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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Investigating the Feasibility and Stability for Modeling Broadband Acoustic Wave Scattering using a Time-Domain Boundary Integral Equation

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. Acoustic liners are an effective tool for reducing aircraft noise and are characterized by a frequency-dependent impedance value. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering by geometric bodies treated with acoustic liners. A Broadband Impedance Model is discussed in which the liner impedance is specified along a wide range of frequencies. An impedance boundary condition is derived and coupled with a time-domain boundary integral equation to model acoustic scattering by a flat plate. It is assumed the flat plate has surfaces treated with acoustic liners. The stability of the numerical algorithm is assessed using eigenvalue analysis.

mathmatics↗
NASA NTRS1975

Remote monitoring of environmental particulate pollution - A problem in inversion of first-kind integral equations

The determination of the microstructure, chemical nature, and dynamical evolution of scattering particulates in the atmosphere is considered. A description is given of indirect sampling techniques which can circumvent most of the difficulties associated with direct sampling techniques, taking into account methods based on scattering, extinction, and diffraction of an incident light beam. Approaches for reconstructing the particulate size distribution from the direct and the scattered radiation are discussed. A new method is proposed for determining the chemical composition of the particulates and attention is given to the relevance of methods of solution involving first kind Fredholm integral equations.

Fymat, A. L.↗
NASA NTRS1993

Experimental and modal verification of an integral equation solution for a thin-walled dichroic plate with cross-shaped holes

In order to add the capability of an X-band uplink onto the 70-m antenna, a new dichroic plate is needed to replace the Pyle-guide-shaped dichroic plate currently in use. The replacement dichroic plate must exhibit an additional passband at the new uplink frequency of 7.165 GHz, while still maintaining a passband at the existing downlink frequency of 8.425 GHz. Because of the wide frequency separation of these two passbands, conventional methods of designing air-filled dichroic plates exhibit grating lobe problems. A new method of solving this problem by using a dichroic plate with cross-shaped holes is presented and verified experimentally. Two checks of the integral equation solution are described. One is the comparison to a modal analysis for the limiting cross shape of a square hole. As a final check, a prototype dichroic plate with cross-shaped holes was built and measured.

Epp, L. W.↗
NASA NTRS1987

Concepts for radically increasing the numerical convergence rate of the Euler equations

Integral equation and finite difference methods have been developed for solving transonic flow problems using linearized forms of the transonic small disturbance and Euler equations. A key element is the use of a strained coordinate system in which the shock remains fixed. Additional criteria are developed to determine the free parameters in the coordinate straining; these free parameters are functions of the shock location. An integral equation analysis showed that the shock is located by ensuring that no expansion shocks exist in the solution. The expansion shock appears as oscillations in the solution near the sonic line, and the correct shock location is determined by removing these oscillations. A second objective was to study the ability of the Euler equation to model separated flow.

Nixon, David↗
NASA NTRS1993

Coupling Finite Element and Integral Equation Representations To Efficiently Model Large Three-Dimensional Scattering Objects

The usefulness of finite element modeling follows from the ability to accurately simulate the gemetry and three-dimensional fields on the scale of a fraction of a wavelength. To make this meodelling practical for engineering design,it is necessary to integrate the stages of geometry modeling and mesh generation, numbeical solution and display of fields.

Integral Equations Finite Element↗
NASA NTRS2018

Addendum to "Impressed Sources and Fields in the Volume-Integral-Equation Formulation of Electromagnetic Scattering by a Finite Object: A Tutorial"

Our recent tutorial referred to in the title has summarized a general theoretical formalism of electromagnetic scattering by an arbitrary finite object in the presence of arbitrarily distributed impressed currents. This addendum builds on the tutorial to provide a streamlined discussion of specific far-field limits and the corresponding reciprocity relations by introducing appropriate far-field operators and linear maps and deriving the reciprocity relations through the pseudo adjoint of these maps. We thereby extend the compact operator calculus used previously to consider the fields and sources near or inside the scattering object.

Impressed Sources↗
NASA NTRS1988

Integral equation solution for transonic and subsonic aerodynamics

Two methods are presented to solve for the subsonic and transonic flows around airfoils. The first method is based on the integral solution of the full-potential equation with a shock-capturing technique only or with shock capturing-shock fitting technique. In the second method, the integral soluton of the full potential equation is coupled with an embedded region of Euler equations around the shock location. The second method is a computationally efficient technique for flows with strong shocks where the entropy increase and vorticity production across the shock are not small. Several numerical examples are presented and compared with the experimental data and other computational results.

Kandil, Osama A.↗
NASA NTRS1996

Singularity Preserving Numerical Methods for Boundary Integral Equations

In the past twelve months (May 8, 1995 - May 8, 1996), under the cooperative agreement with Division of Multidisciplinary Optimization at NASA Langley, we have accomplished the following five projects: a note on the finite element method with singular basis functions; numerical quadrature for weakly singular integrals; superconvergence of degenerate kernel method; superconvergence of the iterated collocation method for Hammersteion equations; and singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. This final report consists of five papers describing these projects. Each project is preceeded by a brief abstract.

Kaneko, Hideaki↗
NASA NTRS1982

An accurate method for evaluating the kernel of the integral equation relating lift to downwash in unsteady potential flow

The method is capable of generating approximations of arbitrary accuracy. It is based on approximating the algebraic part of the nonelementary integrals in the kernel by exponential functions and then integrating termwise. The exponent spacing in the approximation is a geometric sequence. The coefficients and exponent multiplier of the exponential approximation are computed by least squares so the method is completely automated. Exponential approximates generated in this manner are two orders of magnitude more accurate than the exponential approximation that is currently most often used for this purpose. The method can be used to generate approximations to attain any desired trade-off between accuracy and computing cost.

Desmarais, R. N.↗