Numerical analysis of acoustic scattering from a layer of droplets under external action

Abstract

The study of acoustic scattering from small obstacles is important both for studying the fundamental nature of this phenomenon and from a practical point of view, since many applications of acoustic waves are based on the scattering phenomenon. Within the framework of the problem of acoustic scattering from a set of sound-permeable spheres arbitrarily located in space, under external influence, scattering from a layer of drops is studied. The main goal is to determine the parameters at which the system is sensitive to changes in the droplet radius. A special case of a small spheres layer is possible when a region containing many small inhomogeneities is conditionally two-dimensional one (one of the three dimensions can be neglected). The problem is solved numerically using a generalized calculation technique based on the fast multipole method, which allows achieving high accuracy of the results obtained with minimal CPU time. A series of computational experiments was carried out for various ratios of the physical parameters of the drop and the environment (density and sound speed) for a different number of spheres and the density of their arrangement in the configuration. It is shown that the system is most sensitive to changes in the droplet radius in the case when the elasticity of the substance inside the droplet is less than that of the external environment, and with an increase in the sphere number in dense configurations the system is most sensitive when the elasticity of the substance inside the droplet is much greater than that of the external environment. It is found that the sensitivity to changes in the initial data decreases with an increase in the distance between the sphere centers, that is, with a decrease in the density of the arrangement of the spheres in the configuration.