SEARCH · Engineering Papers

Results for “numerical schemes”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,243 records · Page 69

All sources NASA NTRS DOE OSTI

NASA NTRS1980

Photofragmentation-laser induced fluorescence - A new method for detecting atmospheric trace gases

A new method for the in situ detection of nonfluorescing molecular species is proposed: photofragmentation-laser induced fluorescence (PF-LIF). In this approach, the species to be detected is first laser photolyzed at a wavelength lambda (1), producing one or more vibrationally excited photofragments. Before vibrational relaxation occurs, one of these photofragments is pumped into a bonding excited state by a second laser pulse centered at wavelength lambda (2). Fluorescence is sampled at a wavelength lambda (3), where lambda (3) is less then lambda (2) and lambda (1). This pumping configuration thus permits massive discrimination against Rayleigh and Raman scattering as well as white noise fluorescence from the laser wavelengths lambda (1) and lambda (2). The technique should be both highly sensitive and selective for numerous atmospheric trace gases. Specific sampling schemes for detecting NO2, NO3, and HNO2 are proposed. Various noise sources and chemical interferences are discussed. Specific calculations that estimate the sensitivity of the PF-LIF system for detecting NO2, NO3, and HNO2 are given.

Rodgers, M. O.↗

NASA NTRS1982

A comparative study of computational methods in cosmic gas dynamics

Many theoretical investigations of fluid flows in astrophysics require extensive numerical calculations. The selection of an appropriate computational method is, therefore, important for the astronomer who has to solve an astrophysical flow problem. The present investigation has the objective to provide an informational basis for such a selection by comparing a variety of numerical methods with the aid of a test problem. The test problem involves a simple, one-dimensional model of the gas flow in a spiral galaxy. The numerical methods considered include the beam scheme, Godunov's method (G), the second-order flux-splitting method (FS2), MacCormack's method, and the flux corrected transport methods of Boris and Book (1973). It is found that the best second-order method (FS2) outperforms the best first-order method (G) by a huge margin.

Van Albada, G. D.↗

NASA NTRS1982

Computation of transonic viscous-inviscid interacting flow

Transonic viscous-inviscid interaction is considered using the Euler and inverse compressible turbulent boundary-layer equations. Certain improvements in the inverse boundary-layer method are mentioned, along with experiences in using various Runge-Kutta schemes to solve the Euler equations. Numerical conditions imposed on the Euler equations at a surface for viscous-inviscid interaction using the method of equivalent sources are developed, and numerical solutions are presented and compared with experimental data to illustrate essential points.

Whitfield, D. L.↗

NASA NTRS1982

Difference equation state approximations for nonlinear hereditary control problems

Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems.

Rosen, I. G.↗

NASA NTRS1983

Stress and Fracture Analyses Under Elastic-plastic and Creep Conditions: Some Basic Developments and Computational Approaches

A new hybrid-stress finite element algorith, suitable for analyses of large quasi-static deformations of inelastic solids, is presented. Principal variables in the formulation are the nominal stress-rate and spin. A such, a consistent reformulation of the constitutive equation is necessary, and is discussed. The finite element equations give rise to an initial value problem. Time integration has been accomplished by Euler and Runge-Kutta schemes and the superior accuracy of the higher order schemes is noted. In the course of integration of stress in time, it has been demonstrated that classical schemes such as Euler's and Runge-Kutta may lead to strong frame-dependence. As a remedy, modified integration schemes are proposed and the potential of the new schemes for suppressing frame dependence of numerically integrated stress is demonstrated. The topic of the development of valid creep fracture criteria is also addressed.

Reed, K. W.↗

NASA NTRS1983

Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems

New convenient stability criteria are provided in this paper for a large class of finite difference approximations to initial-boundary value problems associated with the hyperbolic system u sub t = au sub x + Bu + f in the quarter plane x or = 0, t or = 0. Using the new criteria, stability is easily established for numerous combinations of well known basic schemes and boundary conditions, thus generalizing many special cases studied in recent literature.

Goldberg, M.↗

NASA NTRS1983

Computation of transonic viscous-inviscid interacting flow

Whitfield, D. L.↗

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

Discrete approximation methods for parameter identification in delay systems

Approximation schemes for parameter identification problems in which the governing state equation is a linear functional differential equation of retarded type are constructed. The basis of the schemes is the replacement of the parameter identification problem having an infinite dimensional state equation by a sequence of approximating parameter identification problems in which the states are given by finite dimensional discrete difference equations. The difference equations are constructed using linear semigroup theory and rational function approximations to the exponential. Sufficient conditions are given for the convergence of solutions to the approximating problems, which can be obtained using conventional methods, to solutions to the original parameter identification problem. Finite difference and spline based schemes using Paderational function approximations to the exponential are constructed, and shown to satisfy the sufficient conditions for convergence. A discussion and analysis of numerical results obtained through the application of the schemes to several examples is included.

