Two approaches to the solution of the scalar problem of diffraction on the plane two-periodic lattice from bodies of revolution located in the liquid layer
Abstract:Background, Objectives and Methods: The problem of diffraction of acoustic waves on the lattices located in the layered media is of great scientific interest in hydroacoustics. There are many methods of the solution of this diffraction problem, such as the method of the surface integral equations, finite element method, boundary element method, etc. One of universal method of solution of diffraction problems is the modified method of discrete sources (MMDS). Earlier this method was applied to the solution of the problems of wave scattering on a single body of revolution, on a group of bodies and on lattices located in free space. The purpose of this study is to develop the numerical algorithms based on MMDS for solution of the scalar problem of diffraction of acoustic waves on the planar grating consisting of identical impedance bodies of revolution which is immersed in a liquid layer. Results: Based on MMDS two techniques of the solution of the scalar three-dimensional problem of diffraction on the planar lattice consisting of identical impedance bodies of revolution located in a liquid layer are developed. The correctness of MMDS is illustrated on the example of diffraction of the plane wave on the single strongly elongated superellipsoid of revolution. Comparison of the results of calculation of the reflection and transmission coefficients for the lattice consisting of spherical elements obtained by means of both techniques offered in the paper is carried out. For validation of MMDS the check of the accuracy of fulfillment of the energy conservation law is executed and the dependence of the residual of the boundary condition on the contour of axial section of the central element of the lattice is plotted. It is shown that the residual has the order $1.5\cdot 10^{-5}$ at the chosen model parameters. Frequency dependences for various geometries of the elements of the lattice (for two types of boundary conditions) and dependences of the absolute value of reflection and transmission coefficients on the filling factor of the lattice are obtained. Conclusion: There is an essential difference between the behavior of the scattered field under diffraction on the lattices located in homogeneous medium and the behavior of the scattered field under diffraction on the lattices immersed in layered medium.
Keywords:wave diffraction on the lattices located in stratified media, method of discrete sources, analytical continuation of wave fields.
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