Collaborative Research: Efficient algorithms for free boundary flows of complex fluids

在工程和生物系统中，流动通常涉及复杂性，因为流动区域的形状可能是未知的，也因为流体可能由或包含赋予不寻常行为的大分子和纳米颗粒组成。这项研究旨在开发新的数值算法来计算这种复杂的流动。由于其稳健性和可靠性，全耦合(整体/隐式)格式通常用于模拟具有自由边界的流动；然而，这些格式可能变得不切实际，特别是在三维几何和流体具有复杂行为时，例如粘弹性。另一方面，分区格式具有更简单的实现和潜在的更低的计算量，但当应用于高度非线性的自由边界流时，表现出严重的稳定性问题。这项研究将开发新的复杂流体自由边界流动的分割算法，该算法将结合良好的稳定性、低计算成本和易于实现。该项目开发的新算法将用于研究和理解生物、医学和工程中的复杂流动。主要应用包括人体动脉中的血液流动，涂层工艺的优化，以及在采油过程中自然出现的乳状液流动。多学科培训将纳入研究，由两名应用数学和化学工程博士生联合提供建议。拟议的研究结果将通过科学计算影响网络基础设施，以及计算发挥核心和关键作用的其他复杂流体力学领域。

In engineered and biological systems, flows often involve complexity because of the shape of the flow domain which can be unknown, and because the fluid can consist of or contain macromolecules and nanoparticles which impart unusual behavior. This research aims at developing novel numerical algorithms for computing flows with such complexity. Because of their robustness and reliability, fully-coupled (monolithic/implicit) schemes are commonly used to simulate flows with free boundaries; however, these schemes may become impractical, especially in three-dimensional geometries and when the fluid has complex behavior, e.g., viscoelasticity. On the other hand, partitioned schemes have simpler implementation and potential lower computational cost, yet have shown severe stability issues when applied to highly nonlinear free boundary flows. This research will develop novel partitioned algorithms for free boundary flows of complex fluids which will combine good stability properties with low computational costs and ease of implementation.The novel algorithms developed in the project will be used to study and understand complex flows arising in biology, medicine, and engineering. Major applications include blood flow in human arteries, the optimization of coating processes, and the flow of emulsions which naturally occur in oil extraction. Multidisciplinary training will be incorporated in the research by joint advising of two PhD students in Applied Mathematics and Chemical Engineering. The outcomes of the proposed research will impact cyberinfrastructures through scientific computing, as well as other areas of complex fluid mechanics where computing plays a central and essential role.