We propose a numerical surface integral method to study complex acoustic systems, for interior and exterior problems. The method is based on a parametric representation in terms of the arc’s lengths in curvilinear orthogonal coordinates. With this method, any geometry that involves quadric or higher order surfaces, irregular objects or even randomly rough surfaces can be considered. In order to validate the method, the modes in cubic, spherical and cylindrical cavities are calculated and compared to analytical results, which produced very good agreement. In addition, as examples, we calculated the scattering in the far field and the near field by an acoustic sphere and a cylindrical structure with a rough cross-section.

Using the tunderwater corner reflector (CR) to simulate the acoustic scattering characteristics of the military target is a new technology to counter active sonar detection. Existing underwater CRs only have the ability to interfere with the acoustic field, but have limitations in acoustic wave modulation. Therefore, acoustic metasurfaces applied on CRs to enhance the ability of acoustic wave modulation has a great application prospect. A fast prediction method based on the Kirchhoff approximation (KA) and the ray tracing theory is proposed to calculate the acoustic scattering characteristics of CR with acoustic metasurfaces in grooves array type. The accuracy of the method is verified by the finite element method (FEM) simulation. The modulation effect of CR with grooves array in different gradient combinations on the structural scattering acoustic field is analyzed. The research shows that the CR with different combinations of the acoustic metasurface has an obvious modulation effect on the amplitude of the acoustic waves and the deflection of acoustic field. In particular, the grooves array in combination with positive and negative gradients has an obvious deflection impact on the scattering acoustic field.

An isogeometric boundary element method is applied to simulate wave scattering problems governed by the Helmholtz equation. The NURBS (non-uniform rational B-splines) widely used in the CAD (computer aided design) field is applied to represent the geometric model and approximate physical field variables. The Burton-Miller formulation is used to overcome the fictitious frequency problem when using a single Helmholtz boundary integral equation for exterior boundary-value problems. The singular integrals existing in Burton-Miller formulation are evaluated directly and accurately using Hadamard’s finite part integration. Fast multipole method is applied to accelerate the solution of the system of equations. It is demonstrated that the isogeometric boundary element method based on NURBS performs better than the conventional approach based on Lagrange basis functions in terms of accuracy, and the use of the fast multipole method both retains the accuracy for isogeometric boundary element method and reduces the computational cost.