Numerical method for calculating nonlinear sound propagation in full acoustic field

Abstract

IntroductionNonlinear sound propagation in the far-field acoustics has been studied by numerically solving the KhokhlovZaboloskya-Kuznetsov (KZK) equation [1][2][3], which is derived from the fluid dynamic equation under the assumption of parabolic approximation [4]. It is well known that the approach based on the KZK equation is efficient enough in the far-field acoustics, whereas it is not accurate enough in the near sound source owing to the parabolic nature of the equation [5,6]. Therefore, the approach based on the KZK equation cannot be applied to nonlinear acoustics in the near field, where the reflection, refraction and interference of sound play an important role in the nonlinear sound propagation. Such a situation can be seen in applications, such as beam focusing by an acoustic phased array, and an acoustic lens.On the other hand, full-field (near-and far-field) acoustics can be studied by the fluid dynamic equation based approach [7][8][9]. This approach uses the compressible form of the Navier-Stokes equation and is solved numerically by the finite difference time domain (FDTD) method, although it requires a large amount of computational time even for a small target area of computation. Therefore, it is difficult to simulate the full-field acoustics using this approach, especially in the huge target acoustic field of underwater acoustics, where full acoustic fields larger than 1 m in axial length must be solved to study the nonlinear sound propagation from parametric and phased arrays.The purpose of this study is to devise a numerical method for nonlinear sound propagation in the full acoustic field with reasonable computational cost by combining two approaches of the Navier-Stokes and KZK equations.