Ultrasonic fields propagating in viscous media undergo changes in shape due to diffraction, attenuation, and dispersion. Until now, some implementations in the transmission line matrix (TLM) method has been developed to simulate either diffraction or attenuation but never both. In this work, the quadratic frequency dependence of the absorption coefficient as well as the dispersive effect of a viscous fluid are introduced in the TLM method. The idea is to decompose the emitted wave into its components at different frequencies using Fourier transform. Then, dispersion and attenuation effects are considered for each wave component separately before superposing them to get the required acoustic response. This is possible because each one of them is characterized by a constant absorption coefficient and propagates at a single speed. This TLM model has been applied to the diffracted ultrasonic field by a circular transducer radiating a short pulse in a viscous fluid. The obtained waveforms are interpreted in terms of plane and edge waves. A study of the influence of the most important parameters on the waveform of the detected ultrasonic pulses is performed. The numerical results obtained highlight the attenuation effect on the waves' shapes and the influence of the dispersion on their arrival times.

中文翻译：

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传输线矩阵法模拟粘性流体中的脉冲超声衍射

在粘性介质中传播的超声场会由于衍射，衰减和分散而发生形状变化。到目前为止，已经开发了传输线矩阵（TLM）方法中的某些实现方式来模拟衍射或衰减，但绝不能同时模拟两者。在这项工作中，在TLM方法中引入了吸收系数的二次频率依赖性以及粘性流体的色散效应。想法是使用傅立叶变换将发射的波分解成不同频率的分量。然后，在将每个波分量叠加以获得所需的声学响应之前，分别考虑其色散和衰减效应。这是可能的，因为它们中的每一个都具有恒定的吸收系数并以单一速度传播。该TLM模型已经通过在粘性流体中辐射短脉冲的圆形换能器应用于衍射超声场。所获得的波形根据平面波和边缘波来解释。研究了最重要的参数对检测到的超声波脉冲波形的影响。获得的数值结果突出了对波形状的衰减影响以及色散对其到达时间的影响。