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Results for “Boundary value problem”

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At least 523 records · Page 29

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NASA NTRS1975

A general algorithm using finite element method for aerodynamic configurations at low speeds

A finite element algorithm for numerical simulation of two-dimensional, incompressible, viscous flows was developed. The Navier-Stokes equations are suitably modelled to facilitate direct solution for the essential flow parameters. A leap-frog time differencing and Galerkin minimization of these model equations yields the finite element algorithm. The finite elements are triangular with bicubic shape functions approximating the solution space. The finite element matrices are unsymmetrically banded to facilitate savings in storage. An unsymmetric L-U decomposition is performed on the finite element matrices to obtain the solution for the boundary value problem.

Balasubramanian, R.↗

NASA NTRS1975

Subsonic flow past an oscillating cascade with steady blade loading - Basic formulation

A nonlinear boundary value problem governing the subsonic flow in a single, extended, blade passage region of a high-deflection, two dimensional, oscillating cascade is derived. The blades are assumed to be undergoing identical harmonic motions of small amplitude with constant phase angle between the motion of adjacent blades. An asymptotic perturbation approach is used to determine the velocity potential. This formulation can be used in the numerical determination of unsteady potential and thus the unsteady aerodynamic force and moment under various combinations of cascade and flow parameters.

Verdon, J. M.↗

NASA NTRS1976

Rotating stratified flow over finite isolated topography

Inviscid, steady, stratified rotating flow over a finite, isolated topographic feature is critically analyzed. The formulation is based on approximating the horizontal momentum by the geostrophic momentum. A boundary value problem governs the perturbation pressure field. The solution is an anticyclonic, topographically-bound vortex whose characteristics are independent of the upstream velocity but do depend on stratification, rotation, and the nature of the topography. The vortex is baroclinic in the vicinity of the mountain but barotropic in the far field. The velocity field is a combination of the bound vortex and an upstream velocity interacting with the perturbation pressure field. The effects of stratification, upstream velocity and the nature of the topography are investigated, and fluid trajectories are plotted.

Merkine, L.-O.↗

NASA NTRS1976

On the Navier-Stokes equations with constant total temperature

For various applications in fluid dynamics, one can assume that the total temperature is constant. Therefore, the energy equations can be replaced by an algebraic relation. The resulting set of equations in the inviscid case is analyzed in this paper. It is shown that the system is strictly hyperbolic and well posed for the initial-value problem. Boundary conditions are described such that the linearized system is well posed. The hopscotch method is investigated and numerical results are presented.

Gottlieb, D.↗

NASA NTRS1976

A systematic method for computer design of supercritical airfoils in cascade

A computer code has been developed for the direct calculation of shockless transonic airfoils whose pressure distributions can be assigned within reasonable limits. The partial differential equations of two-dimensional inviscid gas dynamics are solved by analytic continuation into the domain of two independent complex characteristic coordinates. The domain of integration is mapped conformally onto the unit circle in the hodograph plane of one of these coordinates. It is possible to formulate a boundary value problem on this circle for the stream function that is well posed in the case of transonic flow. This enables the formulation of a procedure for the calculation of an airfoil on which the speed is prescribed as a function of the arc length

Garabedian, P.↗

NASA NTRS1976

Analysis of multicircuit shells of revolution by the field method

The reported investigation represents a continuation of studies conducted by Cohen (1974). The current analysis treats a much broader class of connected graphs which may contain multiple circuits. Attention is given to the definition of a boundary-value problem, the field relations, a plan of the field method, differential equations for field functions, initial values of field functions, and shells of revolution.

Cohen, G. A.↗

NASA NTRS1976

Stress intensity at a crack between bonded dissimilar materials

The contour integral method is extended to general boundary value problems involving imperfect bonding of dissimilar materials. The loading and restraints are shown to have a significant effect on the stress intensity. Example problems are presented to illustrate the results.

Stern, M.↗

NASA NTRS1976

Transonic flow theory of airfoils and wings

There are plans to use the supercritical wing on the next generation of commercial aircraft so as to economize on fuel consumption by reducing drag. Computer codes have served well in meeting the consequent demand for new wing sections. The possibility of replacing wind tunnel tests by computational fluid dynamics is discussed. Another approach to the supercritical wing is through shockless airfoils. A novel boundary value problem in the hodograph plane is studied that enables one to design a shockless airfoil so that its pressure distribution very nearly takes on data that are prescribed.

Garabedian, P. R.↗

NASA NTRS1976

The influence of the atmosphere on geoid and potential coefficient determinations from gravity data

For the precise computation of geoid undulations the effect of the attraction of the atmosphere on the solution of the basic boundary value problem of gravimetric geodesy must be considered. This paper extends the theory of Moritz for deriving an atmospheric correction to the case when the undulations are computed by combining anomalies in a cap surrounding the computation point with information derived from potential coefficients. The correction term is a function of the cap size and the topography within the cap. It reaches a value of 3.0 m for a cap size of 30 deg, variations on the decimeter level being caused by variations in the topography. The effect of the atmospheric correction terms on potential coefficients is found to be small, reaching a maximum of 0.0055 millionths at n = 2, m = 2 when terrestrial gravity data are considered. The magnitude of this correction indicates that in future potential coefficient determination from gravity data the atmospheric correction should be made to such data.

