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Results for “APPROXIMATION METHOD”

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 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS1945

A method for the calculation of external lift, moment, and pressure drag of slender open-nose bodies of revolution at supersonic speeds

An approximate method is presented for the calculation of the external lift, moment, and pressure drag of slender open-nose bodies of revolution of supersonic speeds. The lift, moment, and pressure drag of a typical ram-jet body shape are calculated at Mach numbers 1.45, 1.60, 1.75, and 3.00; and the lift and moment results are compared with available experimental data. The agreement of the calculated lift and moment data with the experimental data is excellent. The pressure-drag comparison was not presented because of the uncertainty of the amount of skin-friction drag present in the experimental results.

Brown, Clinton E↗
NASA NTRS1977

Review of radiative transfer methods in scattering atmospheres

The radiative transfer in a scattering plane-parallel atmosphere is discussed, considering the exact analytical, the computational and the approximate methods. Some results of numerical comparisons are given. Finally, the difficulties of realistic atmospheric models are emphasized.

Lenoble, J.↗
NASA NTRS1951

Method of successive approximations for the solution of certain problems in aerodynamics

A method of successive approximations for the solution of problems in the fields of diffusion, boundary-layer flow, and heat-transfer is illustrated by solving problems in each of these fields. In most of the examples, the approximate solutions are compared with known accurate solutions and the agreement is shown to be good.

FLOW, TURBULENT - DIFFUSION↗
DOE OSTI2025

Solving high-dimensional partial integral differential equations: The finite expression method

Partial integro-differential equations (PIDEs) have broad applications in the sciences, from electro-magnetism to options pricing. Here, in this paper, we introduce a new finite expression method (FEX) to solve PIDEs. This approach builds upon the original FEX and its inherent advantages with new advances: 1) A novel method of parameter grouping is proposed to reduce the number of coefficients in high-dimensional function approximation; 2) A Taylor series approximation method is implemented to significantly improve the computational efficiency and accuracy of the evaluation of the integral terms of PIDEs. The new FEX based method, denoted FEX-PG to indicate the addition of the parameter grouping (PG) step to the algorithm, provides both high accuracy and interpretable numerical solutions, with the outcome being an explicit equation that facilitates intuitive understanding of the underlying solution structures. These features are often absent in traditional methods, such as finite element methods (FEM) and finite difference methods, as well as in deep learning-based approaches. To benchmark our method against recent advances, we apply the new FEX-PG to solve benchmark PIDEs in the literature. In high-dimensional settings, FEX-PG exhibits strong and robust performance, achieving relative errors on the order of single precision machine epsilon, significantly outperforming existing approaches based on neural networks.

Combinatorial optimization↗
NASA NTRS1991

Combining global and local approximations

A method based on a linear approximation to a scaling factor, designated the 'global-local approximation' (GLA) method, is presented and shown capable of extending the range of usefulness of derivative-based approximations to a more refined model. The GLA approach refines the conventional scaling factor by means of a linearly varying, rather than constant, scaling factor. The capabilities of the method are demonstrated for a simple beam example with a crude and more refined FEM model.

Haftka, Raphael T.↗
NASA NTRS1985

Application of axisymmetric analogue for calculating heating in three-dimensional flows

A rapid, approximate method has been developed for calculating the heating rates on three-dimensional vehicles such as the Space Shuttle Orbiter and other advanced reentry configurations. The method is based on the axisymmetric analogue for three-dimensional boundary layers. It uses information obtained from a three-dimensional inviscid flowfield solution, such as HALIS, to calculate inviscid surface streamlines along which approximate heating rates are calculated independent of what happens along other streamlines. Three-dimensional effects are included through the metric coefficient that describes the divergence or convergence of streamlines. Boundary-layer edge properties are obtained from the inviscid flowfield solution by interpolating in the inviscid flowfield at a distance equal to the boundary-layer thickness away from the wall. This accounts, approximately, for the variable boundary-layer edge entropy. Using this method, heating calculations can be made along a typical streamline in a few seconds. This method has been used to accurately predict heating rates for simple shapes such as a spherically blunted cone and more complex shapes such as the Shuttle Orbiter for a variety of wind-tunnel and flight conditions. A unique feature of the method is its ability to accurately predict heating rates on the Shuttle Orbiter wing.

