Numerical Methods for Free Boundary Problems: Two-Phase Flows and Contact Line Dynamics

自由边界问题的数值方法：两相流和接触线动力学

• 批准号: 1115636
• 负责人: Shawn Walker
• 金额: $ 9.07万
• 依托单位: Louisiana State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-08-01 至 2014-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1115636&HistoricalAwards=false
• 关键词: Numerical; Methods; Free; Boundary; Problems

The proposed research will develop numerical methods for a variety of free boundary problems. The research will take advantage of variational/finite element methods, stability/energy estimates, and automatic meshing technology in analyzing multi-physics flow problems that exhibit free interfaces and moving contact lines. The project will push the theory of free boundary problems into new and challenging application areas. Specific objectives are: (A) investigate domain representation and deformation by variational front-tracking, level set methods, diffuse interface, or a combination of these approaches; (B) develop and analyze efficient discrete formulations of Electro-Wetting On Dielectric (EWOD) driven fluid droplets in 2-D (with contact line pinning) and explore well-posedness questions of the time-dependent interface motion; (C) explore reduced order modeling of the electric field in EWOD and higher fidelity models; (D) develop an adaptive phase-field method for electro-wetting in 3-D that couples electro-statics to multi-phase fluid flow with contact line pinning; (E) develop a model and numerical method for 2-phase droplets interacting with a solid substrate that accurately handles the fine-scale details of the moving contact line problem; and (F) advance multi-phase meshing technology to handle 3-D problems in a robust and automatic way with attention given to parallel implementation issues. This project will investigate well-posedness of time dependent domain-deforming problems and study mathematical properties of multi-phase flows with non-smooth dynamics (e.g. contact line pinning). The broader impact of the work arises from its connection with many physical/industrial processes that involve moving boundaries/interfaces. Examples include industrial coating flows that apply a protective layer to a substrate; fluid flows in micro-fluidic devices driven by electric fields (important in the bio-medical field); motion of rigid bodies in a fluid (particulate flows); dynamics of lipid bio-membranes (applications in biology); the peeling of adhesive tape from a rigid support. The research will enable system level modeling and simulation at macroscopic length and time scales for a variety of applications, such as electrowetting 2-phase flow, droplet impacting processes (painting/cooling of surfaces), and coating of solids by films, which can include fine-scale fluid dynamics and chemistry. In addition, the project will create new methods for automatic grid generation of complex shapes that efficiently capture moving boundaries. One outcome of the research will be an automatic meshing tool (i.e. code) which will be made available to the public through the PI's web-site. Finally, a course on shape optimization (with PDE-constraints) will be developed that gives graduate students expertise in optimization with continuum models.

提出的研究将发展各种自由边界问题的数值方法。该研究将利用变分/有限元方法、稳定性/能量估计和自动网格技术来分析具有自由界面和移动接触线的多物理场流动问题。该项目将推动自由边界问题的理论进入新的和具有挑战性的应用领域。具体目标是：(A)通过变分前沿跟踪、水平集方法、扩散界面或这些方法的组合来研究领域表示和变形；(B)开发和分析电润湿介质（EWOD）驱动的二维（接触线钉住）液滴的有效离散公式，并探索随时间变化的界面运动的适定性问题；(C)探索EWOD中电场的降阶建模和更高保真度模型；(D)开发了一种将静电耦合到接触线钉钉多相流体流动的三维电润湿自适应相场方法；(E)建立两相液滴与固体衬底相互作用的模型和数值方法，精确处理移动接触线问题的精细细节；(F)推进多相网格技术，以鲁棒和自动的方式处理三维问题，并注意并行实现问题。本项目将研究时变域变形问题的适定性，并研究具有非光滑动力学（如接触线钉住）的多相流的数学性质。这项工作的更广泛的影响来自于它与许多涉及移动边界/接口的物理/工业过程的联系。示例包括在基材上施加保护层的工业涂层流；电场驱动微流体装置中的流体流动（在生物医学领域很重要）；刚体在流体中的运动（粒子流）；脂质生物膜动力学（在生物学中的应用）胶带从坚硬的支撑物上剥落该研究将在宏观长度和时间尺度上实现系统级建模和仿真，适用于各种应用，如电润湿两相流、液滴冲击过程（表面涂漆/冷却）和薄膜覆盖固体，包括精细尺度的流体动力学和化学。此外，该项目将创建新的方法来自动生成复杂形状的网格，有效地捕捉移动的边界。这项研究的一个成果将是一个自动网格工具（即代码），它将通过PI的网站向公众提供。最后，将开设一门关于形状优化（带有pde约束）的课程，为研究生提供连续体模型优化的专业知识。