Far field patterns for the impedance boundary value problem in acoustic scattering

1983 ◽  
Vol 16 (2) ◽  
pp. 131-139 ◽  
Author(s):  
David Colton
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Acoustic Scattering ◽  
Far Field ◽  
Impedance Boundary ◽  
Field Patterns

scholarly journals RELAXATION APPROXIMATION OF THE KERR MODEL FOR THE THREE-DIMENSIONAL INITIAL-BOUNDARY VALUE PROBLEM

2009 ◽  
Vol 06 (03) ◽  
pp. 577-614 ◽  
Author(s):  
GILLES CARBOU ◽  
BERNARD HANOUZET
Keyword(s):  
Boundary Value Problem ◽  
Response Time ◽  
Boundary Value ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Debye Model ◽  
Impedance Boundary Condition ◽  
Impedance Boundary ◽  
Initial Boundary Value

The electromagnetic wave propagation in a nonlinear medium is described by the Kerr model in the case of an instantaneous response of the material, or by the Kerr–Debye model if the material exhibits a finite response time. Both models are quasilinear hyperbolic and are endowed with a dissipative entropy. The initial-boundary value problem with a maximal-dissipative impedance boundary condition is considered here. When the response time is fixed, in both the one-dimensional and two-dimensional transverse electric cases, the global existence of smooth solutions for the Kerr–Debye system is established. When the response time tends to zero, the convergence of the Kerr–Debye model to the Kerr model is established in the general case, i.e. the Kerr model is the zero relaxation limit of the Kerr–Debye model.

scholarly journals Numerical Solution of Acoustic Scattering by an Adaptive DtN Finite Element Method

2013 ◽  
Vol 13 (5) ◽  
pp. 1277-1244 ◽  
Author(s):  
Xue Jiang ◽  
Peijun Li ◽  
Weiying Zheng
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Scattering Problem ◽  
Acoustic Scattering ◽  
Adaptive Method ◽  
Two Dimensions ◽  
Adaptive Finite Element ◽  
Acoustic Wave Scattering

AbstractConsider the acoustic wave scattering by an impenetrable obstacle in two dimensions, where the wave propagation is governed by the Helmholtz equation. The scattering problem is modeled as a boundary value problem over a bounded domain. Based on the Dirichlet-to-Neumann (DtN) operator, a transparent boundary condition is introduced on an artificial circular boundary enclosing the obstacle. An adaptive finite element based on a posterior error estimate is presented to solve the boundary value problem with a nonlocal DtN boundary condition. Numerical experiments are included to compare with the perfectly matched layer (PML) method to illustrate the competitive behavior of the proposed adaptive method.

Effect of Current on Flexural Gravity Waves

2006 ◽  
Author(s):  
Joydip Bhattacharjee ◽  
Trilochan Sahoo
Keyword(s):  
Boundary Value Problem ◽  
Gravity Waves ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Far Field ◽  
Flexural Gravity Waves ◽  
Uniform Current ◽  
Progressive Waves ◽  
Initial Boundary Value

The effect of uniform current on the propagation of flexural gravity waves due to a floating ice sheet is analyzed in two dimensions. The problem is formulated as an initial boundary value problem in the linearized theory of water waves. By using Laplace transform technique, the initial boundary value problem is reduced to a boundary value problem, which is solved by the application of Fourier transform to obtain the surface elevation in terms of an integral, which is evaluated asymptotically for large distance and time by the application of method of stationary phase to obtain the far field behavior of the progressive waves. The effect of current on the wavelength, phase velocity and group velocity of the flexural gravity waves propagating below the floating ice sheet is analyzed theoretically to obtain certain critical values on the speed of current which are of significant importance. Simple numerical computations are performed to observe the effect of uniform current on the surface elevation, wavelength, phase velocity and group velocity of flexural gravity waves and on the far field behavior of the progressive waves.

Lifting three-dimensional wings in transonic flow

1979 ◽  
Vol 95 (2) ◽  
pp. 223-240 ◽  
Author(s):  
M. S. Cramer
Keyword(s):  
Boundary Value Problem ◽  
Asymptotic Expansions ◽  
Transonic Flow ◽  
Near Field ◽  
Boundary Value ◽  
Three Dimensional ◽  
Matched Asymptotic Expansions ◽  
Far Field ◽  
First Order ◽  
Order Contribution

The far field of a lifting three-dimensional wing in transonic flow is analysed. The boundary-value problem governing the flow far from the wing is derived by the method of matched asymptotic expansions. The main result is to show that corrections which are second order in the near field make a first-order contribution to the far field. The present study corrects and simplifies the work of Cheng & Hafez (1975) and Barnwell (1975).

A note on ‘Lifting three-dimensional wings in transonic flow’ by M. S. Cramer

1981 ◽  
Vol 109 ◽  
pp. 257-258 ◽  
Author(s):  
M. S. Cramer
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Transonic Flow ◽  
Boundary Value ◽  
Three Dimensional ◽  
Far Field ◽  
First Order ◽  
Order Of Magnitude

The purpose of this note is to clarify the discrepancy between the results of Cramer (1979), Barnwell (1975) and Cheng & Hafez (1975). These authors have all derived the boundary-value problem governing the flow far from a three-dimensional lifting wing in transonic flow. The results of both Cramer and Barnwell will provide the lowest-order solution in the far field. The results of Cheng & Hafez are not only accurate to lowest order but to first order as well. That is, the theory of Cheng & Hafez is an order-of-magnitude more accurate than those of Barnwell and Cramer. This is the reason for the discrepancy between the boundary condition derived by Cheng & Hafez and that of Cramer and Barnwell. Because Cheng & Hafez correctly derive the first-order results, the lowest-order theories of Cramer or Barnwell cannot correct those of Cheng & Hafez. It should be recognized that the main contribution of Cramer's work was to clarify the structure of the problem and to simplify the analysis rather than correct the basic results.

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