Hamilton, H. H.↗
NASA NTRS1926

The reduction of airplane flight test data to standard atmosphere conditions

This report was prepared for the National Advisory Committee for Aeronautics in order to supply the need of practical methods of reducing observed performance to standard conditions with a minimum of labor. The first part gives a very simple approximate method of reducing performance in climb, and is particularly adapted to work not requiring extreme accuracy. The second part gives a somewhat more elaborate and more accurate method which is well suited to general flight test reduction. The third part gives the conventional method of calibrating air-speed indicators and reducing the indicated speeds to true air speeds. An appendix gives working tables and charts for the standard atmosphere. (author)

Diehl, Walter S↗
NASA NTRS1993

Polarimetric thermal emission from rough surfaces

Recent theoretical works have suggested the potential of passive polarimetry in the remote sensing of geophysical media. It was shown that the third Stokes parameter U of the thermal emission may become larger for azimuthally asymmetric fields of observation. In order to investigate the potential applicability of passive polarimetry to the remote sensing of ocean surface, measurements of the polarimetric thermal emission from a sinusoidal water surface and a numerical study of the polarimetric thermal emission from randomly rough ocean surfaces were performed. Measurements of sinusoidal water surface thermal emission were performed using a sinusoidal water surface which was created by placing a thin sheet of fiberglass with a sinusoidal profile in two dimensions extended infinitely in the third dimension onto a water surface. The theory of thermal emission from a 'two-layer' periodic surface is derived and the exact solution is performed using both the extended boundary condition method (EBC) and the method of moments (MOM). The theoretical predictions are found to be in good agreement with the experimental results once the effects of the radiometer antenna pattern are included and the contribution of background noise to the measurements is modeled. The experimental results show that the U parameter indicates the direction of periodicity of the water surface and can approach values of up to 30 K for the surface observed. Next, a numerical study of polarimetric thermal emission from randomly rough surfaces was performed. A Monte Carlo technique utilizing an exact method for calculating thermal emission was chosen for the study to avoid any of the limitations of the commonly used approximate methods in rough surface scattering. In this Monte Carlo technique, a set of finite rough surface profiles in two dimensions with desired statistics was generated and extended periodically. The polarimetric thermal emission from each surface of the set was then calculated using both the EBC and the MOM and the results were averaged. The surface statistics chosen were intended to model a wind perturbed ocean surface in the X to Ku band microwave region. The results indicate that the U parameter is sensitive to the azimuthal angle between the surface periodicity and the looking angle and to the rms height of the surface, and that the U parameter is fairly insensitive to variations in polar angle, permittivity, surface power law spectrum, and surface spectrum high frequency cutoff. These properties give further strength to the idea of using the U parameter to detect wind direction over the ocean.

Johnson, J. T.↗
NASA NTRS2022

Numerical Results for Polarized Light Scattering in a Spherical Atmosphere

We report numerical results for polarized light reflection from the top of a Rayleigh scattering spherical atmosphere with height-dependent single scattering albedo over a dark surface. Michael Mishchenko considered this scenario back in the 1990’s, for a plane-parallel atmosphere of unit optical thickness (OT), for which radiance errors arising from neglecting polarization reaches their highest values. To further extend Mishchenko’s results, we consider a value of OT = 0.25, for which the effect of atmospheric curvature is pronounced. New results are generated using three state-of-the art radiative transfer (RT) codes. These are: the MYSTIC and MCSSA models, which simulate light scattering in a true- spherical atmosphere using Monte Carlo methods; and the discrete ordinate code VLIDORT, operating with a new multiple-scatter spherical correction designed to deliver reasonable approximations to spherical-medium scattering. In this work, we report results for both single and multiple scattering; this will help to support the validation of existing and future polarized spherical RT codes, especially those using approximative methods to deal with sphericity.

