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NASA NTRSDate not supplied

TPSAS-NF1676L-33433-DND

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for aircraft noise reduction, and are characterized by a complex valued frequency-dependent impedance. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic scattering of geometric bodies treated with acoustic liners. This work considers using either an impedance boundary condition or admittance boundary condition to allow acoustic scattering problems to be modeled with geometries consisting of both un-lined and lined surfaces; admittance is defined to be the inverse of impedance. Three different acoustic liner models will be discussed: the Extended Helmholtz Resonator Model, the Three-Parameter Impedance Model, and a Broadband Model. In the Extended Helmholtz Resonator Model and Three-Parameter Impedance Model, the liner impedance is specified at a single frequency; the Broadband Model allows for the investigation of multiple frequencies simultaneously. The impedance and admittance boundary conditions for each model will be derived and coupled with a time-domain boundary integral equation. The scattering solution will be obtained iteratively using spatial and temporal basis functions. Stability will be demonstrated through eigenvalue analysis. Moreover, fast algorithms and high performance computing are considered to both assess and reduce the computational cost of the simulation.

Michelle E Rodio↗
NASA NTRS1996

A Numerical Simulation of Scattering from One-Dimensional Inhomogeneous Dielectric Random Surfaces

In this paper, an efficient numerical solution for the scattering problem of inhomogeneous dielectric rough surfaces is presented. The inhomogeneous dielectric random surface represents a bare soil surface and is considered to be comprised of a large number of randomly positioned dielectric humps of different sizes, shapes, and dielectric constants above an impedance surface. Clods with nonuniform moisture content and rocks are modeled by inhomogeneous dielectric humps and the underlying smooth wet soil surface is modeled by an impedance surface. In this technique, an efficient numerical solution for the constituent dielectric humps over an impedance surface is obtained using Green's function derived by the exact image theory in conjunction with the method of moments. The scattered field from a sample of the rough surface is obtained by summing the scattered fields from all the individual humps of the surface coherently ignoring the effect of multiple scattering between the humps. The statistical behavior of the scattering coefficient sigma(sup 0) is obtained from the calculation of scattered fields of many different realizations of the surface. Numerical results are presented for several different roughnesses and dielectric constants of the random surfaces. The numerical technique is verified by comparing the numerical solution with the solution based on the small perturbation method and the physical optics model for homogeneous rough surfaces. This technique can be used to study the behavior of scattering coefficient and phase difference statistics of rough soil surfaces for which no analytical solution exists.

Sarabandi, Kamal↗
NASA NTRS2002

A Two-Dimensional Linear Bicharacteristic FDTD Method

The linear bicharacteristic scheme (LBS) was originally developed to improve unsteady solutions in computational acoustics and aeroacoustics. The LBS has previously been extended to treat lossy materials for one-dimensional problems. It is a classical leapfrog algorithm, but is combined with upwind bias in the spatial derivatives. This approach preserves the time-reversibility of the leapfrog algorithm, which results in no dissipation, and it permits more flexibility by the ability to adopt a characteristic based method. The use of characteristic variables allows the LBS to include the Perfectly Matched Layer boundary condition with no added storage or complexity. The LBS offers a central storage approach with lower dispersion than the Yee algorithm, plus it generalizes much easier to nonuniform grids. It has previously been applied to two and three-dimensional free-space electromagnetic propagation and scattering problems. This paper extends the LBS to the two-dimensional case. Results are presented for point source radiation problems, and the FDTD algorithm is chosen as a convenient reference for comparison.

Beggs, John H.↗
NASA NTRS1992

A finite element: Boundary integral method for electromagnetic scattering

A method that combines the finite element and boundary integral techniques for the numerical solution of electromagnetic scattering problems is presented. The finite element method is well known for requiring a low order storage and for its capability to model inhomogeneous structures. Of particular emphasis in this work is the reduction of the storage requirement by terminating the finite element mesh on a boundary in a fashion which renders the boundary integrals in convolutional form. The fast Fourier transform is then used to evaluate these integrals in a conjugate gradient solver, without a need to generate the actual matrix. This method has a marked advantage over traditional integral equation approaches with respect to the storage requirement of highly inhomogeneous structures. Rectangular, circular, and ogival mesh termination boundaries are examined for two-dimensional scattering. In the case of axially symmetric structures, the boundary integral matrix storage is reduced by exploiting matrix symmetries and solving the resulting system via the conjugate gradient method. In each case several results are presented for various scatterers aimed at validating the method and providing an assessment of its capabilities. Important in methods incorporating boundary integral equations is the issue of internal resonance. A method is implemented for their removal, and is shown to be effective in the two-dimensional and three-dimensional applications.

