Comparison of exact solution and high frecuency asymptotic methods in the cannonical wedge diffraction problem

AbstractThe Sommerfeld exact solution for canonical 2D wedge diffraction problem with perfectly conducting surfaces is presented. From the integral formulation of the problem, the Malyuzhinets solution is obtained and this result is extended to obtain the general impedance solution of canonical 2D wedge problem. Keller’s asymptotic solution is developed and the general formulation of exact solution it’s used to obtain general asymptotic methods for approximate solutions useful from the computational point of view. A simulation tool is used to compare numerical calculations of exact and asymptotic solutions. The numerical simulation of exact solution is compared to numerical simulation of an asymptoticmethod, and a satisfactory agreement found. Accuracy dependence with frequency is verified.

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A Diffraction Problem and Crack Propagation

Journal of Applied Mechanics ◽

10.1115/1.3607607 ◽

1967 ◽

Vol 34 (1) ◽

pp. 100-103 ◽

Cited By ~ 9

Author(s):

A. Jahanshahi

Keyword(s):

Exact Solution ◽

Stress Field ◽

Crack Propagation ◽

Elastic Medium ◽

Half Plane ◽

Diffraction Problem ◽

Shear Waves ◽

Stress Waves ◽

Plane Crack ◽

Antiplane Strain

The exact solution to the problem of diffraction of plane harmonic polarized shear waves by a half-plane crack extending under antiplane strain is constructed. The solution is employed to study the nature of the stress field associated with an extending crack in an elastic medium excited by stress waves.

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Exact solution to diffraction problem by wedges with a class of anisotropic impedance faces: oblique incidence of a plane electromagnetic wave

IEEE Transactions on Antennas and Propagation ◽

10.1109/tap.2003.812277 ◽

2003 ◽

Vol 51 (6) ◽

pp. 1216-1220 ◽

Cited By ~ 24

Author(s):

M.A. Lyalinov ◽

Ning Yan Zhu

Keyword(s):

Exact Solution ◽

Electromagnetic Wave ◽

Oblique Incidence ◽

Plane Electromagnetic Wave ◽

Diffraction Problem

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On the propagation of disturbances in a laminar boundary layer. II

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100077094 ◽

1973 ◽

Vol 73 (3) ◽

pp. 505-514 ◽

Cited By ~ 4

Author(s):

S. N. Brown ◽

K. Stewartson

Keyword(s):

Boundary Layer ◽

Exact Solution ◽

Laminar Boundary Layer ◽

Asymptotic Methods

AbstractThe assumption that disturbances are confined to the neighbourhood of the wall in the problem of Part I is invalidated by an exact solution of the resulting equation which shows that disturbances rapidly travel out of the region in which the equation is applicable. The asymptotic methods of Part I are also applied to this equation, which was studied by Lam and Rott (1), and an assessment is made of the role of the eigensolutions found by these authors.

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THE EFFECT OF AN EXPLOSION IN A COMPRESSIBLE FLUID UNDER GRAVITY

Canadian Journal of Physics ◽

10.1139/p61-157 ◽

1961 ◽

Vol 39 (9) ◽

pp. 1330-1346 ◽

Cited By ~ 1

Author(s):

R. A. Ross

Keyword(s):

Exact Solution ◽

Viscous Fluid ◽

Gravity Waves ◽

Speed Of Sound ◽

Compressible Fluid ◽

Asymptotic Methods ◽

Axially Symmetric ◽

Linearized Theory ◽

The Waves ◽

Special Case

In this paper an investigation is made of the effect of an axially symmetric explosion at any depth in a semi-infinite, compressible, non-viscous fluid, acted upon by gravity. The explosion is represented by a line source of the form δ(x)δ(z – h)δ(t), where h is the depth of the source. An exact solution is given using the linearized theory. This solution is studied in detail by asymptotic methods, for the special case of a surface explosion. It is found that compressibility results in the gravity waves being propagated with a speed less than c, the speed of sound in the fluid. If x is the distance from the explosion and t the time that has elapsed after the explosion, then for [Formula: see text] only "precursor" waves are noticed at the point of observation. For [Formula: see text] large amplitude waves are present, similar to the waves predicted by the incompressible theory.

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Leaky and surface wave diffraction by an asymmetric impedance half plane

Canadian Journal of Physics ◽

10.1139/p83-111 ◽

1983 ◽

Vol 61 (6) ◽

pp. 906-918

Author(s):

W. Nasalski

Keyword(s):

Exact Solution ◽

Surface Wave ◽

Half Plane ◽

Wave Diffraction ◽

Isotropic Medium ◽

Diffraction Problem ◽

Optical Field ◽

Point Of View ◽

Leaky Wave ◽

Uniqueness Of The Solution

An exact solution is obtained for the problem of a leaky or surface wave incident on an impedance half plane in a homogeneous, isotropic medium. The impedance half plane is asymmetric, i.e., with different constant surface impedances at the upper and lower faces, respectively. The incident leaky wave propagates in a direction normal to the edge of the half plane.The diffraction problem leads to a set of two coupled Wiener–Hopf equations, from which two Hilbert problems on a new contour are obtained and solved. The Wiener–Hopf–Hilbert method is used. Expressions for the geometrical optical field are also derived and results arc discussed from the point of view of the uniqueness of the solution.

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