Two-dimensional Numerical Simulations of Nonlinear Ultrasonic Propagation in Bubbly Liquids

This paper deals with the numerical prediction of the behavior of two-dimensional (2-D) ultrasonic waves in bubbly liquids. The purpose of this work is to simulate the propagation of high-amplitude signals in the nonlinear, dissipative (viscous damping), and dispersive bubbly media. A 2-D nonlinear differential system written in acoustic pressure and bubble volume variation, for which the bubbles are spherical and all of the same size, is solved by means of a finite-differences scheme. The numerical simulations allow us to distinguish the nonlinear results obtained at high-amplitude excitations from the linear response obtained at small-amplitude excitations. Several configurations are presented. Acoustic pressure and bubble volume variation are shown. The effects of the dynamics of the bubbles (nonlinearity, dispersion, dissipation) on the acoustic pressure field are analyzed.