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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

The relative merits of several numerical techniques for solving the compressible Navier-Stokes equations

Four explicit finite difference techniques designed to solve the time-dependent, compressible Navier Stokes equations are compared. These techniques are: (1) MacCormack, (2) modified Du Fort-Frankel, (3) modified hopscotch, and (4) Brailovskaya. The comparison was made numerically by solving the quasi-one dimensional Navier Stokes equations for the flow in a converging-diverging nozzle. Solutions with and without standing normal shock waves were computed for unit Reynolds numbers (based on total conditions) ranging from 45374 to 2269. The results indicate that all four techniques are comparable in accuracy; however, the modified hopscotch scheme is two to three times faster than the Brailovskaya and MacCormack schemes and three to six times faster than the modified Du Fort-Frankel scheme.

Holst, T. L.↗
NASA NTRS1977

Some MACSYMA program for solving difference equations

A set of MACSYMA programs are described for finding closed form solutions to linear recurrence relations in equations having either constant or variable coefficients. In the homogenous case, a polymonial equation is obtained and the solution to the recurrence relation can be written as a linear combination of the roots of the polynomial. Exponential generating functions are used to solve variable coefficient relations. Taking successive derivatives and using the recurrence relation, an ordinary differential equation is obtained. Expanding the solution to the differential equation in a Taylor series, shows that the nth term of the series is the solution to the recurrence relation. For second order recurrences, a check is made for those that can be solved in terms of Bessel functions.

Ivie, J.↗
NASA NTRS1977

An efficient numerical method for solving the incompressible Navier-Stokes equations

This paper describes an efficient numerical method for solving the steady incompressible Navier-Stokes equations. The method is a fully implicit method based on the generalized Galerkin method, and the resulting system of equations is solved in a sweeping mode by iterative line relaxation. Results of the present method are compared with published results for separating and reattaching flows, and parametric studies showing the effects of step size, boundary locations, and Reynolds number are presented. The present method is substantially faster than previously published methods; typical run times range from 10 sec to 1 min of 7600 CPU time; and, based on results obtained to date, it is stable at any Reynolds number.

Murphy, J. D.↗
NASA NTRS1977

Studies in interactive communication. II - The effects of four communication modes on the linguistic performance of teams during cooperative problem solving

Two-man teams solved credible, 'real world' problems for which computer assistance has been or could be useful. Conversations were carried on in one of four modes of communication: typewriting, handwriting, voice, and natural unrestricted communication. Performance was assessed on three classes of dependent measures: time to solution, behavioral measures of activity, and linguistic measures. Significant differences among the communication modes were found in each of the three classes. This paper is concerned mainly with the results of the linguistic analyses. Linguistic performance was assessed with 182 measures, most of which turned out to be redundant and some of which were useless or meaningless. Those that remain show that although problems can be solved faster in the oral modes than in the hard-copy modes, the oral modes are characterized by many more messages, sentences, words, and unique words; much higher communication rates; but lower type-token ratios. Although a number of significant problem and job-role effects were found, there were relatively few significant interactions of modes with thsse variables. It appears, therefore, that the mode effects hold for both problems and for both job roles assigned to the subjects.

Chapanis, A.↗
NASA NTRS1979

Modifications to give HOPE/MDC 2.0 the capability to solve for or consider vent forces: Mission planning, mission analysis, and software formulation

The modifications are described as necessary to give the Houston Operations Predictor/Estimator (HOPE) program the capability to solve for or consider vent forces for orbit determination. The model implemented in solving for vent forces is described along with the integrator problems encountered. A summary derivation of the mathematical principles applicable to solve/consider methodology is provided.

Zyla, L. V.↗
NASA NTRS1978

A dependency-based modelling mechanism for problem solving

The paper develops a technique of dependency net modeling which relies on an explicit representation of justifications for beliefs held by the problem solver. Using these justifications, the modeling mechanism is able to determine the relevant lines of inference to pursue during problem solving. Three particular problem-solving difficulties which may be handled by the dependency-based technique are discussed: (1) subgoal violation detection, (2) description binding, and (3) maintaining a consistent world model.

