中文摘要：

在众多描述非线性声波传播的理论模型中,KZK方程能够准确地描述有限振幅声波传播的衍射、吸收及非线性效应,对求解参量阵近场声场有着明显的优势,因而成为描述非线性声场最为精确的方程之一。从KZK方程的频域求解出发,利用二阶对角隐式龙哥库塔法（second-order Diagonal Implicit Runge-Kutta,DIRK2）和Crank-Nicolson有限差分法（Crank-Nicolson Finite Difference,CNFD）相结合的有限差分算法,对在不同媒介中传播的参量阵近场声场特性进行研究,旨在对参量阵能量累积过程有进一步的理解,为参量阵转换效率的提高提供初步的探索,为参量阵的进一步工程应用提供相应的理论指导。

英文摘要：

In numerous theoretical models of describing the nonlinear acoustic wave propagation, the KZK equation can accurately describe diffraction, absorption and the nonlinear propagation effects of finite amplitude sound beam, thus becomes one of the most accurate equation describing nonlinear ultrasonic field. In this paper, based on the frequency domain solution of the KZK equation, using second-order Diagonal Implicit Runge-Kutta（DIRK2） method and the Crank-Nicolson Finite Difference（CNFD） method of finite difference algorithm, the near-field acoustic characteristics of the parametric array in different propagation mediums are studied, the results of this paper may provide the corresponding theoretical basis for further engineering application.