Rummel, R.↗

NASA NTRS1977

Plasma rotation by electric and magnetic fields in a discharge cylinder

A theoretical model for an electric discharge consisting of a spatially diverging plasma sustained electrically between a small ring cathode and a larger ring anode in a cylindrical chamber with an axial magnetic field is developed to study the rotation of the discharge plasma in the crossed electric and magnetic fields. The associated boundary-value problem for the coupled partial differential equations which describe the electric potential and the plasma velocity fields is solved in closed form. The electric field, current density, and velocity distributions are discussed in terms of the Hartmann number and the Hall coefficient. As a result of Lorentz forces, the plasma rotates with speeds as high as 1 million cm/sec around its axis of symmetry at typical conditions. As an application, it is noted that rotating discharges of this type could be used to develop a high-density plasma-ultracentrifuge driven by j x B forces, in which the lighter (heavier) ion and atom components would be enriched in (off) the center of the discharge cylinder.

Wilhelm, H. E.↗

NASA NTRS1977

Exact Green's function method of solar force-free magnetic-field computations with constant alpha. I - Theory and basic test cases

Exact closed-form solutions to the solar force-free magnetic-field boundary-value problem are obtained for constant alpha in Cartesian geometry by a Green's function approach. The uniqueness of the physical problem is discussed. Application of the exact results to practical solar magnetic-field calculations is free of series truncation errors and is at least as economical as the approximate methods currently in use. Results of some test cases are presented.

Chiu, Y. T.↗

NASA NTRS1977

Thermal microwave emission from a random inhomogeneous layer over a homogeneous medium using the method of invariant imbedding

The paper studies thermal microwave emission from an inhomogeneous slab of a random medium, with possible nonuniform absorption, scattering, and temperature profiles, bounded by different dielectrics on both sides. The invariant imbedding method is used to cast the boundary value problem of the radiative transfer equations into an initial value problem at zero slab thickness. As a numerical example, the angular and polarization variations of brightness temperatures for ice over water are considered.

Tsang, L.↗

NASA NTRS1977

Nonlinear stress waves in a perfectly flexible string

This paper discusses nonlinear stress-wave propagation in a perfectly flexible string obeying a quasilinear (rate-dependent) constitutive equation. Wave speeds and compatibility relations valid along various families of characteristics were determined. It was shown that the compatibility relations associated with the transverse as well as the longitudinal waves readily yield a physical interpretation when they are expressed in suitable variables and in vector form. Coding based on the present information was completed for the machine solution of a class of mixed initial- and boundary-value problems of practical interest. Computer simulation of the stress-wave interaction in the 40-foot lanyard in the Arcas 'Rocoz' system during deployment was carried out using a stress-strain relation for nylon at the strain rate of 30/second. A method for estimating the maximum tension and strain in a string during the initial loading phase is proposed.

Fan, D.-N.↗

NASA NTRS1977

Propagation along azimuthally magnetized ferrite-loaded circular waveguides

The paper describes the modal dispersion characteristics of electromagnetic waves traveling along the azimuthally magnetized ferrite-loaded coaxial transmission line and the ferrite-loaded wire. The modal dispersion curves are used to determine the pass and stop bands of normal propagation. Boundary-value problems were solved with Bolle-Heller functions. The dispersion characteristics of transverse electric modes are presented as plots of the normalized propagation constant vs the normalized frequency.

Mueller, R. S.↗

NASA NTRS1977

Generalized Theodorsen solution for singular integral equations of the airfoil class

A class of singular integral equations is considered which arise in various two-dimensional mixed boundary-value problems with simple harmonic time variation. A problem typical of this class is that of determining the lifting pressure distribution on an oscillating airfoil in an unbounded incompressible potential flow. It is shown that Theodorsen's (1935) solution to this problem, with some modification, is valid for a general class of unsteady kernel functions. The technique employed is to consider an equivalent steady problem and then show that the unsteady resolvent and unsteady homogeneous solution can be written directly in terms of the steady solutions and a single frequency-dependent function which reduces to the Theodorsen function for the steady kernel.

Williams, M. H.↗

NASA NTRS1977

Dynamical theory of stability for elastic rods with nonlinear curvature and twist

Considering non-linear terms in the curvature as well as in the twist, the governing boundary value problem for lateral bending of elastic, transverse loaded rods is formulated by means of Hamilton's principle. Using the method of small vibrations, the associated linearized equations of stability are derived, which complete the currently accepted relations. The example of the simplest lateral bending problem illustrates the improved effect of the proposed equations.

Wauer, J.↗

NASA NTRS1978

A high order accurate finite element algorithm for high Reynolds number flow prediction

A Galerkin-weighted residuals formulation is employed to establish an implicit finite element solution algorithm for generally nonlinear initial-boundary value problems. Solution accuracy, and convergence rate with discretization refinement, are quantized in several error norms, by a systematic study of numerical solutions to several nonlinear parabolic and a hyperbolic partial differential equation characteristic of the equations governing fluid flows. Solutions are generated using selective linear, quadratic and cubic basis functions. Richardson extrapolation is employed to generate a higher-order accurate solution to facilitate isolation of truncation error in all norms. Extension of the mathematical theory underlying accuracy and convergence concepts for linear elliptic equations is predicted for equations characteristic of laminar and turbulent fluid flows at nonmodest Reynolds number. The nondiagonal initial-value matrix structure introduced by the finite element theory is determined intrinsic to improved solution accuracy and convergence. A factored Jacobian iteration algorithm is derived and evaluated to yield a consequential reduction in both computer storage and execution CPU requirements while retaining solution accuracy.

Baker, A. J.↗

NASA NTRS1978

System analysis of plasma centrifuges and sputtering

System analyses of cylindrical plasma centrifuges are presented, for which the velocity field and electromagnetic fields are calculated. The effects of different electrode geometrics, induced magnetic fields, Hall-effect, and secondary flows are discussed. It is shown that speeds of 10000 m/sec can be achieved in plasma centrifuges, and that an efficient separation of U238 and U235 in uranium plasmas is feasible. The external boundary-value problem for the deposition of sputtering products is reduced to a Fredholm integral equation, which is solved analytically by means of the method of successive approximations.

Hong, S. H.↗