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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 1,063 records · Page 59
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Legendre-tau approximation for functional differential equations. Part 2: The linear quadratic optimal control problem

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Ito, K.↗
NASA NTRS1987

Legendre-tau approximation for functional differential equations. II - The linear quadratic optimal control problem

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Ito, Kazufumi↗
NASA NTRS1998

Neural Network and Regression Approximations in High Speed Civil Transport Aircraft Design Optimization

Nonlinear mathematical-programming-based design optimization can be an elegant method. However, the calculations required to generate the merit function, constraints, and their gradients, which are frequently required, can make the process computational intensive. The computational burden can be greatly reduced by using approximating analyzers derived from an original analyzer utilizing neural networks and linear regression methods. The experience gained from using both of these approximation methods in the design optimization of a high speed civil transport aircraft is the subject of this paper. The Langley Research Center's Flight Optimization System was selected for the aircraft analysis. This software was exercised to generate a set of training data with which a neural network and a regression method were trained, thereby producing the two approximating analyzers. The derived analyzers were coupled to the Lewis Research Center's CometBoards test bed to provide the optimization capability. With the combined software, both approximation methods were examined for use in aircraft design optimization, and both performed satisfactorily. The CPU time for solution of the problem, which had been measured in hours, was reduced to minutes with the neural network approximation and to seconds with the regression method. Instability encountered in the aircraft analysis software at certain design points was also eliminated. On the other hand, there were costs and difficulties associated with training the approximating analyzers. The CPU time required to generate the input-output pairs and to train the approximating analyzers was seven times that required for solution of the problem.

Patniak, Surya N.↗
NASA NTRS1982

Rapid approximate determination of nonlinear solutions - Application to aerodynamic flows and design/optimization problems

Stahara et al. (1978) have considered the use of an approximation technique which employs two or more nonlinear base solutions determined by the full computational method to predict entire families of related nonlinear solutions. The present investigation provides results for several applications of that method which demonstrate both its accuracy and its utility for engineering applications. Attention is given to the perturbation concept and methods, aspects of coordinate straining, aspects of analytical formulation, and an application to surface properties. In a discussion of the results, single and multiple parameter perturbations are considered along with a combination of the approximation method with optimization procedures. The results show that it is possible to combine in certain cases large savings in computational cost with improved optimization.

Stahara, S. S.↗
NASA NTRS1991

Comparison of hypersonic experiments and PNS predictions. I - Aerothermodynamics. II - Aerodynamics

A 3D parabolized Navier-Stokes (PNS) technique is examined in terms of applications to equilibrium-air and perfect-gas hypersonic flows at different Mach numbers and angles of attack. The method renders sublayer approximation unnecessary, and treats axis-normal coupling effects first followed by a shock solution and a corrector step. Predictions of hypersonic flowfields over several blunt conical configurations are found to agree with established wind-tunnel and flight data, although those for the Dhawan-Narasimha (1958) transition model vary from the experimental data. The PNS technique is also applied to predictions of wall-pressure distributions and force and moment data, and the results agree with experimental values. The PNS method allows the calculation of a wide variety of configurations with only a slight increase over traditional computing times.

Bhutta, Bilal A.↗
NASA NTRS1981

General relaxation schemes in multigrid algorithms for higher order singularity methods

Relaxation schemes based on approximate and incomplete factorization technique (AF) are described. The AF schemes allow construction of a fast multigrid method for solving integral equations of the second and first kind. The smoothing factors for integral equations of the first kind, and comparison with similar results from the second kind of equations are a novel item. Application of the MD algorithm shows convergence to the level of truncation error of a second order accurate panel method.

Oskam, B.↗
NASA NTRS1974

Aerodynamic heating on 3-D bodies including the effects of entropy-layer swallowing

A relatively simple method was developed previously (authors, 1973) for calculating laminar, transitional, and turbulent heating rates on three-dimensional bodies in hypersonic flows. This method was shown to yield reasonably accurate results for laminar heating on blunted circular and elliptical cones and an earlier version of the space shuttle vehicle. As the boundary layer along the surface grows, more and more of the inviscid-flow mass is entrained into the boundary layer, and the streamlines which passed through the nearly normal portion of the bow shock wave are 'swallowed' by the boundary layer. This phenomenon is often referred to as entropy-layer or streamline swallowing, and it can have a significant effect on the calculated heating rates. An approximate, yet simple, method for including the effects of entropy-layer swallowing in the heating-rate calculations is given.

Dejarnette, F. R.↗
NASA NTRS1998

Application of the ENS3DAE Euler/Navier-Stokes Aeroelastic method

This paper discusses recent applications of the ENS3DAE computational aeroelasticity method. In particular, it describes aeroelastic and unsteady aerodynamics calculations performed on wings with trailing edge control surfaces. These simulations include the investigation of control reversal for a structurally flexible wing with a deflected control surface, and a static and dynamic analysis of a rigid wing with an oscillating control surface. The two sets of calculations were performed independently on different wings using different grid topologies. The control reversal simulation represents an inviscid Euler static aeroelastic analysis of a thin wing with a rectangular planform. The geometry of this wing makes it suitable for computations using more approximate, inviscid aerodynamics methods. Thus, the results of the present Euler computations are compared with numerical data generated by a validated computational aeroelasticity code which uses a simpler aerodynamic formulation. The second illustrated case involves the simulation of a significantly more complex flowfield and the static and dynamic analyses of this geometry were performed using the viscous Navier-Stokes equation option in ENS3DAE. Results of both the steady and unsteady calculations on this wing are compared with existing experimental data.

