有限振幅波的三维时域建模

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

通过对二维算法(Texas code)做扩展,建立了求解扩展版KZK(Khokhlov-Zabolotskaya-Kuznetsov)方程的三维时域有限差分算法。该算法先将KZK方程变换成TBE(Transformed Beam Equation),然后依次求解衍射(抛物线近似条件下)、热黏滞吸收、弛豫和非线性作用。数值仿真了圆形、矩形和方形阵列的非线性声场,与前人的结果相符,证明了算法的有效性,并分析了把弛豫吸收系数当成热黏滞吸收系数引入空气中的参量阵的模拟会带来的误差。

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.