Systems in nature and manmade often involves both fluids and solid structures. The behavior and characteristics of such a system are often affected by the interactions between the fluid flows and solid structures. Study of the fluid-structural interaction is of great importance to understand, design and control such systems, and also presents big technical challenges, due to the complexity in geometry of the systems and the coupling of multiple physics (nonlinear solid mechanics, and Navier-Stokes flows). This project aims to develop a Smoothed Finite Element Method (SFEM) for solving general fluid-structural interaction problems with complicated geometry for both fluid media and nonlinear solids undergoing large deformation. This is achieved by developing a set of techniques and properly designed combinations of these techniques based on essentially the weakened weak formulation that allows the use of a much more general functions for field approximation, including a certain class of discontinuous functions (in a proper G space). The formulations for both fluid flows and solid structures will be unified in the some framework of SFEM. The developed computational technique consists largely of 1) an SFEM-Solid solver for modeling the nonlinear and dynamic behavior of solids and structures; 2) an SFEM-Fluid solver for dynamic behavior of fluids; and 3) SFEM-FSI solver for dealing with effectively the coupling at the interfaces of the moving solids in the flowing fluid. The developed SFEM-FSI model is expected to have important "softening" effects so that it can work well with triangular/tetrahedral mesh that can be generated automatically, enabling automation in computation for complicated systems. For the interaction between the fluids and solids, ideas of the immersed boundary/finite element methods will be employed and modified for effectively dealing with the overlaid areas near the interfaces of the fluid media and solids, without re-meshing to generate the body-fitted mesh.
The proposed project is multidiscipline in nature across computational mathematics, fluid dynamics, structure mechanics, and biomechanics. The computational techniques developed in this project are expected to have a significant impact to all these related areas. In particular, the SFEM formulations for the fluid-structural interaction problems are expected to offer a profound new approach in solving complicated problems with coupled multi-physics. Once developed, the SFEM-FSI will be applicable in the modeling and simulation of a wide class of problems in science and engineering, such as flapping wings for special purpose aircrafts (quite, low speed, flapping wings) such as micro air vehicles (MAV), design of large span and flexible membrane structural systems, modeling blood flows in human hearts and vascular systems, etc. Because the SFEM-FSI allows the use of triangular/tetrahedral mesh, it enables automation-in-computation, and thus is expected to have a pervasive impact in significantly saving resources for manual operations in the meshing and re-meshing process. It is anticipated to change significantly the capability and applicability of the existing modeling and simulation software packages largely written in the past half a century based on the standard weak formulations. In addition, through this project students will be well-trained in the related STEM (science, technology, engineering and mathematics) area important for the long-term and sustainable development of knowledge-based economy in the United States.
