Time-domain modeling of finite-amplitude sound beams in three-dimensional Cartesian coordinate system

A three-dimensional time-domain algorithm,which is based on the augmented KZK (Khokhlov-Zabolotskaya-Kuznetsov) equation,is proposed to simulate the nonlinear field of the parametric array.First,KZK equation is transformed into TBE(Transformed beam equation). Then,the effects of diffraction(in parabolic approximation),thermoviscous absorption,relaxation, and nonlinearity are solved with finite difference methods.The numerical results of this code agree well with the theoretical and experimental results presented in previous studies, which demonstrates the validity of the three-dimensional algorithm.Using this code to calculate the nonlinear field of the parametric array in air,it is found that the small time interval is important to the accuracy of the simulation results of the difference frequency wave in the case of high sound pressure level,and the errors caused by taking relaxation absorption for thermoviscous absorption are influenced by the characteristic frequency.