Higher-order stationary-phase approximations in semiclassical scattering.
Higher order stationary-phase approximations in calculating corrections to classical differential cross section for elastic scattering
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The formation of cyanopolyyne molecules in IRC + 10216
Molecule formation in the outer envelope of the carbon-rich star IRC + 10216 is investigated, with special emphasis on the chemistry of the cyanopolyynes HC(i)N (i = 3, 5, 7). Basic elements of the photochemical model of Glassgold et al. (1986) are revised. A dust model suitable to IRC + 10216 is used for which the extinction properties in the far-UV are those of 500 A amorphous carbon particles. A new chemical route to the formation of large cyanopolyynes is proposed, based on reactions of the radicals C3N and C5N with acetylene, and shown to be efficient. Our results agree qualitatively with observations of the spatial distributions of HCN, CN, HC3N, and C3N, but the calculated column densities of the higher-order cyanopolyynes appear to be too small. The amount of the allenic radical HC2N produced by molecular ion reactions with atomic N agrees with recent observations.
Cherchneff, Isabelle↗
Effective Potential Energies and Transport Properties for Nitrogen and Oxygen
The results of recent theoretical studies for N--N2, O--O2, N2--N2 interactions are applied to the transport properties of nitrogen and oxygen gases. The theoretical results are used to select suitable oxygen interaction energies from previous work for determining the diffusion and viscosity coefficients at high temperatures. A universal formulation is applied to determine the collision integrals for O2--O2 interactions at high temperatures and to calculate certain ratios for determining higher-order collision integrals.
Stallcop, James R.↗
Using Derivatives Of Higher Order In Sensitivity Analysis
"What if" questions answered exactly, without using "increment-and-reevaluate" approach, and without finite differencing of system analysis, by use of sensitivity analysis to calculate first derivatives of behaviors of coupled systems with respect to design variables. If problem strongly nonlinear, efficiency improved by making derivatives of higher orders available to search algorithms. Extension effected by recursive application of same implicit function theorem that underlies previous method. Useful in design calculations for almost any system, including structures, machines, and distribution networks. Feedback control of processes improved by inclusion of derivative terms of higher order.
Sobieski, Jaroslaw↗
Use of shape-preserving interpolation methods in surface modeling
In many large-scale scientific computations, it is necessary to use surface models based on information provided at only a finite number of points (rather than determined everywhere via an analytic formula). As an example, an equation of state (EOS) table may provide values of pressure as a function of temperature and density for a particular material. These values, while known quite accurately, are typically known only on a rectangular (but generally quite nonuniform) mesh in (T,d)-space. Thus interpolation methods are necessary to completely determine the EOS surface. The most primitive EOS interpolation scheme is bilinear interpolation. This has the advantages of depending only on local information, so that changes in data remote from a mesh element have no effect on the surface over the element, and of preserving shape information, such as monotonicity. Most scientific calculations, however, require greater smoothness. Standard higher-order interpolation schemes, such as Coons patches or bicubic splines, while providing the requisite smoothness, tend to produce surfaces that are not physically reasonable. This means that the interpolant may have bumps or wiggles that are not supported by the data. The mathematical quantification of ideas such as physically reasonable and visually pleasing is examined.
Ftitsch, F. N.↗
An Introduction to the BFS Method and Its Use to Model Binary NiAl Alloys
We introduce the Bozzolo-Ferrante-Smith (BFS) method for alloys as a computationally efficient tool for aiding in the process of alloy design. An intuitive description of the BFS method is provided, followed by a formal discussion of its implementation. The method is applied to the study of the defect structure of NiAl binary alloys. The groundwork is laid for a detailed progression to higher order NiAl-based alloys linking theoretical calculations and computer simulations based on the BFS method and experimental work validating each step of the alloy design process.
Bozzolo, Guillermo↗
Quantification of Inlet Impedance Concept and a Study of the Rayleigh Formula for Noise Radiation from Ducted Fan Engines
This paper addresses two aspects of duct propagation and radiation which can contribute to more efficient fan noise predictions. First, we assess the effectiveness of Rayleigh's formula as a ducted fan noise prediction tool. This classical result which predicts the sound produced by a piston in a flanged duct is expanded to include the uniform axial inflow case. Radiation patterns using Rayleigh's formula with single radial mode input are compared to those obtained from the more precise ducted fan noise prediction code TBIEM3D. Agreement between the two methods is excellent in the peak noise regions both forward and aft. Next, we use TBIEM3D to calculate generalized radiation impedances and power transmission coefficients. These quantities are computed for a wide range of operating parameters. Results were obtained for higher Mach numbers, frequencies, and circumferential mode orders than have been previously published. Viewed as functions of frequency, calculated trends in lower order inlet impedances and power transmission coefficients are in agreement with known results. The relationships are more oscillatory for higher order modes and higher Mach numbers.
