论文标题
比较两相流的AMR/C模拟中对流的水平集和Allen-CAHN相位场方法
Comparing the convected level-set and the Allen-Cahn phase-field methods in AMR/C simulations of two-phase flows
论文作者
论文摘要
两相流的建模和模拟仍然是一个主动研究区域，主要是存在表面张力。建模不同阶段的一种方法是使用接口捕获方法。两种公认的接口捕获方法是级别和相位场方法。水平集方法以其准确计算表面张力的能力而闻名，相位场模型满足了热力学的第二定律。本文审查并比较了模拟两相流的水平集和相位方法。我们使用修改的级别集方法，称为对流级别集。标准级别方法的区别在于，重新定位步骤嵌入对流方程中，避免在计算过程中单独的步骤。我们还采用了全球质量保护程序来实现阶段之间的质量平衡。另一方面，相位场方法使用带有拉格朗日乘数的保守的艾伦 - 卡恩方程来节省质量。这些方法使用相同的有限元公式，时间构建方案，求解器和网格自适应策略在Libmesh（Libmesh）中实现，这是一个并行的自适应有限元库。我们提出了考虑自适应网状细化和粗化（AMR/C）的两种方法的数值解。结果进行分析和讨论。
The modeling and simulation of two-phase flows is still an active research area, mainly when surface tension is present. One way to model the different phases is with interface capturing methods. Two well-established interface capturing approaches are the level-set and phase-field methods. The level-set method is known for its ability to compute the surface tension accurately, and phase-field models satisfy the second law of thermodynamics. This paper reviews and compares a level-set and a phase-field approach to simulate two-phase flows. We use 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. We also apply a global mass conservation procedure to enforce the mass balance between phases. On the other hand, the phase-field approach uses a conservative Allen-Cahn equation with a Lagrange multiplier to conserve the mass. The methods are implemented in libMesh, a parallel adaptive finite element library, using the same finite element formulations, time-marching schemes, solvers, and mesh adaptivity strategies. We present numerical solutions for the two methods considering adaptive mesh refinement and coarsening (AMR/C). Results are analyzed and discussed.
