The active cavitation threshold of a dual-frequency driven single spherical gas bubble is studied numerically. This threshold is defined as the minimum intensity required to generate a given relative expansion (Rmax-RE)/RE, where RE is the equilibrium size of the bubble and Rmax is the maximum bubble radius during its oscillation. The model employed is the Keller-Miksis equation that is a second order ordinary differential equation. The parameter space investigated is composed by the pressure amplitudes, excitation frequencies, phase shift between the two harmonic components and by the equilibrium bubble radius (bubble size). Due to the large 6-dimensional parameter space, the number of the parameter combinations investigated is approximately two billion. Therefore, the high performance of graphics processing units is exploited; our in-house code is written in C++ and CUDA C software environments. The results show that for (Rmax-RE)/RE=2, the best choice of the frequency pairs depends on the bubble size. For small bubbles, below 3μm, the best option is to use just a single frequency of a low value in the giant response region. For medium sized bubbles, between 3μm and 6μm, the optimal choice is the mixture of low frequency (giant response) and main resonance frequency. For large bubbles, above 6μm, the main resonance dominates the active cavitation threshold. Increasing the prescribed relative expansion value to (Rmax-RE)/RE=3, the optimal choice is always single frequency driving with the lowest value (20kHz here). Thus, in this case, the giant response always dominates the active cavitation threshold. The phase shift between the harmonic components of the dual-frequency driving (different frequency values) has no effect on the threshold.

中文翻译：

---

GPU加速了对6维参数空间中双频驱动的单个气泡的研究：主动气蚀阈值。

数值研究了双频驱动的单个球形气泡的空化阈值。该阈值定义为产生给定相对膨胀（Rmax-RE）/ RE所需的最小强度，其中RE是气泡的平衡大小，Rmax是其振荡期间的最大气泡半径。所使用的模型是Keller-Miksis方程，它是二阶常微分方程。所研究的参数空间由压力振幅，激励频率，两个谐波分量之间的相移以及平衡气泡半径（气泡大小）组成。由于6维参数空间很大，所研究的参数组合数约为20亿。因此，利用了图形处理单元的高性能。我们的内部代码是用C ++和CUDA C软件环境编写的。结果表明，对于（Rmax-RE）/ RE = 2，频率对的最佳选择取决于气泡大小。对于3μm以下的小气泡，最佳选择是在巨大的响应区域中仅使用一个低值的单个频率。对于3μm至6μm之间的中型气泡，最佳选择是低频（巨大响应）和主共振频率的混合。对于大于6μm的大气泡，主共振主导着主动空化阈值。将规定的相对扩展值增加到（Rmax-RE）/ RE = 3，最佳选择始终是最低频率（此处为20kHz）的单频驱动。因此，在这种情况下，巨大的响应始终主导着有效的气蚀阈值。