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At least 1,045 records · Page 58
All sourcesNASA NTRSDOE OSTI
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 NTRS1978

Three dimensional thermal pollution models. Volume 1: Review of mathematical formulations

A mathematical model package for thermal pollution analyses and prediction is presented. These models, intended as user's manuals, are three dimensional and time dependent using the primitive equation approach. Although they have sufficient generality for application at sites with diverse topographical features; they also present specific instructions regarding data preparation for program execution and sample problems. The mathematical formulation of these models is presented including assumptions, approximations, governing equations, boundary and initial conditions, numerical method of solution, and same results.

Lee, S. S.↗
NASA NTRS1980

Mountain winds (revisited)

The prediction of extremely high wind speeds, at ground level on the downstream side of a mountain range, is possible by solving the initial value problem for a two-layered nonlinear shallow water model of the atmosphere. Three different numerical methods are described to find the solutions which may involve shocks: (1) the vonNeumann-Richtmyer artificial viscosity method, (2) a filtering scheme, and (3) a hybrid method.

Isaacson, E.↗
NASA NTRS1980

An experimental and analytical investigation of a hypersonic cruise vehicle at Mach 6

Flow field properties over a hypersonic vehicle are measured and compared with results from the numerical analysis of inviscid supersonic flow theory. Good agreement between theory and experiment at zero angle of attack, and significant discrepancy at angles of attack greater than or equal to 5 deg are found. The experiments indicate that turbulent boundary layer without flow separation exists over the model surface at zero angle of attack. Vortex lift-off, flow separation, and shock boundary layer interaction occur over the leeward surface, and near the wing-fuselage junction with angles of attack greater than or equal to 5 deg. Improvements of the existing numerical method to compute hypersonic cruise vehicle flow field at large angle of attack are presented.

Wang, C. R.↗
NASA NTRS1979

A definition of the degree of controllability - A criterion for actuator placement

The unsolved problem of how to control the attitude and shape of future very large flexible satellite structures represents a challenging problem for modern control theory. One aspect of this problem is the question of how to choose the number and locations throughout the spacecraft of the control system actuators. Starting from basic physical considerations, this paper develops a concept of the degree of controllability of a control system, and then develops numerical methods to generate approximate values of the degree of controllability for any spacecraft. These results offer the control system designer a tool which allows him to rank the effectiveness of alternative actuator distributions, and hence to choose the actuator locations on a rational basis. The degree of controllability is shown to take a particularly simple form when the satellite dynamics equations are in modal form. Examples are provided to illustrate the use of the concept on a simple flexible spacecraft.

C N Viswanathan↗
NASA NTRS1980

Stress analysis of bonded plates and joints

The paper presents a general numerical method of solution to the transverse normal stress and longitudinal shear stress distributions in the adhesive layers of bonded stiffener plates, double lap joints, and strap joints, all of dissimilar orthotropic adherends. The bending deformations and the transverse shear deformations are included in the analytical model. The present influence of bending deformations of adherends on both the normal and shear stresses in adhesive layers is discussed in detail for practical cases.

Yuceoglu, U.↗
NASA NTRS1980

A two-dimensional finite-difference solution for the transient thermal behavior of a tubular solar collector

A numerical procedure was established using the finite-difference technique in the determination of the time-varying temperature distribution of a tubular solar collector under changing solar radiancy and ambient temperature. Three types of spatial discretization processes were considered and compared for their accuracy of computations and for selection of the shortest computer time and cost. The stability criteria of this technique were analyzed in detail to give the critical time increment to ensure stable computations. The results of the numerical analysis were in good agreement with the analytical solution previously reported. The numerical method proved to be a powerful tool in the investigation of the collector sensitivity to two different flow patterns and several flow control mechanisms.

Lansing, F. L.↗
NASA NTRS1980

A comprehensive comparison between experiment and prediction for a transonic turbulent separated flow

Attempts to predict surface pressure distributions on lifting surfaces have been relatively unsuccessful in the transonic regime when the shock wave is of sufficient strength to produce an extensive region of turbulent separated flow. For these conditions, the viscous flow behavior must be accurately described even to obtain reasonable predictions of surface pressure. The present paper addresses this problem. Detailed comparisons between prediction and experiment are made for a transonic, turbulent boundary-layer separation (freestream Mach number = 0.875) for which the turbulent flow properties (including the turbulent Reynolds stress) had been measured by the laser velocimeter technique from upstream of the separated region through reattachment. The flow was generated on an axisymmetric 'bump' model designed to simulate the flow on an airfoil at transonic conditions. The numerical methods used in the comparisons include the solution of the time-dependent, mass-averaged Navier-Stokes equations, and the solution of the compressible boundary-layer equations by the inverse method. Solutions were obtained for the well established Cebeci-Smith algebraic turbulence model and the more recently developed Wilcox-Rubesin two-equation turbulence model.

Johnson, D. A.↗
NASA NTRS1980

A simple numerical orthogonal coordinate generator for fluid dynamic applications

An application of a simple numerical technique which allows for the rapid construction of orthogonal coordinate systems about two dimensional and axisymmetric bodies is presented. The technique is based on a predictor corrector numerical method. It can be used to generate orthogonal meshes which have unequally spaced points in two directions. These orthogonal meshes in their transformed computational plane are, however, equally spaced so that the differencing for the metric coefficients and the fluid dynamic equation terms can be easily determined using equally spaced central finite differences. Solutions to the Navier-Stokes equations for flow over blunt bodies with reverse curvature are presented. The coupling of the time dependent fluid dynamic equations and the coordinate generator worked well with no undesirable effects noted.