S Korkin↗
NASA NTRS1987

Suboptimal shape control for quasi-static distributed-parameter systems

An on-line control approach which will adjust the steady-state shape of a large antenna arbitrarily close to any achievable desired profile is approached. The method makes use of distributed-parameter system theory and allows refocusing using a limited number of control actuators and sensors. The controller gains are calculated by approximating the solution to an infinite-dimensional optimal quasi-static control problem. The controller gain calculation is computationally simpler than that previously proposed. The Galerkin (finite element) approximation method is used for model reduction. It is proved that both gain and state convergence can be achieved by using the proposed approximation scheme.

Balas, M. J.↗
DOE OSTI2026

Deep Neural Networks are Adaptive to Function Regularity and Data Distribution in Approximation and Estimation

Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Nev- ertheless, the majority of these studies examine how well deep neural networks can model functions with uniform regularities. In this paper, we explore a different angle: how deep neural networks can adapt to varying degrees of smoothness in functions and nonuni- form data distributions across different locations and scales. More precisely, we focus on a broad class of functions defined by nonlinear tree-based approximation methods. This class encompasses a range of function types, such as functions with uniform regularities and discontinuous functions. We develop nonparametric approximation and estimation theories for this class using deep ReLU networks. Our results show that deep neural networks are adaptive to the nonuniform smoothness of functions and nonuniform data distributions at different locations and scales. We apply our results to several function classes, and derive the corresponding approximation and generalization errors. The validity of our results is demonstrated through numerical experiments.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1974

Applicability of the diffusion approximation

Several methods using an approximate form of the scattering indicatrix are discussed for simplifying the calculation of radiation transport in planetary atmospheres.

Biryukov, Y. L.↗
NASA NTRS1979

A new approach to the solution of large, full matrix equations: A two-dimensional potential flow feasibility study

An approach to the solution of matrix problems resulting from integral equations of mathematical physics is presented. Based on the inherent smoothness in such equations, the problem is reformulated using a set of orthogonal basis vectors, leading to an equivalent coefficient problem which can be of lower order without significantly impairing the accuracy of the solution. This approach was evaluated using a two-dimensional Neumann problem describing the inviscid, incompressible flow over an airfoil. Two different kinds of mode functions were investigated, namely eigenfunction series and Fourier series. The method using Fourier series was found preferable. It uses all of the coefficients from a Fast Fourier Transform algorithm in an approximate method which exploits the known structure of the transformed coefficient matrix and very promising results for the flow over a realistic airfoil are obtained. On the basis of the results presented here, an order of magnitude reduction in this computer time can be expected for such problems as compared with the time for a direct matrix solution.

James, R. M.↗
NASA NTRS1991

Unified Aeroacoustics Analysis for High Speed Turboprop Aerodynamics and Noise: Development of Theory for Blade Loading, Wakes, and Noise - Volume 1

A unified theory for the aerodynamics and noise of advanced turboprops are presented. Aerodynamic topics include calculation of performance, blade load distribution, and non-uniform wake flow fields. Blade loading can be steady or unsteady due to fixed distortion, counter-rotating wakes, or blade vibration. The aerodynamic theory is based on the pressure potential method and is therefore basically linear. However, nonlinear effects associated with finite axial induction and blade vortex flow are included via approximate methods. Acoustic topics include radiation of noise caused by blade thickness, steady loading (including vortex lift), and unsteady loading. Shielding of the fuselage by its boundary layer and the wing are treated in separate analyses that are compatible but not integrated with the aeroacoustic theory for rotating blades.

Hanson, D. B.↗
NASA NTRS1935

Computation of the two-dimensional flow in a laminar boundary layer

A comparison is made of the boundary-layer flow computed by the approximate method developed by K. Pohlhausen with the exact solutions which have been published for several special cases. A modification of Pohlhausen's method has been developed which extends the range of application at the expense of some decrease in the accuracy of the approximations.

Dryden, Hugh L↗
NASA NTRS1983

Methods for Estimating Payload/Vehicle Design Loads

Several methods compared with respect to accuracy, design conservatism, and cost. Objective of survey: reduce time and expense of load calculation by selecting approximate method having sufficient accuracy for problem at hand. Methods generally applicable to dynamic load analysis in other aerospace and other vehicle/payload systems.

Chen, J. C.↗