London, P.↗
NASA NTRS1980

Problem solving and decisionmaking: An integration

An attempt was made to redress a critical fault of decisionmaking and problem solving research-a lack of a standard method to classify problem or decision states or conditions. A basic model was identified and expanded to indicate a possible taxonomy of conditions which may be used in reviewing previous research or for systematically pursuing new research designs. A generalization of the basic conditions was then made to indicate that the conditions are essentially the same for both concepts, problem solving and decisionmaking.

Dieterly, D. L.↗
NASA NTRS1978

An efficient explicit-implicit-characteristic method for solving the compressible Navier-Stokes equations

Explicit, implicit, and characteristic finite-difference methods are applied to solve model equations representative of the compressible Navier-Stokes equations. An approach is then formulated for solving the Navier-Stokes equation at high Reynolds numbers. The approach has drastically reduced the computation time required to obtain viscous flow solutions. Computational results for shock wave separated flows are presented.

Maccormack, R. W.↗
NASA NTRS1980

Problem solving in a distributed environment

Distributed problem solving is anayzed as a blend of two disciplines: (1) problem solving and ai; and (2) distributed systems (monitoring). It may be necessary to distribute because the application itself is one of managing distributed resources (e.g., distributed sensor net) and communication delays preclude centralized processing, or it may be desirable to distribute because a single computational engine may not satisfy the needs of a given task. In addition, considerations of reliability may dictate distribution. Examples of multi-process language environment are given.

Rashid, R. F.↗
NASA NTRS1981

Weighted-mean scheme for solving incompressible viscous flow

The problem of how a boundary layer responds to the motion of a convexed vortex on a porous wall was investigated. The wall velocity is approximately given by Darcy's law. The vorticity-stream function approach was adopted for solving Navier-Stokes equations of two dimensional incompressible viscous flows. The weighted-mean scheme was used for constructing finite difference approximations of spatial derivatives. Several test problems were solved and numerical results demonstrate clearly the accuracy, stability, and efficiency of the scheme. The weighted mean scheme then can be applied to the vortical flow problem.

Huynh, Q. Q.↗
NASA NTRS1981

Some observations on a new numerical method for solving Navier-Stokes equations

An explicit-implicit technique for solving Navier-Stokes equations is described which, is much less complex than other implicit methods. It is used to solve a complex, two-dimensional, steady-state, supersonic-flow problem. The computational efficiency of the method and the quality of the solution obtained from it at high Courant-Friedrich-Lewy (CFL) numbers are discussed. Modifications are discussed and certain observations are made about the method which may be helpful in using it successfully.

Kumar, A.↗
NASA NTRS1984

A model of asynchronous iterative algorithms for solving large, sparse, linear systems

Solving large, sparse, linear systems of equations is one of the fundamental problems in large scale scientific and engineering computation. A model of a general class of asynchronous, iterative solution methods for linear systems is developed. In the model, the system is solved by creating several cooperating tasks that each compute a portion of the solution vector. This model is then analyzed to determine the expected intertask data transfer and task computational complexity as functions of the number of tasks. Based on the analysis, recommendations for task partitioning are made. These recommendations are a function of the sparseness of the linear system, its structure (i.e., randomly sparse or banded), and dimension.

Reed, D. A.↗
NASA NTRS1982

A general algorithm for solving the algebraic Riccati equation

The generalized eigenvalue problem provides a suitable framework for reliable solutions of many system theoretic, control, and estimation problems. A general algorithm for solving the matrix algebraic Riccati equation (ARE) which utilizes a pencil structure is described here. This algorithm avoids unnecessary inversion of cost or transition matrices, making it a numerically sound way to solve for the gains and/or ARE with singular quadratic costs, for cases satisfying detectability and stabilizability conditions. Examples are solution with discrete dead-beat control, noiseless measurements in Kalman filters and time-delays in discrete-time systems, which cause difficulties in the Hamiltonian standard eigenvalue problem formulation. The ARE algorithm implementatiton and numerical examples are shown.

