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

在工程和生物系统中，流动往往涉及复杂性，因为流域的形状可能是未知的，因为流体可能由或含有赋予不寻常行为的大分子和纳米颗粒组成。本研究旨在开发新的数值算法来计算这种复杂的流。由于其鲁棒性和可靠性，全耦合（单片/隐式）方案通常用于模拟具有自由边界的流；然而，这些方案可能变得不切实际，特别是在三维几何形状和流体具有复杂行为时，例如粘弹性。另一方面，分区格式实现简单，计算成本可能更低，但当应用于高度非线性的自由边界流动时，显示出严重的稳定性问题。本研究将为复杂流体的自由边界流动开发新的分区算法，该算法将具有良好的稳定性，计算成本低，易于实现。该项目开发的新算法将用于研究和理解生物学、医学和工程学中出现的复杂流程。主要应用包括人体动脉的血液流动，涂层工艺的优化，以及在石油开采中自然产生的乳剂的流动。本研究将由两名应用数学和化学工程博士研究生联合指导进行多学科训练。拟议研究的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基本作用的复杂流体力学的其他领域。

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.