This paper presents a generalisation of the mathematical model and numerical study of the acoustic scattering problem from multiple spheres in the case of spheres through which the wave passes and whose centers are located on the same axis (the case of sound-penetrable and coaxial spheres) under the action of spherical waves from a monopoly radiation source arbitrarily located in space. When solving the Helmholtz equations, a numerical technique based on the fast multipole method has been adapted for this task, which allows one to achieve high accuracy of the results obtained with minimal computer time. Comparison of the different approaches to truncation infinite series in the expansion showed the following: the result with a good degree of accuracy by a single calculation gives approach based on the truncation of all the rows with a fixed number in each expansion, and the result with a certain degree of accuracy gives an approach based on comparing two consecutive values of the sum of the series. A numerical parametric analysis of the pressure distribution inside and outside the spheres is carried out for various values of their radii, physical characteristics of the external and internal media, the number of spheres, the distances between the centers of the spheres, the frequency of exposure and the location of the monopole radiation source. It is shown that at certain values of the parameters, the appearance of zones of decrease or increase in pressure behind sound-penetrable spheres is possible. The obtained results will further allow to carry out test calculations to verify the general numerical algorithm for the case of a multitude of spheres arbitrarily located in space.
monopole radiation source,
When an acoustic wave interacts with small obstacles that differ in density and/or compressibility from the main medium, additional (scattered) waves appear that propagate in all directions from the obstacles. This phenomenon is called scattering (diffraction) of sound. Its study is one of the important problems of acoustics, because it is based on many of the practical application of acoustic waves, such as sonar, non-destructive testing equipment, medical scanners, sensing of the atmosphere and ocean, etc. Therefore, the problem of acoustic scattering from small obstacles under external influences is relevant.
In the paper a generalization of mathematical models is presented and numerical studies were made for the problem acoustic scattering from multiple spheres in the case of a spheres through which the wave passes and whose centers are located on the same axis (the case of sound- penetrable and coaxial spheres) under the influence of a spherical wave from the monopoly of the radiation source arbitrarily located in space.
Purpose: investigation of scattering of an acoustic wave from sound- penetrable spheres (spheres through which surface a wave can pass) with centers located on the same axis in the presence of a monopole radiation source.
Methods: When solving the Helmholtz equations, a numerical technique based on the fast multipole method was adapted for the problem under consideration. This calculation technique allows to achieve high accuracy of the results with minimal use of computer time. The problem is considered in axisymmetric formulation. As a result of numerical modeling, program codes were written in the Fortran 90 language.
The following numerical studies were made:
As a findings of the research, it has been determined that
Value: The generalized model and calculation procedure in the future will allow to made parametric analysis in a wider range of parameters, including the different values of the radii of the spheres, the distance between their centers, the location and frequency of the monopole radiation source, physical parameters of the surrounding and internal environments, etc. Besides the results obtained will allow to carry out test calculations to verify the general numerical algorithm for the case of many spheres arbitrarily located in space.