Collins, J. D.↗
NASA NTRS1987

New main reflector, subreflector and dual chamber concepts for compact range applications

A compact range is a facility used for the measurement of antenna radiation and target scattering problems. Most presently available parabolic reflectors do not produce ideal uniform plane waves in the target zone. Design improvements are suggested to reduce the amplitude taper, ripple and cross polarization errors. The ripple caused by diffractions from the reflector edges can be reduced by adding blended rolled edges and shaping the edge contour. Since the reflected edge continues smoothly from the parabola onto the rolled surface, rather than being abruptly terminated, the discontinuity in the reflected field is reduced which results in weaker diffracted fields. This is done by blending the rolled edges from the parabola into an ellipse. An algorithm which enables one to design optimum blended rolled edges was developed that is based on an analysis of the continuity of the surface radius of curvature and its derivatives across the junction. Futhermore, a concave edge contour results in a divergent diffracted ray pattern and hence less stray energy in the target zone. Design equations for three-dimensional reflectors are given. Various examples were analyzed using a new physical optics method which eliminates the effects of the false scattering centers on the incident shadow boundaries. A Gregorian subreflector system, in which both the subreflector and feed axes are tilted, results in a substantial reduction in the amplitude taper and cross polarization errors. A dual chamber configuration is proposed to eliminate the effects of diffraction from the subreflector and spillover from the feed. A computationally efficient technique, based on ray tracing and aperture integration, was developed to analyze the scattering from a lossy dielectric slab with a wedge termination.

Pistorius, C. W. I.↗
NASA NTRS1995

A 3D High-Order Unstructured Finite-Volume Algorithm for Solving Maxwell's Equations

A three-dimensional finite-volume algorithm based on arbitrary basis functions for time-dependent problems on general unstructured grids is developed. The method is applied to the time-domain Maxwell equations. Discrete unknowns are volume integrals or cell averages of the electric and magnetic field variables. Spatial terms are converted to surface integrals using the Gauss curl theorem. Polynomial basis functions are introduced in constructing local representations of the fields and evaluating the volume and surface integrals. Electric and magnetic fields are approximated by linear combinations of these basis functions. Unlike other unstructured formulations used in Computational Fluid Dynamics, the new formulation actually does not reconstruct the field variables at each time step. Instead, the spatial terms are calculated in terms of unknowns by precomputing weights at the beginning of the computation as functions of cell geometry and basis functions to retain efficiency. Since no assumption is made for cell geometry, this new formulation is suitable for arbitrarily defined grids, either smooth or unsmooth. However, to facilitate the volume and surface integrations, arbitrary polyhedral cells with polygonal faces are used in constructing grids. Both centered and upwind schemes are formulated. It is shown that conventional schemes (second order in Cartesian grids) are equivalent to the new schemes using first degree polynomials as the basis functions and the midpoint quadrature for the integrations. In the new formulation, higher orders of accuracy are achieved by using higher degree polynomial basis functions. Furthermore, all the surface and volume integrations are carried out exactly. Several model electromagnetic scattering problems are calculated and compared with analytical solutions. Examples are given for cases based on 0th to 3rd degree polynomial basis functions. In all calculations, a centered scheme is applied in the interior, while an upwind matching scheme is employed at material interfaces and the Engquist-Majda non-reflecting boundary condition is implemented at the numerical outer boundaries. The staggered leapfrog scheme and the Runge-Kutta methods are utilized for the time integration. Excellent agreements are found between the numerical and analytical solutions.

Liu, Yen↗
NASA NTRS1972

Generalized pseudopotential approach for electron-atom scattering.

A generalized many-electron pseudopotential approach is presented for electron-neutral-atom scattering problems. A calculation based on this formulation is carried out for the singlet s-wave and p-wave electron-hydrogen phase shifts with excellent results. We compare the method with other approaches as well as discuss its applications for inelastic and rearrangement collision problems.

Zarlingo, D. G.↗
NASA NTRS1977

Hybrid methods are helpful

Multiple scattering problems in a plane layer often permit the convenient use of different methods joined together. Sample numerical results to illustrate this point refer to X- and Y-functions, asymptotic fitting, the small-loss approximations, polarization in high orders, and photon path distribution.

