Project Grant 2205695

This $229,965 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support research at the University of Notre Dame focused on developing mathematical theory and numerical methods for the diffuse interface method applied to coupled fluid dynamics systems. Over a three year period from September 2022 through August 2025, the grantee will study a hierarchy of coupled flow models including fluid-porous medium interaction, fluid-poroelastic structure interaction, and fluid-elastic structure interaction. For each model, work will include proving well-posedness of the underlying diffuse interface problem, demonstrating convergence to the corresponding sharp interface model as the width of the interfacial layer approaches zero, and calculating convergence rates accounting for modeling and numerical approximation errors using finite element methods. Numerical methods will also be developed and implemented for each model. Graduate students will receive training through involvement in the research.