Numerical solution for nonlinear acoustic beam radiated from non-axisymmetric plane transducers using the operator splitting method

Abstract

A numerical code is developed to compute the nonlinear acoustic beam radiated by non axisymmetric plane transducers. The model is based on the Khokhlov-Zabolotskaya-Kuznetsov (KZK) parabolic wave equation, which takes into account the combined effects of nonlinearity, diffraction and absorption. The aim is to simulate nonlinear propagation of plane waves from lower to higher intensity and to predict shock formation for a non-axisymmetric plane transducer. The simulation is performed in the frequency domain. A Fourier series expansion of the acoustic pressure is used, and the resulting equations are solved using operator splitting and finite difference methods. The numerical scheme is performed in a cartesian coordinate system in order to consider any geometric shapes of transducers. A first and fourth order scheme are used for the modeling of the propagation and the diffusion phenomena, respectively. The modeling proposed for a plane circular transducer is compared with the well-known polar coordinates model, and subsequently known experimental measurements. Good agreement has been found. Results for square and rectangular plane piston are then presented and discussed.