Rosen, I. G.↗

NASA NTRS1984

Difference equation state approximations for nonlinear hereditary control problems

Rosen, I. G.↗

NASA NTRS1985

A 3-dimensional mass conserving element for compressible flows

A variety of finite element schemes has been used in the numerical approximation of compressible flows particularly in underwater acoustics. In many instances instabilities have been generated due to the lack of mass conservation. Two- and three-dimensional elements are developed which avoid these problems.

Fix, G.↗

NASA NTRS1985

Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems

New convenient stability criteria are provided in this paper for a large class of finite difference approximations to initial-boundary value problems associated with the hyperbolic system u sub t = au sub x + Bu + f in the quarter plane x or = 0, t or = 0. Using the new criteria, stability is easily established for numerous combinations of well known basic schemes and boundary conditins, thus generalizing many special cases studied in recent literature.

Goldberg, M.↗

NASA NTRS1985

New stability criteria for difference approximations of hyperbolic initial-boundary value problems

New convenient stability criteria are provided for a large class of finite difference approximations to initial-boundary value problems associated with the hyperbolic system u sub t = Au sub x + Bu + f in the quarter plane x greater than or equal to 0, t greater than or equal to 0. The criteria are used to easily establish stability for numerous combinations of well known basic schemes and boundary conditions, thus generalizing many special cases studied in the recent literature. A number of examples are examined, including the unitary unconditionally stable Crank-Nicholson scheme and an almost-dissipative unconditionally stable backward Euler scheme.

Goldberg, M.↗

NASA NTRS1985

Synopsis of the Fifth Conference on the Meteorology of the Stratosphere and Mesosphere

The papers presented at the Fifth Conference on the Meteorology of the Stratosphere and Mesosphere held on April 23-26, 1985, are reviewed. The observational aspects of large-scale circulation, such as summer and winter circulation in the Southern Hemisphere, and analysis schemes, like the multivariate statistical analysis scheme, are discussed. The topics of numerical simulations of the general circulation and sudden-warming are examined. Papers concerning processes of O3, NO2, H2, and HNO3 are described. Research on large-scale mixing processes in the stratosphere is presented. The topic of equatorial dynamics and stability is analyzed. Papers focusing on the effect of gravity waves on the general circulation are studied.

Schoeberl, M. R.↗

NASA NTRS1985

A three-dimensional boundary-layer method for flow over delta wings with leading-edge separation

A three-dimensional, laminar boundary-layer method is applied to the incompressible flow over a slender delta wing at incidence. The predictor-corrector finite-difference scheme of Matsuno is used to difference the governing equations. The method has the advantages that no iterations are required to advance the solution and the cross-flow derivatives are formed independent of the cross-field direction. The difference scheme is demonstrated to yield accurate numerical results when compared to the exact solution of the three-dimensional boundary-layer equations for parabolic flow over a moving flat plate. The method is applied to delta wings of various sweep angles at angles of attack up to 20 deg., with the inviscid solution determined using a higher-order, three-dimensional panel method.

Woodson, S. H.↗

NASA NTRS1986

Computational fluid mechanics utilizing the variational principle of modeling damping seals

A computational fluid dynamics code for application to traditional incompressible flow problems has been developed. The method is actually a slight compressibility approach which takes advantage of the bulk modulus and finite sound speed of all real fluids. The finite element numerical analog uses a dynamic differencing scheme based, in part, on a variational principle for computational fluid dynamics. The code was developed in order to study the feasibility of damping seals for high speed turbomachinery. Preliminary seal analyses have been performed.

Abernathy, J. M.↗

NASA NTRS1987

The minimal residual QR-factorization algorithm for reliably solving subset regression problems

A new algorithm to solve test subset regression problems is described, called the minimal residual QR factorization algorithm (MRQR). This scheme performs a QR factorization with a new column pivoting strategy. Basically, this strategy is based on the change in the residual of the least squares problem. Furthermore, it is demonstrated that this basic scheme might be extended in a numerically efficient way to combine the advantages of existing numerical procedures, such as the singular value decomposition, with those of more classical statistical procedures, such as stepwise regression. This extension is presented as an advisory expert system that guides the user in solving the subset regression problem. The advantages of the new procedure are highlighted by a numerical example.

Verhaegen, M. H.↗

NASA NTRS1987

Wave envelope technique for multimode wave guide problems

A numerical solution technique for two-dimensional EM waveguide problems is developed analytically and demonstrated. The frequency-domain waveguide problem is transformed to a time-dependent problem and treated following the limiting-amplitude principle; the wave-envelope technique is applied; and the resulting problem is solved numerically using a finite-difference scheme based on a variation of the finite-area method (Baumeister, 1977 and 1984). Results for several sample problems, obtained in 10 min or less of execution time on PCs, are presented in tables.

Hariharan, S. I.↗