An Efficient and Accurate Method for Calculating Nonlinear Diffraction Beam Fields

Abstract

This study develops an efficient and accurate method for calculating nonlinear diffraction beam fields propagating in fluids or solids. The Westervelt equation and quasilinear theory, from which the integral solutions for the fundamental and second harmonics can be obtained, are first considered. A computationally efficient method is then developed using a multi-Gaussian beam (MGB) model that easily separates the diffraction effects from the plane wave solution. The MGB models provide accurate beam fields when compared with the integral solutions for a number of transmitter-receiver geometries. These models can also serve as fast, powerful modeling tools for many nonlinear acoustics applications, especially in making diffraction corrections for the nonlinearity parameter determination, because of their computational efficiency and accuracy.

Diffraction Corrections for Second Harmonic Beam Fields and Effects on the Nonlinearity Parameter Evaluation

“…[15] depend on the receiver types, and the diffraction corrections will change accordingly. In this study, we will consider an ideal point receiver and a circular area receiver to calculate received signals and diffraction corrections.…”

“…=25 expansion coefficients are used here to calculate the MGB model-based diffraction corrections because a larger number of expansion coefficients provided better beam fields [15]. The expansion coefficients are listed in [16].…”