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Results for “Elliptic problems”

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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

On the far-field stream function condition for two-dimensional incompressible flows

The present demonstration of the usefulness of the integral series expansion of the stream function as a far-field computational boundary condition shows the method to require only a 10-percent/time-step increase in computational effort over alternative boundary conditions, in the case of implementation of unsteady problems using a direct elliptic solver. So long as the vorticity was encompassed within the computational domain, the method proved sufficiently accurate to yield virtually identical results for two widely different domains. While the integral-series condition yielded the best results for periodic flow, the Neumann condition gave comparable accuracy with less computation time for the steady-flow case despite its inability to treat periodic flow with vortex shedding.

Sa, Jong-Youb↗
NASA NTRS1991

The Titan-Hyperion orbital resonance

Considerable effort was spent investigating the applicability of a Hamiltonian averaged over high frequency terms, where long period and secular terms up to second order in eccentricity were kept. The Hamiltonian that is given from the planar, elliptic, restricted three body problem applied to Titan-Hyperion, when the Kepler terms are also expanded to second order in small quantities and several conical transformations are carried out, is presented and discussed.

Peale, S. J.↗
NASA NTRS1993

Efficient Minimum-Polynomial And Reduced-Rank Extrapolation

MPERRE computer program accelerates convergence of sequence of vectors by use of minimum-polynomial extrapolation (MPE) and reduced-rank extrapolation (RRE). Effective in accelerating convergences of such sequences of vectors as those obtained from iterative solution of systems of linear and nonlinear equations. In conjunction with various iterative techniques, successfully employed in finite-difference solution of large-scale elliptic boundary-value problems and problems in computational-fluid-dynamics. Only input required is sequence of vectors, convergence of which is accelerated. Program economical and easy to use. Written in FORTRAN 77.

Sidi, Avram↗
NASA NTRS1987

Algebraic multigrid

The state of the art in algebraic multgrid (AMG) methods is discussed. The interaction between the relaxation process and the coarse grid correction necessary for proper behavior of the solution probes is discussed in detail. Sufficient conditions on relaxation and interpolation for the convergence of the V-cycle are given. The relaxation used in AMG, what smoothing means in an algebraic setting, and how it relates to the existing theory are considered. Some properties of the coarse grid operator are discussed, and results on the convergence of two-level and multilevel convergence are given. Details of an algorithm particularly studied for problems obtained by discretizing a single elliptic, second order partial differential equation are given. Results of experiments with such problems using both finite difference and finite element discretizations are presented.

Ruge, J. W.↗
NASA NTRS1971

Method for constructing periodic orbits in nonlinear dynamic systems

Method is modification of generalized Newton-Ralphson algorithm for analyzing two-point boundary problems. It constructs sequence of solutions that converge to precise dynamic solution in the sequence limit. Program calculates periodic orbits in either circular or elliptical restricted three-body problems.

Bennett, A. G.↗
NASA NTRS1977

Elastohydrodynamic lubrication of elliptical contacts for materials of low elastic modulus. I - Fully flooded conjunction

A complete numerical solution is presented to the problem of isothermal elastohydrodynamic lubrication of elliptical contacts for low-elastic-modulus materials operating under fully loaded conditions. No assumption is made for the pressure or film thickness within the contact, and compressibility and viscous effects are taken into account. Because of the dimensionless representation of the coordinates, the actual Hertzian contact ellipse becomes a circle regardless of the value of the ellipticity parameter. A minimum-film-thickness relation and a central-film-thickness relation are derived from examining 17 different cases. Contour plots for detailed illustration of the pressure distribution and film thickness in the conjunction are provided.

