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At least 1,063 records · Page 59
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

An algorithm for constructing minimal order inverses

In this paper an algorithm is presented for constructing minimal order inverses of linear, time invariant, controllable and observable, multivariable systems. By means of simple matrix operations, a 'state-overdescribed' system is first constructed which is an inverse of the given multivariable system. A simple Gauss-Jordan type reduction procedure is then used to remove the redundancy in the state vector of the inverse system to obtain a minimal order inverse. When the given multivariable system is not invertible, the algorithm enables a minimal order inverse of an invertible subsystem to be constructed. Numerical examples are given to illustrate the use of the algorithm.

Patel, R. V.↗
NASA NTRS1979

NASF transposition network: A computing network for unscrambling p-ordered vectors

The viewpoints of design, programming, and application of the transportation network (TN) is presented. The TN is a programmable combinational logic network that connects 521 memory modules to 512 processors. The unscrambling of p-ordered vectors to 1-ordered vectors in one cycle is described. The TN design is based upon the concept of cyclic groups from abstract algebra and primitive roots and indices from number theory. The programming of the TN is very simple, requiring only 20 bits: 10 bits for offset control and 10 bits for barrel switch shift control. This simple control is executed by the control unit (CU), not the processors. Any memory access by a processor must be coordinated with the CU and wait for all other processors to come to a synchronization point. These wait and synchronization events can be a degradation in performance to a computation. The TN application is for multidimensional data manipulation, matrix processing, and data sorting, and can also perform a perfect shuffle. Unlike other more complicated and powerful permutation networks, the TN cannot, if possible at all, unscramble non-p-ordered vectors in one cycle.

Lim, R. S.↗
NASA NTRS1980

On the practical use of high-order methods for hyperbolic systems

The paper tests a number of high order methods on a variety of dynamic problems in one, two, and three space dimensions. The problems covered include wave propagation phenomena as well as an asymptotic approach to a steady state. Consideration is given to both smooth and shocked flows. It is shown that the methods compared require only minor modifications of many existing second-order schemes. Further, the results show that significant gains can be expected from the use of fourth-order methods. Finally, spectral methods are also considered for some of the problems presented.

Turkel, E.↗
NASA NTRS1980

Low order equivalent models of highly augmented aircraft determined from flight data using maximum likelihood estimation

This paper presents the results of a study of the feasibility of using low order equivalent mathematical models of a highly augmented aircraft, the F-8 digital fly-by-wire (DFBW), for flying qualities research. Increasingly complex models were formulated and evaluated using flight data and maximum likelihood estimation techniques. The aircraft actuator was modeled alone first. Next the equivalent derivatives were used to model the longitudinal unaugmented F-8 DFBW aircraft dynamics. The most complex model incorporated a pure time shift of the pilot input, a first order lag, and the basic longitudinal airframe model. This same model was then implemented for the F-8 DFBW aircraft in a highly augmented mode. Excellent matching of the dynamics resulted for this model, indicating that low order equivalent models which are good representations of the highly augmented F-8 DFBW aircraft can be formulated with these methods.

Shafer, M. F.↗
NASA NTRS1981

High order multi-grid methods to solve the Poisson equation

High order multigrid methods based on finite difference discretization of the model problem are examined. The following methods are described: (1) a fixed high order FMG-FAS multigrid algorithm; (2) the high order methods; and (3) results are presented on four problems using each method with the same underlying fixed FMG-FAS algorithm.

Schaffer, S.↗
NASA NTRS1982

Solution of second-order linear system by matched asymptotic expansions

Matched asymptotic expansions (MAE) are used to obtain a first order approximation to the solution of a singularly perturbed second order system. A special case is considered in which the uniform asymptotic solution obtained by MAE is shown to converge to the exact solution. Ways in which the method can be used to sole higher-order linear systems, including those which are not singularly perturbed, are also discussed.

Ardema, M. D.↗
NASA NTRS1982

Higher-order flow angle corrections for three-dimensional wind tunnel wall interference

A second-order theory including camber effects in wind tunnel wall interference corrections is described. Changes in the geometrical configuration of the model tested are avoided by introducing the camber correction as an equivalent angle-of-attack correction. Tabular and graphic data are presented which indicate improved accuracy for second-order over first-order theory.

Rizk, M. H.↗
NASA NTRS1982

Pole placement and order reduction in two-time-scale control systems through Riccati iteration

A transformation of variables taken from singular perturbations may be applied to two-time-scale linear systems in state space form to reduce the system to block-diagonal form with slow and fast modes decoupled. The transformation is easily computed by applying the new Riccati iteration. The iteration yields a solution to the nonsymmetric algebraic Riccati equation obtained by partitioning the original system matrix A. The numerical procedure is initiated with the trivial iterate L(0) = 0, and is globally convergent to the desired unique time scale decoupling solution. After transformation, the decoupled system may be used in controller design to achieve exact closed loop pole placement in the slow subsystem without altering the poles of the fast subsystem. The decoupled form may also be used to reduce system order by wetting a small parameter to zero. Provided the fast subsystem is stable, the order reduction can be expected to yield a good approximation to the original system. These methods are demonstrated using the 16th order linear model of a turbofan engine.

Anderson, L. R.↗
NASA NTRS1984

A modified least squares formulation for a system of first order equations

Second order equations in terms of auxiliary variables similar to potential and stream functions are obtained by applying a weighted least squares formulation to a first order system. The additional boundary conditions which are necessary to solve the higher order equations are determined and numerical results are presented for the Cauchy-Riemann equations.

