Jarvis Andrew J C, Cegla Frederic B
IEEE Trans Ultrason Ferroelectr Freq Control. 2014 Jul;61(7):1179-90. doi: 10.1109/TUFFC.2014.3017.
The challenge of accurately simulating how incident scalar waves interact with rough boundaries has made it an important area of research within many scientific disciplines. Conventional methods, which in the majority of cases focus only on scattering in two dimensions, often suffer from long simulation times or reduced accuracy, neglecting phenomena such as multiple scattering and surface self-shadowing. A simulation based on the scalar wave distributed point source method (DPSM) is presented as an alternative which is computationally more efficient than fully meshed numerical methods while obtaining greater accuracy than approximate analytical techniques. Comparison is made to simulated results obtained using the finite element method for a sinusoidally periodic surface where scattering only occurs in two dimensions, showing very good agreement (<0.2 dB). In addition to two-dimensional scattering, comparison to experimental results is also carried out for scattering in three dimensions when the surface has a Gaussian roughness distribution. Results indicate that for two-dimensional scattering and for rough surfaces with a correlation length equal to the incident wavelength (λ) and a root mean square height less than 0.2λ, the scalar wave approximation predicts reflected pulse shape change and envelope amplitudes generally to within 1 dB. Comparison between transducers within a three-element array also illustrate the sensitivity pulse amplitude can have to sensor position above a rough surface, differing by as much as 17 dB with a positional change of just 1.25λ.
精确模拟入射标量波如何与粗糙边界相互作用这一挑战，使其成为许多科学学科中的一个重要研究领域。传统方法在大多数情况下仅专注于二维散射，常常面临模拟时间长或精度降低的问题，忽略了诸如多次散射和表面自阴影等现象。本文提出了一种基于标量波分布点源法（DPSM）的模拟方法，它在计算上比完全网格化的数值方法更高效，同时比近似解析技术具有更高的精度。对于仅在二维发生散射的正弦周期表面，将其模拟结果与使用有限元法获得的结果进行比较，显示出非常好的一致性（<0.2 dB）。除了二维散射外，当表面具有高斯粗糙度分布时，还对三维散射的实验结果进行了比较。结果表明，对于二维散射以及相关长度等于入射波长（λ）且均方根高度小于0.2λ的粗糙表面，标量波近似预测的反射脉冲形状变化和包络幅度通常在1 dB以内。三元阵列内换能器之间的比较还表明，脉冲幅度对粗糙表面上方传感器位置的敏感性，位置仅变化1.25λ时差异就可达17 dB。