Vandehulst, H. C.↗
NASA NTRS1977

Microwave scattering properties of snow fields

Experimental results were presented showing backscatter dependence on frequency, angle of incidence, snow wetness, and frequency modulation. Theoretical studies were made of the inverse scattering problem yielding some preliminary results concerning the determination of the dielectric constant of the snow layer. The experimental results lead to the following conclusions: (1) snow layering affects backscatter; (2) layer response was significant up to 45 degrees of incidence; (3) wetness modifies snow layer effects; and (4) frequency modulation masks the layer response.

Angelakos, D. J.↗
NASA NTRS1978

Research of microwave scattering properties of snow fields

The results obtained in the research program of microwave scattering properties of snow fields are presented. Experimental results are presented showing backscatter dependence on frequency (5.8-8.0 GHz), angle of incidence (0-60 degrees), snow wetness (time of day), and frequency modulation (0-500 MHz). Theoretical studies are being made of the inverse scattering problem yielding some preliminary results concerning the determination of the dielectric constant of the snow layer. The experimental results lead to the following conclusions: snow layering affects backscatter, layer response is significant up to 45 degrees of incidence, wetness modifies snow layer effects, frequency modulation masks the layer response, and for the proper choice of probing frequency and for nominal snow depths, it appears to be possible to measure the effective dielectric constant and the corresponding water content of a snow pack.

Angelakos, D. J.↗
NASA NTRS1978

Ionosphere/microwave beam interaction study

The microwave beam of the Solar Power Satellite (SPS) is predicted to interact with the ionosphere producing thermal runaway up to an altitude of about 100 kilometers at a power density threshold of 12 mW/cm sq (within a factor of two). The operation of the SPS at two frequencies, 2450 and 5800 MHz, is compared. The ionosphere interaction is less at the higher frequency, but the tropospheric problem scattering from heavy rain and hail is worse at the higher frequency. Microwave signals from communication satellites were observed to scintillate, but there is some concern that the uplink pilot signal may be distorted by the SPS heated ionosphere. The microwave scintillations are only observed in the tropics in the early evenings near the equinoxes. Results indicate that large phase errors in the uplink pilot signal can be reduced.

Gordon, W. E.↗
NASA NTRS1984

A tentative unified sea model for scattering and emission

This work is an attempt to relate active and passive observations of the sea surface to each other, considering that more information can be obtained from a set of instruments when they are not just considered as a juxtaposition of separate and independent boxes, but as a single complex instrument. A careful review of several approaches to the solution of the scattering problem for a random rough surface has been performed. Inherent simplifications, and inconsistencies, are pointed out. To reduce the computation time to reasonable values, an approximate model is selected and some numerical results will be presented in order to illustrate the benefit that can be gained by a unified approach.

Guissard, A.↗
NASA NTRS1986

Further atomic calculations for Fe XXIII

Electron collision strengths for Fe XXIII have been obtained using the 'distorted wave' approximation. Previous results (Bhatia and Mason, 1981) were obtained including the configurations 2s(2), 2s2p, 2p(2), 2s3s, 2s3p, and 2s3d. In this paper, the correlation configurations 2p3s, 2p3p and 2p3d have also been included in the solution of the electron scattering problem.

Bhatia, A. K.↗
NASA NTRS1987

How good is the impedance boundary condition?

The impedance boundary condition (IBC) is often used in scattering problems involving material-coated conducting bodies. It is shown that for some commonly encountered coating configurations, the value of the impedance varies significantly as functions of the incident angle and polarization. Hence, the use of IBC in a rigorously formulated problem may affect the accuracy of the final solution.

Lee, Shung-Wu↗
NASA NTRS1988

Electromagnetic scattering analysis on a hypercube parallel architecture

The applicability of a parallel architecture to the solution of large electromagnetic scattering problems is demonstrated. Two techniques, finite difference and the method of moments, are used to provide insight into the comparative speedups which can be attained for several algorithms. The flexibility of the hypercube architecture for different analysis algorithms is illustrated.

Patterson, Jean E.↗
NASA NTRS1988

Ray-tube integration in shooting and bouncing ray method

Based on three formulations of the Huygen's principle, explicit expressions is given for the far field contribution from a small ray tube. This expression is useful in shooting and bouncing rays for solving complex scattering problems.

Lee, S. W.↗