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.