Numerical simulation of two-dimensional multiple scattering of sound by a large number of circular cylinders

The purpose of this article is to present an innovative resolution method for investigating problems of sound scattering by infinite cylinders immersed in a fluid medium. The study is based on the analytical solution of multiple scattering, where incident and scattered waves are expressed in cylindrical harmonics. This modeling leads to dense linear systems, which are made sparse by introducing a cutoff radius around each particle. This cutoff radius is deeply studied and quantified. Numerical resolution is performed using parallel computing methods designed to solve very large sparse linear systems. Comparisons with direct calculations made with another numerical software and homogenization techniques follow and show good agreement with the implemented method. The last part is dedicated to a comparison between the propagation of waves in a circular cluster made of a random distribution of cylinders and the propagation in the corresponding homogenized cluster where the multiple scattering formalism is combined with a statistical analysis to provide an effective medium.