Numerical Algorithms and Simulations for Multiphase Flows of Multiple Immiscible Incompressible Fluids

该研究项目旨在开发数学和计算工具、方法和算法来模拟和理解一类具有实际工程意义和基本物理意义的多相多组分流动问题。该项目中正在研究的系统与环境、能源和材料科学相关。例如，这样的多相系统出现在溢油补救的建模中。另一个例子是在过去的十年中发现的一种被称为液体注入表面的新型功能表面，它表现出各种吸引人的特性，如自清洁、防结冰和防污垢。这些多相多组分问题是许多技术进步的基础，从印刷电子电路和传感器，到光流控显微镜和波导，到防水织物，再到石油回收和碳封存。该项目旨在开发改进的高效和有效的计算方法，以应对此类系统模拟中的挑战。该项目为研究生和本科生提供研究培训机会。这项研究旨在设计有效的方法来模拟和理解三种或三种以上不相容的不可压缩流体系统的动力学，这些流体具有不同的物理性质，如密度、粘度和成对的表面张力。这些系统给数值模拟带来了巨大的计算和算法挑战，因为涉及到大量的流体界面、三相线、接触线和接触角。该项目建立在近年来开发的还原一致性和热力学一致性公式的基础上，并将提供计算预测能力和有效技术，以阐明和了解多种流体成分、多种类型的流体界面和多种类型的接触线之间的相互作用。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This research project aims to develop mathematical and computational tools, methods, and algorithms for simulating and understanding a class of multiphase multicomponent flow problems that are of practical engineering significance and fundamental physical importance. The systems under study in this project have relevance to the environment, energy, and materials science. For example, such multiphase systems occur in modeling for remediation of oil spills. Another example is the novel class of functional surfaces called liquid infused surfaces discovered in the past decade, which exhibit a variety of attractive properties such as self-cleaning, anti-icing and anti-fouling. These multiphase multicomponent problems underlie numerous technological advances, from printed electronic circuits and sensors, to opto-fluidic microscopes and waveguides, to water-resistant fabrics, to oil recovery and carbon sequestration. The project aims to develop improved efficient and effective computational methods to tackle the challenges in simulations for such systems. This project provides research training opportunities for graduate and undergraduate students. The research aims at devising efficient and effective methods for simulating and understanding the dynamics of a system of three or more immiscible incompressible fluids with different physical properties such as densities, viscosities, and pairwise surface tensions. These systems pose enormous computational and algorithmic challenges to numerical simulations, because of the multitude of fluid interfaces, three-phase lines, and contact lines and contact angles involved. The project builds upon the reduction-consistent and thermodynamically-consistent formulations developed in recent years and will provide computational prediction capability and effective techniques for illuminating and understanding the interactions among multiple fluid components, multiple types of fluid interfaces, and multiple types of contact lines.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.