Professor John Blake spent a considerable part of his scientific career on studying bubble dynamics and acoustic cavitation. As Blake was a mathematician, we will be focusing on the theoretical and numerical studies (and much less on experimental results). Rather than repeating what is essentially already known, we will try to present the results from a different perspective as much as possible. This review will also be of interest for readers who wish to know more about the boundary element method in general, which is a method often used by Blake and his colleagues to simulate bubbles. We will, however, not limit the discussion to bubble dynamics but try to give a broad discussion on recent advances and improvements to this method, especially for potential problems (Laplace) and wave equations (Helmholtz). Based on examples from Blake’s work, we will guide the reader and show some of the mysteries of bubble dynamics, such as why jets form in collapsing bubbles near rigid surfaces. Where appropriate, we will illustrate the concepts with examples drawn from numerical simulations and experiments.

中文翻译：

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布雷克，气泡和边界元方法

约翰·布雷克（John Blake）教授在科学生涯中花费了大量时间来研究气泡动力学和声空化。由于布雷克（Blake）是数学家，因此我们将专注于理论和数值研究（而较少关注实验结果）。我们将不尝试重复本质上已知的内容，而是尝试从不同的角度尽可能多地呈现结果。对于希望全面了解边界元素方法的读者来说，本评论也将引起人们的兴趣，该方法通常是Blake和他的同事用来模拟气泡的方法。但是，我们将讨论的范围不仅限于气泡动力学，而是尝试对这种方法的最新进展和改进进行广泛的讨论，尤其是对于潜在问题（拉普拉斯）和波动方程（Helmholtz）。根据布雷克的作品，我们将指导读者并说明气泡动力学的一些奥秘，例如，为什么在刚性表面附近的气泡破裂时会形成喷流。在适当的地方，我们将通过数值模拟和实验得出的例子说明这些概念。