects of compressibility, streamline curvature, low-Reynolds number, and preferential stress dissipation. Numerical solutions to the conservation equations were obtained by the highly efficient implicit-factored method of Beam and Warming. The grid system needed to obtain solutions were generated by an algebraic grid generation technique based on transfinite interpolation. Results of the numerical study are presented in graphical form illustrating the flow patterns during intake, compression, gaseous fuel injection, expansion, and exhaust.

Shih, T. I. P.↗