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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 703 records · Page 39
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

An efficient, direct finite difference method for computing sound propagation in arbitrarily shaped two-dimensional and axisymmetric ducts without flow

An efficient, direct finite difference method is presented for computing sound propagation in non-stepped two-dimensional and axisymmetric ducts of arbitrarily varying cross section without mean flow. The method is not restricted by axial variation of acoustic impedance of the duct wall linings. The non-uniform two-dimensional or axisymmetric duct is conformally mapped numerically into a rectangular or cylindrical computational domain using a new procedure based on a method of fast direct solution of the Cauchy-Riemann equations. The resulting Helmholtz equation in the computational domain is separable. The solution to the governing equation and boundary conditions is expressed as a linear combination of fundamental solutions. The fundamental solutions are computed only once for each duct shape by means of the fast direct cyclic reduction method for the discrete solution of separable elliptic equations. Numerical results for several examples are presented to show the applicability and efficiency of the method.

Chakravarthy, S.↗
NASA NTRS1978

The stability of numerical methods for second order ordinary differential equations

An important characterization of a numerical method for first order ODE's is the region of absolute stability. If all eigenvalues of the linear problem dy/dt = Ay are inside this region, the numerical method is stable. If the second order system d/dt(dy/dt) = 2Ady/dt - By is solved as a first order system, the same result applies to the eigenvalues of the generalized eigenvalue problem (lambda-squared)I 2(lambda)A + B. No such region exists for general methods for second order equations, but in some cases a region of absolute stability can be defined for methods for the single second order equation d/dt(dy/dt) = 2ady/dt - by. The absence of a region of absolute stability can occur when different members of a system of first order equations are solved by different methods.

Gear, C. W.↗
NASA NTRS1978

Extrapolation methods for dynamic partial differential equations

Several extrapolation procedures are presented for increasing the order of accuracy in time for evolutionary partial differential equations. These formulas are based on finite difference schemes in both the spatial and temporal directions. On practical grounds the methods are restricted to schemes that are fourth order in time and either second, fourth or sixth order in space. For hyperbolic problems the second order in space methods are not useful while the fourth order methods offer no advantage over the Kreiss-Oliger method unless very fine meshes are used. Advantages are first achieved using sixth order methods in space coupled with fourth order accuracy in time. Computational results are presented confirming the analytic discussions.

Turkel, E.↗
NASA NTRS1978

The artificial compression method for computation of shocks and contact discontinuities. III - Self-adjusting hybrid schemes

This paper presents a new computational method for the calculation of discontinuous solutions of hyperbolic systems of conservation laws, which deal effectively with both shock and contact discontinuities. The method consists of two stages: in the first stage a standard finite-difference scheme is hybridized with a nonoscillatory first order accurate method to provide for the monotonic variation of the solution near discontinuities, and in the second stage artificial compression is applied to sharpen transitions at discontinuities. This modification of a standard finite-difference method results in a scheme which preserves the order of truncation error of the original method and yet yields a sharp and oscillation free transition for both shocks and contact discontinuities. The modification can be easily implemented in existing computer codes.

Harten, A.↗
NASA NTRS1978

Interpolation and extrapolation of creep rupture data by the minimum commitment method. II - Oblique translation

An outline is presented of a new procedure, termed the oblique translation method, which emerged in the development of the focal point convergence method. Approaches for implementing the oblique translation method are discussed. It is shown that the new method is essentially a minimum commitment method when manually-graphically implemented, in the sense that the form of the functions involved are not forced into particular analytical forms. The individual constants and functions are independently determined. The minimum commitment concept is extended to the analysis of creep rupture data wherein each isothermal is to be generated by an oblique translation of the 'master curve' when plotted. Attention is given to a manual-graphical analysis, the preassessment of data, and an analysis by computer code.

Manson, S. S.↗
NASA NTRS1978

The cost of applying current helicopter external noise reduction methods while maintaining realistic vehicle performance

Analytical methods were developed and/or adopted for calculating helicopter component noise, and these methods were incorporated into a unified total vehicle noise calculation model. Analytical methods were also developed for calculating the effects of noise reduction methodology on helicopter design, performance, and cost. These methods were used to calculate changes in noise, design, performance, and cost due to the incorporation of engine and main rotor noise reduction methods. All noise reduction techniques were evaluated in the context of an established mission performance criterion which included consideration of hovering ceiling, forward flight range/speed/payload, and rotor stall margin. The results indicate that small, but meaningful, reductions in helicopter noise can be obtained by treating the turbine engine exhaust duct. Furthermore, these reductions do not result in excessive life cycle cost penalties. Currently available main rotor noise reduction methodology, however, is shown to be inadequate and excessively costly.

Bowes, M. A.↗
NASA NTRS1979

Studies on remote sensing method of particle size and water density distribution in mists and clouds using laser radar techniques

A method of remote measurement of the particle size and density distribution of water droplets was developed. In this method, the size of droplets is measured from the Mie scattering parameter which is defined as the total-to-backscattering ratio of the laser beam. The water density distribution is obtained by a combination of the Mie scattering parameter and the extinction coefficient of the laser beam. This method was examined experimentally for the mist generated by an ultrasonic mist generator and applied to clouds containing rain and snow. Compared with the conventional sampling method, the present method has advantages of remote measurement capability and improvement in accuracy.

Shimizu, H.↗
NASA NTRS1978

Study report on a double isotope method of calcium absorption

Some of the pros and cons of three methods to study gastrointestinal calcium absorption are briefly discussed. The methods are: (1) a balance study; (2) a single isotope method; and (3) a double isotope method. A procedure for the double isotope method is also included.