Posey, Joe W.↗
High-Order Polynomial Expansions (HOPE) for flux-vector splitting
The Van Leer flux splitting is known to produce excessive numerical dissipation for Navier-Stokes calculations. Researchers attempt to remedy this deficiency by introducing a higher order polynomial expansion (HOPE) for the mass flux. In addition to Van Leer's splitting, a term is introduced so that the mass diffusion error vanishes at M equals 0. Several splittings for pressure are proposed and examined. The effectiveness of the HOPE scheme is illustrated for 1-D hypersonic conical viscous flow and 2-D supersonic shock-wave boundary layer interactions. Also, the authors give the weakness of the scheme and suggest areas for further investigation.
Liou, Meng-Sing↗
High-Order Polynomial Expansions (HOPE) for flux-vector splitting
The Van Leer flux splitting is known to produce excessive numerical dissipation for Navier-Stokes calculations. Researchers attempt to remedy this deficiency by introducing a higher order polynomial expansion (HOPE) for the mass flux. In addition to Van Leer's splitting, a term is introduced so that the mass diffusion error vanishes at M = 0. Several splittings for pressure are proposed and examined. The effectiveness of the HOPE scheme is illustrated for 1-D hypersonic conical viscous flow and 2-D supersonic shock-wave boundary layer interactions.
Liou, Meng-Sing↗
A method for computing the leading-edge suction in a higher-order panel method
Experimental data show that the phenomenon of a separation induced leading edge vortex is influenced by the wing thickness and the shape of the leading edge. Both thickness and leading edge shape (rounded rather than point) delay the formation of a vortex. Existing computer programs used to predict the effect of a leading edge vortex do not include a procedure for determining whether or not a vortex actually exists. Studies under NASA Contract NAS1-15678 have shown that the vortex development can be predicted by using the relationship between the leading edge suction coefficient and the parabolic nose drag. The linear theory FLEXSTAB was used to calculate the leading edge suction coefficient. This report describes the development of a method for calculating leading edge suction using the capabilities of the higher order panel methods (exact boundary conditions). For a two dimensional case, numerical methods were developed using the double strength and downwash distribution along the chord. A Gaussian quadrature formula that directly incorporates the logarithmic singularity in the downwash distribution, at all panel edges, was found to be the best method.
Ehlers, F. E.↗
Calculation of compressible flow in and about three-dimensional inlets with and without auxiliary inlets by a higher-order panel method
A three dimensional higher order panel method was specialized to the case of inlets with auxiliary inlets. The resulting program has a number of graphical input-output features to make it highly useful to the designer. The various aspects of the program are described instructions for its use are presented.
Hess, J. L.↗
Preliminary Evaluation of the Simplified Higher Order Closure (SHOC) in the NASA Goddard Earth Observing System (GEOS)
Here we evaluate alternative planetary boundary layer (PBL) schemes in the NASA Goddard Earth Observing System (GEOS) model. The model currently calculates turbulent diffusivities with a local Richardson number-based scheme for stable layers, and a K-profile scheme with surface- and cloud-driven plumes based on Lock et al. (2000) for unstable layers. In this study, these are replaced with the TKE-based Simplified Higher Order Closure (SHOC). SHOC combines a 1.5-order turbulence closure with a double-Gaussian PDF serving as a subgrid condensation scheme. The new diffusivity calculations are paired with two new shallow mass flux schemes. First, the University of Washington shallow cumulus scheme of Park and Bretherton (2009), a buoyancy-sorting entraining-detraining bulk plume with overshooting entrainment and a TKE/CIN-based closure. Second, an Eddy Diffusivity Mass Flux (EDMF) scheme based on the multiple plume model of Suselj et al. (2013) with stochastic lateral entrainment. Global climatologies of low level temperature, humidity, and wind are evaluated against MERRA-2 and ERA-Interim reanalyses, and significant reductions in bias are seen with both mass flux schemes. The diurnal cycle over the continental United States is evaluated using MERRA-2 and an in situ network of surface Lidar profilers.
