图书馆订阅: Guest
Begell Digital Portal Begell 数字图书馆 电子图书 期刊 参考文献及会议录 研究收集
国际流体力学研究期刊
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.5

ISSN 打印: 2152-5102
ISSN 在线: 2152-5110

国际流体力学研究期刊

DOI: 10.1615/InterJFluidMechRes.v26.i5-6.140
pages 742-757

The Reflection Principle in Two-Dimensional Boundary-Value Problems for the Helmholtz Equation

A. M. Gomilko
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
Victor T. Grinchenko
Institute of Hydromechanics, National Academy of Science of Ukraine, Kyiv, Ukraine
Ye. V. Lobova
Fluid Mechanics Institute, Ukrainian Academy of Sciences, Kiev, Ukraine

ABSTRACT

The possibility of employing the principle of reflection in constructing solutions and internal and external boundary-value problems for the Helmholtz equation in two-dimensional domains whose boundaries contain rectilinear segments is analyzed. The principal idea of the approach consists in extending the desired solution in a canonical domain such as a circle by employing the reflection principle for solving the Helmholtz equation through the rectilinear segments of the boundary (at homogeneous boundary conditions). In this case the solution of the boundary-value problem is expressed in terms of series in particular solutions of the Helmholtz equation in polar coordinates; the unknown coefficients of this series can be found from an infinite set of linear algebraic equations. The closure equations at the segments of the circle that do not serve as physical boundaries of the original domain are formulated here by reflection of the desired equation. Various examples of boundary-value problems for the Helmholtz equation for a rectilinear-circular lune (internal and external problems) are analyzed. The manner in which allowance can be made for local singularities of the wave field associated with corner points of the domain under study and the mixed nature of the boundary conditions is shown. Numerical computations that verify the suggested method are performed for one of the problems.


Articles with similar content:

Numerical-Analytical Computation Method for Cutoff Wavenumbers of Waveguides with Complicated Cross-Section
Telecommunications and Radio Engineering, Vol.61, 2004, issue 1
Victor Ivanovich Tkachenko, N. G. Don, A. Ye. Poyedinchuk
RESONANT CAVITIES IN THE FORM OF BODIES OF REVOLUTION OF COMPLEX GEOMETRY: A NUMERICAL ALGORITHM FOR CALCULATING THE SPECTRUM
Telecommunications and Radio Engineering, Vol.69, 2010, issue 4
A.Ye. Poedinchuk, I. K. Kuzmichev, A. Yu. Popkov
Analytical Regularization of Dual Series Equations in the Basis of Prolate Angular Spheroidal Functions
Telecommunications and Radio Engineering, Vol.55, 2001, issue 10-11
V. N. Koshparyonok
SCATTERING OF H-POLARIZED WAVES BY PRE-FRACTAL DIFFRACTION GRATINGS
Telecommunications and Radio Engineering, Vol.71, 2012, issue 11
G. I. Koshovy
SYSTEMS APPROACH TO INVESTIGATING PRE-FRACTAL DIFFRACTION GRATINGS
Telecommunications and Radio Engineering, Vol.71, 2012, issue 6
G. I. Koshovy