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At least 505 records · Page 28
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NASA NTRSDate not supplied

Comparison of Two Approaches to Constructing Second- and Third-Order Nodal-Gradient Cell-Centered Finite-Volume Methods for Mixed-Element Grids

In this paper, we introduce a third-order nodal-gradient cell-centered finite volume scheme applicable to mixed-element grids based on a single numerical flux per face. Previously, we considered a split-quadrilateral-face approach, where we split each quadrilateral face of a non-tetrahedral cell into two triangles and then apply second- and third-order schemes designed for tetrahedral grids. This approach is relatively simple to implement but expensive because it requires two numerical flux evaluations per quadrilateral face. In this study, we consider another approach, where the surface flux quadrature is performed with a single numerical flux per face with flux corrections. It requires a 3×3 correction matrix to be stored at each face but is more economical than the split-quadrilateral-face approach. The two approaches are compared for three-dimensional flows on irregular hexahedral grids, and their relative merits are discussed.

Third-order scheme↗
NASA NTRS1968

Tool reconstructs data input points corresponding to first order output graph

Tool aids in graphic determination of input values for any first order lag system of known gain and time constant where the corresponding output function is displayed graphically and can be described by a first order differential equation. This tool permits a rapid reconstruction of input points.

Biggs, R. E.↗
NASA NTRS1972

Nth-order flat approximation of the signum function by a polynomial

In the interval studied, the signum function, sgn x, was demonstrated to be uniquely approximated by an odd polynomial f sub n (x) of order 2n-1, for which the approximation is nth order flat with respect to the points (1,1) and (-1,-1). A theorem was proved which states that for even integers n or = 2, the approximating polynomial has a pair of nonzero real roots + or - x sub n such that the x sub n form a monotonically decreasing sequence which converges to the root of 2 as n approaches infinity. For odd n i, f sub n (x) represents a strictly increasing monotonic function for all real x. As n tends to infinity, f sub n (x) converges to sgn x uniformly in two interval ranges.

Hosenthien, H. H.↗
NASA NTRS1972

Some higher order analyses of earth and lunar orbiters

The accurate modelling of the translational behavior of a drag-free satellite in an almost circular near-earth orbit is investigated. All short and long period position fluctuations in the satellite's coordinates down to 1 m are determined. The general zonal and tesseral harmonic effects are considered as well as lunar and solar effects. A noncanonical approach is followed. A mean orbital plane is chosen so that no short period out-of-plane fluctuations greater than second order occur. Short period radial and cross-track fluctuations and in-track fluctuations are computed. Long period and secular rates of the mean elements which define the slowly varying plane of reference are determined to third order in the small quantities. The equations of motion are integrated analytically away from critical inclination and tesseral resonance. The resonant situation of a sun-synchronous orbit is discussed as a special case. The long-period behavior of a lunar orbiter is also considered, including the effects due to the inclination of the earth's apparent orbit about the moon and those described by Cassini laws on the equations of motion. Both resonant and nonresonant low orbits, and high orbits are discussed.

Dasenbrock, R. R.↗
NASA NTRS1971

Field-ion microscopy of ordered Cu-Au alloy.

A method is proposed for overcoming current difficulties in measuring atomic order parameters of nonrefractory metals when using the field-ion microscope (FIM). Near stoichiometric CuAu and Cu3Au were tested by means of this method. Images of substantially fully ordered CuAu and Cu3Au thus obtained are presented and discussed.

Son, U. T.↗
NASA NTRS1973

The relationship between eddy-transport and second-order closure models for stratified media and for vortices

The question is considered of how complex a model should be used for the calculation of turbulent shear flows. At the present time there are models varying in complexity from very simple eddy-transport models to models in which all the equations for the nonzero second-order correlations are solved simultaneously with the equations for the mean variables. A discussion is presented of the relationship between these two models of turbulent shear flow. Two types of motion are discussed: first, turbulent shear flow in a stratified medium and, second, the motion in a turbulent line vortex. These two cases are instructive because in the first example eddy-transport methods have proven reasonably effective, whereas in the second, they have led to erroneous conclusions. It is not generally appreciated that the simplest form of eddy-transport theory can be derived from second-order closure models of turbulent flow by a suitably limiting process. This limiting process and the suitability of eddy-transport modeling for stratified media and line vortices are discussed.

Donaldson, C. D.↗
NASA NTRS1973

Interpretation of land use and stream order, Pawnee River Basin, Kansas

The author has identified the following significant results. Land use and stream orders were mapped from ERTS-1 imagery covering the Pawnee River Basin. Total area of the basin, irrigated dry land crop area, and rangeland area were determined. The stream order of the basin was calculated by the Strahler method and provided more detail than is available on the comparable 1:250,000 sheets. This study has demonstrated the feasibility of using ERTS-1 imagery to map stream networks in greater detail than is required for 1:250,000 scale. The utility of ERTS-1 has also been demonstrated for mapping and mensuration of data relating to performance of ground cover types and the extent of irrigation.

Morain, S. A.↗
NASA NTRS1972

On higher order discrete phase-locked loops.

An exact mathematical model is developed for a discrete loop of a general order particularly suitable for digital computation. The deterministic response of the loop to the phase step and the frequency step is investigated. The design of the digital filter for the second-order loop is considered. Use is made of the incremental phase plane to study the phase error behavior of the loop. The model of the noisy loop is derived and the optimization of the loop filter for minimum mean-square error is considered.

Gill, G. S.↗
NASA NTRS1974

Third-order phase-locked loop receiver

Third-order extension to present second-order systems extends their Doppler tracking capabilities. It widens receiver pull-in range, decreases pull-in time, lowers voltage-controlled oscillator (VCO) noise (determining when no signal is present), and lessens susceptibility to VCO drift.

Crow, R. B.↗
NASA NTRS1974

The 13th order resonance from Navy tracking on a diademe 2 fragment

A strong constraint on 13th order (odd degree) terms in the geopotential has been derived from Navy tracking on a DIADEME 2 fragment (1967-14F). This object (perigee height: 580 km, orbit inclination: 38.9 deg) is presently decaying slowly through perfect commensurability with these terms. The resonance forces will increase its inclination by 0.02 deg when the passage is complete by late 1974. The constraint (lumped harmonics), derived by adjustment of a pair of harmonic coefficients to the Navy inclination data (principally) is: 10 to the 9th power (14.8 + or - 0.8, 48.3 + or - 0.7) = 0.023(C,S)13,13 -0.172(C,S)15,13 0.505(C,S)17,13 - 0.884(C,S)19,13 + (C,S)21,13 0.673(C,S)23,13 0.099(C,S)25,13 0.295(C,S)27,13 -0.279(C,S)29,13 0.018(C,S)31,13 + There should be a significant contribution to this result from terms as high as 29th degree. But current geopotential solutions (for 13th order terms) to this degree are about 20% in error when judged by this independent data.

Wagner, C. A.↗