Graves, R. A., Jr.↗
NASA NTRS1979

Two-dimensional zonal mean flow model

The interactions of dynamics, photochemistry and radiation in the stratosphere can be described by the continuity, momentum, and energy equations. A more comprehensive model for stratospheric transport theory was developed for the purpose of aiding predictions of changes in the stratospheric ozone content as a consequence of natural and anthropogenic processes. This model is time dependent and the dependent variables are zonal means of the relevant meteorological quantities which are functions of latitude and height. The detailed formulation of a numerical model both in physics and mathematics is given. A set of fundamental dynamical equations, and the numerical method used in the integration are described.

Chen, H. C.↗
NASA NTRS1981

Numerical solution of compressible viscous flows at high Reynolds numbers

A new numerical method which was used to reduce the computation time required in fluid dynamics to solve the Navier-Stokes equations at flight Reynolds numbers is described. The method is the implicit analogue of the explicit finite different method. It uses this as its first stage, while the second stage removes the restrictive stability condition by recasting the difference equations in an implicit form. The resulting matrix equations to be solved are either upper or lower block bidiagonal equations. The new method makes it possible and practical to calculate many important three dimensional, high Reynolds number flow fields on computers.

Maccormack, R. W.↗
NASA NTRS1981

An experimental and analytical investigation of the aerodynamics of a hypersonic vehicle at free stream Mach 6

The goal of this research is the assessment of the validity of existing three dimensional numerical programs in the prediction of the flow fields about general three dimensional hypersonic bodies. A detailed experimental research program was performed in which surface and flow field pressures were mapped. The results of the experimental work were compared with existing inviscid programs. Improvements were made on the existing numerical methods to include angle of attack. A summary of this work is presented.

Zakkay, V.↗
NASA NTRS1981

Analysis of starvation effects on hydrodynamic lubrication in nonconforming contacts

Numerical methods were used to determine the effects of lubricant starvation on the minimum film thickness under conditions of a hydrodynamic point contact. Starvation was effected by varying the fluid inlet level. The Reynolds boundary conditions were applied at the cavitation boundary and zero pressure was stipulated at the meniscus or inlet boundary. A minimum-fill-thickness equation as a function of both the ratio of dimensionless load to dimensionless speed and inlet supply level was determined. By comparing the film generated under the starved inlet condition with the film generated from the fully flooded inlet, an expression for the film reduction factor was obtained. Based on this factor a starvation threshold was defined as well as a critically starved inlet. The changes in the inlet pressure buildup due to changing the available lubricant supply are presented in the form of three dimensional isometric plots and also in the form of contour plots.

Brewe, D. E.↗
NASA NTRS1980

Hybrid-finite-element analysis of some nonlinear and 3-dimensional problems of engineering fracture mechanics

In this paper, efficient numerical methods for the analysis of crack-closure effects on fatigue-crack-growth-rates, in plane stress situations, and for the solution of stress-intensity factors for arbitrary shaped surface flaws in pressure vessels, are presented. For the former problem, an elastic-plastic finite element procedure valid for the case of finite deformation gradients is developed and crack growth is simulated by the translation of near-crack-tip elements with embedded plastic singularities. For the latter problem, an embedded-elastic-singularity hybrid finite element method, which leads to a direct evaluation of K-factors, is employed.

Atluri, S. N.↗
NASA NTRS1979

Large Eddy Simulation of turbulent shear flows

The conceptual foundation underlying Large Eddy Simulation (LES) is summarized, and the numerical methods developed for simulation of the time-developing turbulent mixing layer and turbulent plane Poiseuille flow are discussed. Computational results show that the average Reynolds stress profile nearly attains the equilibrium shape which balances the downstream mean pressure gradient in the regions away from the walls. In the vicinity of the walls, viscous stresses are shown to be significant; together with the Reynolds stresses, these stresses balance the mean pressure gradient. It is stressed that the subgrid scale contribution to the total Reynolds stress is significant only in the vicinity of the walls. The continued development of LES is urged.

Moin, P.↗
NASA NTRS1981

Simulation of charge exchange plasma propagation near an ion thruster propelled spacecraft

A model describing the charge exchange plasma and its propagation is discussed, along with a computer code based on the model. The geometry of an idealized spacecraft having an ion thruster is outlined, with attention given to the assumptions used in modeling the ion beam. Also presented is the distribution function describing charge exchange production. The barometric equation is used in relating the variation in plasma potential to the variation in plasma density. The numerical methods and approximations employed in the calculations are discussed, and comparisons are made between the computer simulation and experimental data. An analytical solution of a simple configuration is also used in verifying the model.

Robinson, R. S.↗
NASA NTRS1981

Quantitative simulation of a magnetospheric substorm. I - Model logic and overview

Results of a comprehensive computer simulation of the behavior of the earth's inner magnetosphere during a substorm-type event are reported. It is pointed out that the computer model self-consistently computes electric fields, currents, and plasma distributions and velocities in the inner-magnetosphere/ionosphere system; parallel electric fields and ionospheric neutral winds, however, are not included. The basic equations of the model are derived, and the inputs are described. An overview of the results is also given. The first appendix contains derivations of general, useful laws of bounce-averaged gradient, curvature, and E x B drifts in a plasma with isotropic pitch angle distribution. The second appendix gives a description of the numerical method used in the simulation.

Harel, M.↗