Multiple scattering of a spherical acoustic wave from fluid spheres

The multiple scattering of a spherical acoustic wave from an arbitrary number of fluid spheres is investigated theoretically. The tool to attack the multiple scattering problem is a kind of addition formulas for the spherical wave functions, which are presented in the paper, based on the bicentric expansion form of Green function in the spherical coordinates. For an arbitrary configuration of NN fluid spheres, the kind of addition formulas permits the field expansions (all referred to the center of each sphere). With these the sound fields scattered by each sphere can be described by a set of NN equations. The interactions between any two fluid spheres are taken into account in these equations exactly and their coefficients are coupled through double sums in the spherical wave functions. By truncating the infinite series in the equations depending on certain calculation accuracy and solving the coefficients matrix by using the Gauss–Seidel iteration method, we can obtain the scattered sound field by the configuration of the fluid spheres. Finally, the scattering calculations by using the kind of addition formulas are carried out.