Source record↗
NASA NTRS1979

Numerical comparisons of panel methods at subsonic and supersonic speeds

Numerical comparisons between some recently developed surface panel methods and well-established methods are made to assess their accuracy at subsonic and supersonic speeds. The results at subsonic speeds indicate similar improvements for the methods investigated over the low order source method. At supersonic speeds, stable and accurate results were obtained with the surface panel methods. Significant differences between tangential mass flux and tangential velocity boundary conditions occurred, especially at low fineness ratios and higher Mach numbers. The advantages of the general source/doublet panel formulation at both subsonic and supersonic speeds are noted.

Thomas, J. L.↗
NASA NTRS1979

A method to estimate critical volumes

Methods for estimating the volume of the critical temperature used for the estimation of thermodynamic properties of substances are described. The possibility to estimate the critical temperature by using a combination of only eighteen atomic and structural contributions is shown. These contributions are listed and the critical temperature is given by a linear expression. By comparing the Vetere (1976) and Lydersen (1955) methods with the method discussed it is noted that while all three methods yield about the same average error (about 3%), the new method is superior in that it requires a smaller number of increments to fit data points.

Fedors, R. F.↗
NASA NTRS1979

An accurate method for two-point boundary value problems

A second-order method for solving two-point boundary value problems on a uniform mesh is presented where the local truncation error is obtained for use with the deferred correction process. In this simple finite difference method the tridiagonal nature of the classical method is preserved but the magnitude of each term in the truncation error is reduced by a factor of two. The method is applied to a number of linear and nonlinear problems and it is shown to produce more accurate results than either the classical method or the technique proposed by Keller (1969).

Walker, J. D. A.↗
NASA NTRS1979

Solution of a few nonlinear problems in aerodynamics by the finite elements and functional least squares methods

The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.

Periaux, J.↗
NASA NTRS1979

New methods for predicting the magnitude of sunspot maximum

Three new and independent methods of predicting the magnitude of a forthcoming sunspot maximum are suggested. The longest lead time is given by the first method, which is based on a terrestrial parameter measured during the declining phase of the preceding cycle. The second method, with only a slightly shorter foreknowledge, is based on an interplanetary parameter derived around the commencement of the cycle in question (sunspot minimum). The third method, giving the shortest prediction lead-time, is based entirely on solar parameters measured during the initial progress of the cycle in question. Application of all three methods to forecast the magnitude of the next maximum (Cycle 21) agree in predicting that it is likely to be very similar to that of Cycle 18.

Brown, G. M.↗
NASA NTRS1980

An advanced panel method for analysis of arbitrary configurations in unsteady subsonic flow

An advanced method is presented for solving the linear integral equations for subsonic unsteady flow in three dimensions. The method is applicable to flows about arbitrary, nonplanar boundary surfaces undergoing small amplitude harmonic oscillations about their steady mean locations. The problem is formulated with a wake model wherein unsteady vorticity can be convected by the steady mean component of flow. The geometric location of the unsteady source and doublet distributions can be located on the actual surfaces of thick bodies in their steady mean locations. The method is an outgrowth of a recently developed steady flow panel method and employs the linear source and quadratic doublet splines of that method.

Dusto, A. R.↗
NASA NTRS1980

A correlation method to predict the surface pressure distribution of an infinite plate or a body of revolution from which a jet is issuing

A correlation method to predict pressures induced on an infinite plate by a jet exhausting normal to the plate into a subsonic free stream was extended to jets exhausting at angles to the plate and to jets exhausting normal to the surface of a body revolution. The complete method consisted of an analytical method which models the blockage and entrainment properties of the jet and an empirical correlation which accounts for viscous effects. For the flat plate case, the method was applicable to jet velocity ratios up to ten, jet inclination angles up to 45 deg from the normal, and radial distances up to five diameters from the jet. For the body of revolution case, the method was applicable to a body at zero degrees angle of attack, jet velocity ratios 1.96 and 3.43, circumferential angles around the body up to 25 deg from the jet, axial distances up to seven diameters from the jet, and jet-to-body diameter ratios less than 0.1.

Perkins, S. C., Jr.↗
NASA NTRS1979

Asymptotic continuation method for trajectory optimization

A continuation method is applied to a singular perturbation parameter to obtain a new numerical method for computing optimal trajectories. This method allows one to use simply calculated reduced order approximations as starting solutions and continue the perturbation parameter until the optimal full-order solution is obtained. The method does not require the calculation of higher order correction terms nor does it require the perturbation parameter to be small - thus, it has potentially superior convergence properties compared to conventional asymptotic expansions when the perturbation parameter is large. A simple trajectory optimization problem is considered to illustrate the method.

Washburn, R. B., Jr.↗
NASA NTRS1979

On finite element methods for the Helmholtz equation

The numerical solution of the Helmholtz equation is considered via finite element methods. A two-stage method which gives the same accuracy in the computed gradient as in the computed solution is discussed. Error estimates for the method using a newly developed proof are given, and the computational considerations which show this method to be computationally superior to previous methods are presented.

Aziz, A. K.↗
NASA NTRS1980

The Finite Analytic Method for steady and unsteady heat transfer problems

A new numerical method called the Finite Analytical Method for solving partial differential equations is introduced. The basic idea of the finite analytic method is the incorporation of the local analytic solution in obtaining the numerical solution of the problem. The finite analytical method first divides the total region of the problem into small subregions in which local analytic solutions are obtained. Then an algebraic equation is derived from the local analytic solution for each subregion relating an interior nodal value at a point P in the subregion to its neighboring nodal values. The assembly of all the local analytic solutions thus provides the finite-analytic numerical solution of the problem. In this paper the finite analytic method is illustrated in solving steady and unsteady heat transfer problems.

Chen, C.-J.↗