The investigator and collaborators develop two classes of modern, hybrid numerical methods to study fluid-structure interaction for multi-phase flows in two and three dimensions. The hybrid computational methodologies merge two sets of usually disjoint approaches, front capturing (both through the level set method and through phase field based models) and front tracking (immersed boundary setting) on one hand, and moving meshes and adaptive mesh refinements on the other, to produce an efficient method that exploits the best features of each individual approach. In addition, controlled adaptive front-tracking in concert with a leading small-scales semi-implicit time discretization is used to overcome the long-standing time stepping problem (stiffness) associated with interfacial tension. The blending of all these ingredients produces fully adaptive and non-stiff hybrid methods for capturing accurately small-scale effects, high interfacial deformations, and flow-structure interaction in multi-phase and complex flows. The understanding of how flow-structure interaction influences the macroscopic behavior of multi-phase flows is of both fundamental and practical significance. Surfactants, viscoelastic fibers, fluid interfaces, and polymeric microstructures and nanostructures can radically change the behavior of a flow and ultimately determine the properties of complex soft matter formulations. The methodologies are an important tool to study flow-structure interaction for a wide variety of problems of direct interest to nanotechnology, the soft materials industry, and to some biomedical applications. The project also serves an important education goal: the interdisciplinary education and training of undergraduate and graduate students.
