Cervenka Milan, Bednarik Michal
CTU in Prague, FEE, Technicka 2, 166 27 Prague 6, Czech Republic.
Ultrasonics. 2006 Dec 22;44 Suppl 1:e773-6. doi: 10.1016/j.ultras.2006.05.008. Epub 2006 Jun 2.
This paper deals with 2-D simulation of finite-amplitude standing waves behavior in rectangular acoustic resonators. Set of three partial differential equations in third approximation formulated in conservative form is derived from fundamental equations of gas dynamics. These equations form a closed set for two components of acoustic velocity vector and density, the equations account for external driving force, gas dynamic nonlinearities and thermoviscous dissipation. Pressure is obtained from solution of the set by means of an analytical formula. The equations are formulated in the Cartesian coordinate system. The model equations set is solved numerically in time domain using a central semi-discrete difference scheme developed for integration of sets of convection-diffusion equations with two or more spatial coordinates. Numerical results show various patterns of acoustic field in resonators driven using vibrating piston with spatial distribution of velocity. Excitation of lateral shock-wave mode is observed when resonant conditions are fulfilled for longitudinal as well as for transversal direction along the resonator cavity.
本文研究矩形声学谐振器中有限振幅驻波行为的二维模拟。从气体动力学基本方程推导出一组以保守形式表示的三阶近似的三个偏微分方程。这些方程构成了声速矢量和密度两个分量的封闭方程组，该方程组考虑了外部驱动力、气体动力学非线性和热粘性耗散。通过解析公式从方程组的解中获得压力。这些方程在笛卡尔坐标系中给出。使用为积分具有两个或更多空间坐标的对流扩散方程组而开发的中心半离散差分格式，在时域中对模型方程组进行数值求解。数值结果显示了在使用具有速度空间分布的振动活塞驱动的谐振器中声场的各种模式。当沿谐振器腔的纵向和横向满足共振条件时，观察到横向冲击波模式的激发。