Arnold, Nathan↗
DNS, Enstrophy Balance, and the Dissipation Equation in a Separated Turbulent Channel Flow
The turbulent flows through a plane channel and a channel with a constriction (2-D hill) are numerically simulated using DNS and RANS calculations. The Navier-Stokes equations in the DNS are solved using a higher order kinetic energy preserving central schemes and a fifth order accurate upwind biased WENO scheme for the space discretization. RANS calculations are performed using the NASA code CFL3D with the komega SST two-equation model and a full Reynolds stress model. Using DNS, the magnitudes of different terms that appear in the enstrophy equation are evaluated. The results show that the dissipation and the diffusion terms reach large values at the wall. All the vortex stretching terms have similar magnitudes within the buffer region. Beyond that the triple correlation among the vorticity and strain rate fluctuations becomes the important kinematic term in the enstrophy equation. This term is balanced by the viscous dissipation. In the separated flow, the triple correlation term and the viscous dissipation term peak locally and balance each other near the separated shear layer region. These findings concur with the analysis of Tennekes and Lumley, confirming that the energy transfer terms associated with the small-scale dissipation and the fluctuations of the vortex stretching essentially cancel each other, leaving an equation for the dissipation that is governed by the large-scale motion.
Balakumar, Ponnampalam↗
Propagation of sound in elliptic ducts
The paper studies the propagation of sound in an elliptic duct, which is of considerable interest in the field of jet-engine noise reduction. The cutoff frequencies of the higher-order circumferential modes in an elliptic duct are calculated for various duct eccentricities. The results indicate that, if equal inlet area is retained, even major deformations of the inlet shape will have virtually no influence on the cutoff conditions of the radiated sound.
Lowson, M. V.↗
Potential flow past axisymmetric bodies at angle of attack
The Karamcheti (1966) suggestion concerning the use of higher order singularity techniques has been developed for the calculation of incompressible flow past an axisymmetric body at angle of attack. Attention is given to the results of a convergence study using this axial singularity method, where solution accuracy has been investigated for ellipsoids of slenderness ratio in the 1-10 range for both axial and inclined flow. Effects of singularity type, element number and size distribution, and singularity line inset distance, are noted, and a paneling scheme is developed which yields accurate results for the class of axisymmetric bodies having continuous body slopes with discontinuous curvature jumps.
Kuhlman, J. M.↗
Analysis of developing laminar flows in circular pipes using a higher-order finite-difference technique
A higher-order finite-difference technique is developed to calculate the developing-flow field of steady incompressible laminar flows in the entrance regions of circular pipes. Navier-Stokes equations governing the motion of such a flow field are solved by using this new finite-difference scheme. This new technique can increase the accuracy of the finite-difference approximation, while also providing the option of using unevenly spaced clustered nodes for computation such that relatively fine grids can be adopted for regions with large velocity gradients. The velocity profile at the entrance of the pipe is assumed to be uniform for the computation. The velocity distribution and the surface pressure drop of the developing flow then are calculated and compared to existing experimental measurements reported in the literature. Computational results obtained are found to be in good agreement with existing experimental correlations and therefore, the reliability of the new technique has been successfully tested.
Gladden, Herbert J.↗
Multiple scattering of electromagnetic waves by rain
As the operating frequencies of communications systems move higher into the millimeter wave region, the effects of multiple scattering in precipitation media become more significant. In this paper, general formulations are presented for single, first-order multiple, and complete multiple scattering. Included specifically are distributions of particle size, shape, and orientation angle, as well as variation in the medium density along the direction of wave propagation. Calculations are performed for rain. It is shown that the effects of higher-order scattering are not noticeable in either attenuation or channel isolation on a dual-polarized system until frequencies of about 30 GHz are reached. The complete multiple-scattering formulation presented gives accurate results at high millimeter wave frequencies as well as including realistic medium parameter distributions. Furthermore, it is numerically efficient.
Tsolakis, A.↗
Energy Levels of C IV: The Polarization Method
In a previous publication [Can. J. Phys. 75, 11 (1997)] we calculated the generalized polarizabilities up to multipole order 3 as well as certain higher-order hyperpolarizabilities for two-electron atoms and ions of Z=2-6 and 10. In this paper we apply some of these results to calculate excited-state energies in three times ionized (lithium-like) carbon. For states with angular momentum L greater than or equal to 3 accurate results are obtained using an asymptotic polarizability expansion that includes nonadiabatic effects. Comparison is made with recent optical measurements, and a critical discussion of the correct form of the expansion is given. In addition, the possibility of very accurate measurements of the fine-structure splitting encourages us to present a table of such splittings to very high accuracy. An appendix contains similar results for lithium-like oxygen and neon ions.
Bhatia, A. K.↗