A versatile computational approach for the numerical modelling of parametric acoustic array

Abstract

This work presents a versatile computational approach for the numerical modelling of a parametrically generated low-frequency sound. The proposed method is based on the quasi-linear approximation, and it does not employ the paraxial approximation. The primary acoustic field is calculated by the Rayleigh integral or the boundary element method; the secondary difference-frequency field is calculated by the finite element method. As governing wave equations, a general second-order wave equation for acoustic pressure, the Westervelt equation, and Kuznetsov equation are tested, and the corresponding numerical results are compared. The proposed approach allows studying the near-field, far-field, as well as the off-axis field of the difference-frequency wave parametrically radiated from complex emitters. As numerical examples, parametric radiation from a baffled piston and a piston combined with a horn are examined.