An algebraic correction for the Westervelt equation to account for the local nonlinear effects in parametric acoustic array

Abstract

This work presents a simple computational approach for the calculation of parametrically generated low-frequency sound fields. The Westervelt wave equation is employed as a model equation that accounts for the wave diffraction, attenuation, and nonlinearity. As it is known that the Westervelt equation captures the cumulative nonlinear effects correctly and not the local ones, an algebraic correction is proposed, which includes the local nonlinear effects in the solution of the Westervelt equation. This way, existing computational approaches for the Westervelt equation can be used even in situations where the generated acoustic field differs significantly from the plane progressive waves, such as in the near-field, and where the local effects manifest themselves strongly. The proposed approach is demonstrated and validated on an example of the parametric radiation from a baffled circular piston.