Hamrock, B. J.↗
NASA NTRS1990

Raked circular-cone aerobraking orbital transfer vehicle

An aerobraking orbital transfer vehicle (AOTV) (80) has aerobrake (82) with a blunted raked-off circular-cone configuration. The other components of the AOTV, including command/control module (95), fuel tanks (86, 88, 89 and 91), rocket engines (94) and afterbody (84), are positioned substantially along resultant force axis (104) of the AOTV (80). The axis (104) coincides with the resultant (sum of lift and drag) force vector. Afterbody (84) is mounted behind the aerobrake (82) with its length extending rearwardly from the aerobrake. The base flow clearance angle .phi. of the aerobrake (80) is 25.degree., thus allowing the afterbody (84) to extend rearwardly from the aerobrake (82) to a much greater extent than possible with a raked-off elliptic-cone aerobraking shield configuration. Afterbody size limitation and other problems associated with the raked-off elliptic-cone aerobraking shield configuration are alleviated by the combination of the aerobrake shape and positioning of the fuel tanks (86, 88, 89 and 91), rocket engines (94) and afterbody (84).

Park, Chul↗
NASA NTRS1975

Isothermal elastohydrodynamic lubrication of point contacts. II - Ellipticity parameter results

A numerical solution of the isothermal elastohydrodynamic problem for point contacts has been presented which reproduces all the essential features of the previously reported experimental observations based upon optical interferometry. In particular, the two 'side lobes' in which minimum film thickness regions occur are shown to emerge in the theoretical solutions. The influence of the ellipticity parameter upon solutions to the point contact problem has been explored in the present paper. The ellipticity parameter (k) was varied from one (a ball on a plate) to eight (a configuration approaching line contact), and it has been shown that both the central and minimum film thicknesses can be related to the well known line contact solutions by remarkably simple expressions involving either (k) or the effective radius of curvature ratio (Ry/Rx).

Hamrock, B. J.↗
NASA NTRS1973

Solution of the stochastic control problem in unbounded domains.

Bellman's dynamic programming equation for the optimal index and control law for stochastic control problems is a parabolic or elliptic partial differential equation frequently defined in an unbounded domain. Existing methods of solution require bounded domain approximations, the application of singular perturbation techniques or Monte Carlo simulation procedures. In this paper, using the fact that Poisson impulse noise tends to a Gaussian process under certain limiting conditions, a method which achieves an arbitrarily good approximate solution to the stochastic control problem is given. The method uses the two iterative techniques of successive approximation and quasi-linearization and is inherently more efficient than existing methods of solution.

Robinson, P.↗
NASA NTRS1983

Analysis of surface pressure distributions on two elliptic missile configurations

The state-of-the-art methods for predicting missile aerodynamic characteristics do not accurately predict the loads of missile configurations with bodies of elliptic cross section. An investigation of this problem found significant nonlinear flow disturbance on the windward surface of a 3:1 elliptic body at Mach 2.50 in addition to the nonlinear vortical flows which develop on the leeside. A nonlinear full-potential flow method (NCOREL) was found to provide extremely accurate pressure estimates for attached-flow conditions and the vortex prediction method contained in the state-of-the-art method (NOSEVTX) was shown to accurately calculate body vortices and leeside pressures.

Allen, J. M.↗
NASA NTRS1987

Isoparametric finite element methods to estimate discontinuous coefficients in two-dimensional elliptic equations

A summary of findings is presented on the problem of estimating discontinuous coefficients, including the locations of interfaces at which discontinuities occur, for elliptic equations on a two-dimensional domain. Finite-element approximations are constructed that are based on an underlying grid that adaptively moves to follow locations of interfaces as they are iteratively updated in the numerical estimation process.

