The immersed interface method employs fixed grids and associated fast solvers to efficiently solve a variety of PDEs involving interfaces. It accurately captures the effects of interfaces by incorporating interface-induced jump conditions into numerical schemes. The main objective of this research is to enhance the robustness of this method to tackle 3-D large-size multi-scale flow problems. The PI proposes: (1) to derive and implement jump conditions for the method with a triangular mesh representation of a 3-D fluid-solid interface, (2) to handle solid collisions in a flow by incorporating into the method the lubrication theory, (3) to extend boundary condition capturing in the method from rigid solids to deformable solids, and (4) to use the domain decomposition and master-slave techniques for distributed-memory parallelization of the method for fluid-solid interaction and two-fluid flows. The PI and his students apply the enhanced method to investigate the dynamics of a collection of solid particles falling in a fluid and the aerodynamic control strategies in insect flight.
The proposed research is to push a computational method, the immersed interface method, so that it can be used to compute various interesting and important 3-D flow problems that are of large sizes and multiple scales. In particular, the PI and his students apply the method to study the dynamics of a collection of solid particles falling in a fluid and the aerodynamic control strategies in insect flight. A wide range of biological and physical systems involve the collective dynamics of objects, for example, schooling, microorganism colony, and particle suspension and sedimentation. The proposed study in this area will help understand, model, and design such systems. Winged insects are nature's answer to perfect small-scale flying machines. Understanding insect aerodynamics is of great interest to engineers in designing flapping-wing micro air vehicles, which can be employed in military surveillance, biological warfare detection, and reconnaissance in confined spaces. The PI plans to disseminate on his web page a user-friendly software and the associated tutorials on the immersed interface method to benefit undergraduate and graduate students who want to use the method for their research. Other educational impact of this research includes the support of an under-represented graduate student and the involvement of undergraduate students in computational research.
