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

A time-domain finite difference algorithm has been extended from two-dimensional version(Texas code) to three-dimensional version for solving an augmented KZK(Khokhlov-Zabolotskaya-Kuznetsov)equation.First,KZK equation was transformed into TBE(Transformed Beam Equation).Then,the code solved diffraction(in parabolic approximation),thermoviscous absorption,relaxation and nonlinearity effects successively.The simulation results of this code agreed well with the nonlinear wave filed of previous studies for the circular,the rectangular and the square array sources,which demonstrated the validity of the three-dimensional algorithm.The errors of modeling the parametric array in air which were caused by taking relaxation absorption for thermoviscous absorption were also analyzed.