Hafez, M. M.↗
NASA NTRS1983

Second-order explicit finite-difference methods for transient-flow analysis

Three second-order accurate numerical methods - MacCormack's method, Lambda scheme and Gabutti scheme - are introduced to solve the quasi-linear, hyperbolic partial differential equations describing transient flows in closed conduits. The details of these methods and the treatment of boundary conditions are presented and the results computed by using these methods for a typical piping system are compared. It is shown that for the same accuracy, second-order methods require considerably lesser number of computational nodes and computer time as compared to those required by the first-order methods.

Chaudhry, M. H.↗
NASA NTRS1984

The application of a second generation low-order panel method - program 'Vsaero' - to powerplant installation studies

Results from the application of a second generation low-order panel method to a number of powerplant installations are presented. The method, which retains the advantages of ease of use and low operating cost of earlier panel methods while retaining the aerodynamic modelling rigor of higher-order methods was used to predict the flow in and around typical nacelles and aircraft for a wide range of conditions. The ability of the second generation low-order analysis to calculate internal flows without the leakage problems associated with earlier programs is demonstrated and correlation between calculated and measured surface pressures and flow behavior, including predicting streamlines and locating regions of separated flow, is presented.

Clark, D. R.↗
NASA NTRS1982

Application of a polynomial spline in higher-order accurate viscous-flow computations

A quartic spline, S(4,2), is proposed which overcomes some of the difficulties associated with the use of splines S(5,3) and S(3,1) and provides fourth-order accurate results with relatively few grid points. The accuracy of spline S(4,2) is comparable to or better than that of the fourth-order box scheme and the compact differencing scheme. The use of spline S(4,2) is suggested as a possible way of obtaining fourth-order accurate solutions to Navier-Stokes equations.

Turner, M. G.↗
NASA NTRS1985

Comparison of Two Orographical Data Sets for the GLAS Fourth Order GCM

The development of a 2 deg latitude by 2.5 deg longitude version of the GLAS Fourth Order General Circulation Model has necessitated the specification of a correspondingly fine horizontal resolution orographic data set to act as a lower boundary condition for the GCM. The S1 topography attempts to relate the mean areally averaged height of such terrain while the Q3 topography emphasizes the effect of the flow of the tallest peaks in such regions by specifying an exaggerated significant height. In order to assess the relative merits of these two orographic data sets. A series of tests was initiated to evaluate the comparative weather forecasting and climate simulation skills of the GLAS Fourth Order GCM when the S1 and Q3 topographies are applied to the lower boundary. Three sets of Northern Hemispheric winter forecasts at the 2 deg x 2.5 deg resolution indicate that the Q3 topography gives slightly better results over the Northern Hemisphere than does the S1 topography. It is apparent that more forecasts will be necessary at both horizontal resolutions before any definitive conclusions are made regarding the choice of an optimal orographic data set.

Helfand, H. M.↗
NASA NTRS1985

Study of second order upwind differencing in a recirculating flow

The accuracy and stability of the second order upwind differencing scheme was investigated. The solution algorithm employed is based on a coupled solution of the nonlinear finite difference equations by the multigrid technique. Calculations have been made of the driven cavity flow for several Reynolds numbers and finite difference grids. In comparison with the hybrid differencing, the second order upwind differencing is somewhat more accurate but it is not monotonically accurate with mesh refinement. Also, the convergence of the solution algorithm deteriorates with the use of the second order upwind differencing.

Vanka, S. P.↗
NASA NTRS1983

Sufficient excitation criteria for reduced-order adaptive observers

Sufficient excitation conditions are derived for three adaptive observation schemes for the case in which the order of the observer is less than that of the plant being observed. The reduced-order excitation requirement, found to be identical for all three observers, is that the input contain more than (n+N-1)/2 frequencies, where n is the observer order, and N is the dimension of the portion of the plant which is both controllable and observable.

Lilly, J. H.↗
NASA NTRS1985

Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory

A higher-order shear deformation theory is used to demonstrate the natural frequencies and buckling loads of elastic plates. The theory accounts for parabolic distribution of the transverse shear strains through the thickness of the plate and rotary inertia. Exact solutions of simply supported plates are obtained and the results are compared with the exact solutions of three-dimensional elasticity theory, the first-order shear deformation theory, and the classical plate theory. The present theory predicts the frequencies and buckling loads more accurately when compared to the first-order and classical plate theories.

Reddy, J. N.↗
NASA NTRS1985

Ladder and cross terms in second-order distorted Born approximation

In the strong fluctuation theory for a bounded layer of random discrete scatterers, the second moments of the fields in the second-order distorted Born approximation are obtained for copolarized and cross-polarized fields. The backscattering cross sections per unit area are calculated by including the mutual coherence of the fields due to the coincidental ray paths, and that due to the opposite ray paths, corresponding to the ladder and cross terms in the Feynman diagramatic representation. It is proved that the contributions from ladder and cross terms for the copolarized backscattering cross sections are the same, while the contributions for the cross-polarized backscattering cross sections are of the same order. The bistatic scattering coefficients in the second-order approximation for both the ladder and cross terms are also obtained. The contributions from the cross terms explain the enhancement in the backscattering direction.

Jin, Y. Q.↗
NASA NTRS1985

The effect of carbon concentration and plastic deformation on ultrasonic higher order elastic properties of steel

The behavior of higher order elastic properties, which are much more sensitive to material state than are second order properties, has been studied for steel alloys AISI 1016, 1045, 1095, and 8620 by measuring the stress derivative of the acoustic natural velocity to determine the stress acoustic constants (SAC's). Results of these tests show a 20 percent linear variation of SAC's with carbon content as well as even larger variations with prestrain (plastic deformation). The use of higher order elastic characterization permits quantitative evaluation of solids and may prove useful in studies of fatigue and fracture.

Heyman, J. S.↗