Schuster, David M.↗
NASA NTRS1973

On singlet s-wave electron-hydrogen scattering.

Discussion of various zeroth-order approximations to s-wave scattering of electrons by hydrogen atoms below the first excitation threshold. The formalism previously developed by the author (1967, 1968) is applied to Feshbach operators to derive integro-differential equations, with the optical-potential set equal to zero, for the singlet and triplet cases. Phase shifts of s-wave scattering are computed in the zeroth-order approximation of the Feshbach operator method and in the static-exchange approximation. It is found that the convergence of numerical computations is faster in the former approximation than in the latter.

Madan, R. N.↗
NASA NTRS1982

Development of a reduced basis technique for transient thermal analysis

A technique to reduce the degrees of freedom in static and dynamic problems, the reduced basis method, is described. The method combines the classical Rayleigh-Ritz approximation with contemporary finite element methods to retain modeling versatility as the degrees of freedom are reduced. Applications to a nonlinear dynamic response problem are discussed efforts to apply the method to nonlinear transient thermal response problems are summarized. The selection of basis vectors for reducing the system of equations is addressed.

Shore, C. P.↗
NASA NTRS1994

On the wavelet optimized finite difference method

When one considers the effect in the physical space, Daubechies-based wavelet methods are equivalent to finite difference methods with grid refinement in regions of the domain where small scale structure exists. Adding a wavelet basis function at a given scale and location where one has a correspondingly large wavelet coefficient is, essentially, equivalent to adding a grid point, or two, at the same location and at a grid density which corresponds to the wavelet scale. This paper introduces a wavelet optimized finite difference method which is equivalent to a wavelet method in its multiresolution approach but which does not suffer from difficulties with nonlinear terms and boundary conditions, since all calculations are done in the physical space. With this method one can obtain an arbitrarily good approximation to a conservative difference method for solving nonlinear conservation laws.

Jameson, Leland↗
NASA NTRS1976

Evaluation of two swept-infinite-wing potential/viscous-flow computer programs

Two computer programs capable of predicting the potential and viscous interacting flow around wings of infinite aspect ratio was evaluated. The programs are compared in terms of their capabilities, the approximations and the methods of solution used, and the input requirements. Six airfoils, each representative of a class of airfoils, are used as test airfoils. The results predicted by the programs are presented for each airfoil at sweep angles of 0, 20, and 40 degrees over a range of angles of attack. The results show that at zero sweep both programs predicted the aerodynamic coefficients well and generally in good agreement with measurements. At 20 and 40 degrees of sweep, as there are no experimental data available, definitive conclusions cannot be drawn about the accuracy of the predictions although the results are presented and discussed. The execution times are approximately the same for the two programs.

Arimilli, R. V.↗
NASA NTRS1985

A fast, time-accurate unsteady full potential scheme

The unsteady form of the full potential equation is solved in conservation form by an implicit method based on approximate factorization. At each time level, internal Newton iterations are performed to achieve time accuracy and computational efficiency. A local time linearization procedure is introduced to provide a good initial guess for the Newton iteration. A novel flux-biasing technique is applied to generate proper forms of the artificial viscosity to treat hyperbolic regions with shocks and sonic lines present. The wake is properly modeled by accounting not only for jumps in phi, but also for jumps in higher derivatives of phi, obtained by imposing the density to be continuous across the wake. The far field is modeled using the Riemann invariants to simulate nonreflecting boundary conditions. The resulting unsteady method performs well which, even at low reduced frequency levels of 0.1 or less, requires fewer than 100 time steps per cycle at transonic Mach numbers. The code is fully vectorized for the CRAY-XMP and the VPS-32 computers.

Shankar, V.↗
NASA NTRS1993

Automated Finite Element Modeling of Wing Structures for Shape Optimization

The displacement formulation of the finite element method is the most general and most widely used technique for structural analysis of airplane configurations. Modem structural synthesis techniques based on the finite element method have reached a certain maturity in recent years, and large airplane structures can now be optimized with respect to sizing type design variables for many load cases subject to a rich variety of constraints including stress, buckling, frequency, stiffness and aeroelastic constraints (Refs. 1-3). These structural synthesis capabilities use gradient based nonlinear programming techniques to search for improved designs. For these techniques to be practical a major improvement was required in computational cost of finite element analyses (needed repeatedly in the optimization process). Thus, associated with the progress in structural optimization, a new perspective of structural analysis has emerged, namely, structural analysis specialized for design optimization application, or.what is known as "design oriented structural analysis" (Ref. 4). This discipline includes approximation concepts and methods for obtaining behavior sensitivity information (Ref. 1), all needed to make the optimization of large structural systems (modeled by thousands of degrees of freedom and thousands of design variables) practical and cost effective.

Harvey, Michael Stephen↗
NASA NTRS1986

Solving Nonlinear Coupled Differential Equations

Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.

Mitchell, L.↗
NASA NTRS1989

Nonlinear filters for efficient shock computation

A new type of methods for the numerical approximation of hyperbolic conservation laws with discontinuous solution is introduced. The methods are based on standard finite difference schemes. The difference solution is processed with a nonlinear conservation form filter at every time level to eliminate spurious oscillations near shocks. It is proved that the filter can control the total variation of the solution and also produce sharp discrete shocks. The method is simpler and faster than many other high resolution schemes for shock calculations. Numerical examples in one and two space dimensions are presented.

Engquist, Bjorn↗