Lamm, Patricia K.↗
NASA NTRS2010

GOATS - Orbitology Component

The GOATS Orbitology Component software was developed to specifically address the concerns presented by orbit analysis tools that are often written as stand-alone applications. These applications do not easily interface with standard JPL first-principles analysis tools, and have a steep learning curve due to their complicated nature. This toolset is written as a series of MATLAB functions, allowing seamless integration into existing JPL optical systems engineering modeling and analysis modules. The functions are completely open, and allow for advanced users to delve into and modify the underlying physics being modeled. Additionally, this software module fills an analysis gap, allowing for quick, high-level mission analysis trades without the need for detailed and complicated orbit analysis using commercial stand-alone tools. This software consists of a series of MATLAB functions to provide for geometric orbit-related analysis. This includes propagation of orbits to varying levels of generalization. In the simplest case, geosynchronous orbits can be modeled by specifying a subset of three orbit elements. The next case is a circular orbit, which can be specified by a subset of four orbit elements. The most general case is an arbitrary elliptical orbit specified by all six orbit elements. These orbits are all solved geometrically, under the basic problem of an object in circular (or elliptical) orbit around a rotating spheroid. The orbit functions output time series ground tracks, which serve as the basis for more detailed orbit analysis. This software module also includes functions to track the positions of the Sun, Moon, and arbitrary celestial bodies specified by right ascension and declination. Also included are functions to calculate line-of-sight geometries to ground-based targets, angular rotations and decompositions, and other line-of-site calculations. The toolset allows for the rapid execution of orbit trade studies at the level of detail required for the early stage of mission concept development.

Haber, Benjamin M.↗
NASA NTRS1976

Dynamical study of the Hilda asteroids. I - Resonant orbital motion of the PLS objects from the Palomar-Leiden Survey

Schubart's (1968) model of a planar elliptic restricted three-body problem is used to study the orbital motion of the Hilda asteroids from the Palomar-Leiden Survey. The 3:2 resonant coupling to Jupiter of some of these small asteroids is found to be stable. However, some of the small asteroids with absolute magnitude greater than 15 have large amplitude of variation in their orbital elements in one libration period. Since the lifetime scales against catastrophic collision of the Hilda asteroids are estimated to be several times larger than those of the main-belt objects, a significant portion of these resonant asteroids could be the original members of the Hilda group. From this point of view, it is suggested that such 'size dependence' of resonant orbital motions might be the result of cosmogonic effects of jet-stream accretion.

Ip, W.-H.↗
NASA NTRS1980

Numerical investigation of the onset of separation of an incompressible viscous flow from objects in ducts

Simulation has been used to investigate the phenomenon of separation of a steady flow of an incompressible viscous fluid from a symmetric object in a duct. Two essentially two-dimensional problems were studied: (1) an elliptical cylinder located between two parallel plates, and (2) a sphere placed on the axis of a cylindrical pipe. The steady-state vorticity transport equation and the second order differential equation relating vorticity and the stream function were iterated using the method of overrelaxation to obtain a solution for each set of initial conditions. The relationship between the Reynolds number corresponding to the onset of separation and the size of the object relative to the duct was found to be linear over a wide range.

Winchester, L. W., Jr.↗
NASA NTRS1982

The origin of the Kirkwood gaps - A mapping for asteroidal motion near the 3/1 commensurability

A mapping of the phase space onto itself with the same low-order resonance structure as the 3/1 commensurability in the planar-elliptic restricted three-body problem is obtained. This mapping is about 1,000 times faster than the usual method of numerically integrating the averaged equations of motion. It exhibits some surprising behavior that might provide a key to the origin of the Kirkwood gaps. It is noted that a test asteroid placed in the gap may evolve for a million years with low eccentricity (less than 0.05) and then suddenly jump to large eccentricity (greater than 0.3), becoming a Mars crosser. The removal of the asteroid by a close encounter with Mars would then be possible. As a first test of this hypothesis, a distribution of 300 test asteroids in the area of the 3/1 commensurability was evolved for two million years. When the Mars crossers are removed, the distribution of initial conditions reveals a gap at the location of the 3/1 Kirkwood gap.

Wisdom, J.↗
NASA NTRS1985

A perturbative treatment of motion near the 3/1 commensurability

A semianalytic perturbation theory for motion near the 3/1 commensurability in the planar elliptic restricted three-body problem is presented. The predictions of the theory are in good agreement with the features found on numerically generated surfaces of section; a global understanding of the phase space is achieved. The principal cause of the large chaotic zone near the 3/1 commensurability is identified, and a new criterion for the existence of large-scale chaotic behavior is presented.

Wisdom, J.↗