Walker, R. A.↗
NASA NTRS1983

Models of human problem solving - Detection, diagnosis, and compensation for system failures

The role of the human operator as a problem solver in man-machine systems such as vehicles, process plants, transportation networks, etc. is considered. Problem solving is discussed in terms of detection, diagnosis, and compensation. A wide variety of models of these phases of problem solving are reviewed and specifications for an overall model outlined.

Rouse, W. B.↗
NASA NTRS1985

Computational aspects of zonal algorithms for solving the compressible Navier-Stokes equations in three dimensions

Transonic flow fields about wing geometries are computed using an Euler/Navier-Stokes approach in which the flow field is divided into several zones. The flow field immediately adjacent to the wing surface is resolved with fine grid zones and solved using a Navier-Stokes algorithm. Flow field regions removed from the wing are resolved with less finely clustered grid zones and are solved with an Euler algorithm. Computational issues associated with this zonal approach, including data base management aspects, are discussed. Solutions are obtained that are in good agreement with experiment, including cases with significant wind tunnel wall effects. Additional cases with significant shock induced separation on the upper wing surface are also presented.

Holst, T. L.↗
NASA NTRS1986

Solving large-scale dynamic systems using band Lanczos method in Rockwell NASTRAN on CRAY X-MP

The improved cost effectiveness using better models, more accurate and faster algorithms and large scale computing offers more representative dynamic analyses. The band Lanczos eigen-solution method was implemented in Rockwell's version of 1984 COSMIC-released NASTRAN finite element structural analysis computer program to effectively solve for structural vibration modes including those of large complex systems exceeding 10,000 degrees of freedom. The Lanczos vectors were re-orthogonalized locally using the Lanczos Method and globally using the modified Gram-Schmidt method for sweeping rigid-body modes and previously generated modes and Lanczos vectors. The truncated band matrix was solved for vibration frequencies and mode shapes using Givens rotations. Numerical examples are included to demonstrate the cost effectiveness and accuracy of the method as implemented in ROCKWELL NASTRAN. The CRAY version is based on RPK's COSMIC/NASTRAN. The band Lanczos method was more reliable and accurate and converged faster than the single vector Lanczos Method. The band Lanczos method was comparable to the subspace iteration method which was a block version of the inverse power method. However, the subspace matrix tended to be fully populated in the case of subspace iteration and not as sparse as a band matrix.

Gupta, V. K.↗
NASA NTRS1985

Approximate-factorization schemes for solving the transonic full-potential equation

The present paper provides a general discussion of approximate-factorization techniques applied to the transonic full-potential equation. Giving particular attention to the AF2 approximate-factorization scheme. This scheme was first introduced by Ballhaus and Steger (1975) for solving the low-frequency (unsteady), transonic small-disturbance equation. The full-potential equation algorithm is examined, taking into account the governing equations, grid generation, the artificial density scheme (spatial differencing), the alternating direction implicit scheme, the AF2 iteration scheme, temporal damping, and boundary conditions. Computed results are also presented. It is shown that fast, fully-implicit algorithms of the approximate-factorization variety are both efficient and reliable for solving the conservative full-potential equation.

Holst, T. L.↗
NASA NTRS1987

Parallel Algorithm Solves Coupled Differential Equations

Numerical methods adapted to concurrent processing. Algorithm solves set of coupled partial differential equations by numerical integration. Adapted to run on hypercube computer, algorithm separates problem into smaller problems solved concurrently. Increase in computing speed with concurrent processing over that achievable with conventional sequential processing appreciable, especially for large problems.

Hayashi, A.↗