Vanhille C, Conde C, Campos-Pozuelo C
ESCET, Universidad Rey Juan Carlos, Tulipán s/n, Móstoles, Madrid 28933, Spain.
Ultrasonics. 2004 Apr;42(1-9):315-8. doi: 10.1016/j.ultras.2004.01.024.
In the framework of the application of high-power ultrasonics in industrial processing in fluid media, the mathematical prediction of the acoustical parameters inside resonators should improve the development of practical systems. This can be achieved by the use of numerical tools able to treat the nonlinear acoustics involved in these phenomena. In particular, effects like nonlinear distortion and nonlinear attenuation are fundamental in applications. In this paper, three one-dimensional numerical models in the time domain for calculating the nonlinear acoustic field inside a one-dimensional resonant cavity are presented and compared. They are based on the finite-difference and the finite-volume methods. These different algorithms solve the differential equations, from the linear up to the strongly nonlinear case (including weak shock). Some physical results obtained from the modelling of ultrasonic waves and a comparison of the efficiency of the different algorithms are presented.
在高功率超声波应用于流体介质工业加工的框架内，谐振器内部声学参数的数学预测应能推动实际系统的发展。这可以通过使用能够处理这些现象中涉及的非线性声学的数值工具来实现。特别是，诸如非线性失真和非线性衰减等效应在应用中至关重要。本文提出并比较了三个用于计算一维谐振腔内非线性声场的时域一维数值模型。它们基于有限差分法和有限体积法。这些不同的算法求解从线性到强非线性情况（包括弱激波）的微分方程。给出了从超声波建模获得的一些物理结果以及不同算法效率的比较。
