Abstract The rise of bubbles in viscous liquids is not only a widespread process in many industrial applications but also an essential fundamental problem in fluid physics. The modeling and simulation of such problems is still an area of active research, mainly when surface tension is present, as in the case of single and multiple bubbles rising in viscous liquids. We treat the interface between the two fluids by a modified level-set method, called convected level-set. The difference to the standard level-set method is that the re-initialization step is embedded in the convection equation, avoiding a separate step during the calculation. In this work, we use a new truncated signed distance function to get a smooth truncation close to the interface. We couple this interface-capturing method with the Navier-Stokes equations, and we apply a global mass conservation procedure to enforce the mass balance between phases. We implement the whole model in libMesh , an open finite element library that provides a framework for multiphysics, considering adaptive mesh refinement. Numerical results are presented for 2D and 3D bubble problems, and quantities of interest are compared with others. We also compare our results with experimental observations, both in the aspect of terminal bubble shapes and terminal bubble velocities, for several regimes of single and multiple bubbles rising in viscous liquids.

中文翻译：

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一种新的气泡动力学对流水平集方法

摘要 粘性液体中气泡的产生不仅是许多工业应用中普遍存在的过程，而且是流体物理学中必不可少的基本问题。此类问题的建模和模拟仍然是一个活跃的研究领域，主要是在存在表面张力的情况下，例如在粘性液体中上升的单个和多个气泡的情况。我们通过一种改进的水平集方法处理两种流体之间的界面，称为对流水平集。与标准水平集方法的不同之处在于重新初始化步骤嵌入在对流方程中，避免了计算过程中的单独步骤。在这项工作中，我们使用新的截断符号距离函数来获得接近界面的平滑截断。我们将这种界面捕获方法与 Navier-Stokes 方程结合起来，我们应用全局质量守恒程序来强制各阶段之间的质量平衡。我们在 libMesh 中实现了整个模型，这是一个开放的有限元库，为多物理场提供了一个框架，考虑了自适应网格细化。给出了 2D 和 3D 气泡问题的数值结果，并将感兴趣的数量与其他数量进行了比较。我们还将我们的结果与实验观察结果进行了比较，无论是在终端气泡形状还是终端气泡速度方面，对于在粘性液体中上升的单个和多个气泡的几种情况。给出了 2D 和 3D 气泡问题的数值结果，并将感兴趣的数量与其他数量进行了比较。我们还将我们的结果与实验观察结果进行了比较，无论是在终端气泡形状还是终端气泡速度方面，对于在粘性液体中上升的单个和多个气泡的几种情况。给出了 2D 和 3D 气泡问题的数值结果，并将感兴趣的数量与其他数量进行了比较。我们还将我们的结果与实验观察结果进行比较，无论是在终端气泡形状还是终端气泡速度方面，对于在粘性液体中上升的单个和多个气泡的几种情况。