Collaborative Research: Efficient surface-based numerical methods for 3D interfacial flow with surface tension

合作研究：基于表面的高效数值方法，用于具有表面张力的 3D 界面流动

• 批准号: 1016406
• 负责人: Michael Siegel
• 金额: $ 28.28万
• 依托单位: New Jersey Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-10-01 至 2014-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1016406&HistoricalAwards=false
• 关键词: Collaborative; Research; Efficient; surface; based

The investigators develop and apply efficient boundary integral methods for the motion of interfaces in 3D flow. The methods address a significant difficulty in the numerical computation of fluid interfaces with surface tension or elastic forces in 3D flow. Such forces introduce high order (i.e., high derivative) terms into the evolution equations, which lead to severe stability constraints or `stiffness' for explicit time-integration methods. Furthermore, the high order terms appear in nonlinear and nonlocal operators, making the efficient application of stable implicit methods difficult.The investigators' method relies on using the first and second fundamental coefficients of the surface as dynamical variables, and employs a special parameterization of the interface combined with an analysis of the governing equations at small scales. This enables the efficient application of implicit time-integration methods for 3D flow. The investigators implement the method in canonical interface problems for inviscid fluids, including the Kelvin-Helmholtz, Rayleigh-Taylor, and water wave problems, and study the dynamics of inextensible elastic sheets in inviscid flow and vesicles in 3D viscous flow. Most importantly, they develop a version of the numerical method which uses domain decomposition or overlapping coordinate patches to describe the interface. This has the added benefit of providing a framework for the implementation of spectrally accurate and spatially adaptive methods.Moving boundary problems occur in many diverse areas in, for example, fluid dynamics, materials science, and biology. Specific examples include traveling ocean waves, growing cancer tumors, beating hearts and moving cells and organisms. The investigators develop accurate and efficient `boundary integral'numerical methods for the simulation of moving boundaries in applications.Boundary integral methods are among the most accurate numerical methods for the simulation of moving interfaces, but are often inefficient when the interface is acted on by surface tension or elastic forces. The development of fast and accurate boundary integral methods for 3D interfacial flow with surface tension or elastic forces will be of great benefit in understanding existing applications and developing technology further.

研究人员开发并应用了有效的边界积分方法，用于3D流中界面的运动。 该方法解决了与3D流动中表面张力或弹性力的流体接口计算的严重困难。这样的力将高阶（即高导数）项引入进化方程，从而导致严重的稳定性约束或“刚度”，以实现明确的时间整合方法。 此外，高阶术语出现在非线性和非局部运算符中，使稳定隐式方法的有效应用变得困难。研究者的方法依赖于将表面的第一和第二基本系数用作动力学变量，并采用了界面的特殊参数，并与小规模量表的界面分析结合了界面。这可以有效地应用于3D流的隐式时间整合方法。研究人员在无粘性流体的规范界面问题中实施了该方法，包括开尔文 - 霍尔姆尔兹，雷利 - 泰勒和水波问题，并研究了无粘性流动中不可扩展的弹性片和3D粘性流中的囊泡的动力学。最重要的是，他们开发了数值方法的版本，该方法使用域分解或重叠坐标贴片来描述接口。这具有为实施频谱准确和空间适应性方法提供框架的额外好处。在许多不同的领域中，在例如流体动力学，材料科学和生物学中，发生边界问题。 具体的例子包括旅行海浪，生长的癌症肿瘤，跳动的心脏以及移动的细胞和生物。研究人员开发了用于模拟应用中移动边界的准确有效的“边界积分”方法。结合的积分方法是模拟移动接口的最准确的数值方法之一，但是当表面张力或弹性力对界面作用时，通常效率低下。 与表面张力或弹性力的3D界面流的快速，准确的边界积分方法的开发将在理解现有应用和进一步开发技术方面具有很大的好处。