Advanced Modeling, Numerical Studies and Analysis of Fluid-Structure Interaction Problems

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The purpose of this project is to develop advanced modeling and novel numerical techniques in order to effectively perform stable, precise, and state of the art simulations for a type of dynamic fluid-structure interaction (FSI) problem with a possibly large rotational and deformable elastic structure. Coupled fluid-structure problems, which are characterized by the interaction of fluid forces and structural deformations/rotations, play prominent roles in many scientific and engineering fields such as aerodynamics, bio-engineering and hydrodynamics. Yet, a comprehensive study of such problems remains a challenge due to their strongly nonlinear coupling and multidisciplinary nature, so a correct mathematical model equation to precisely demonstrate the basic characteristics of FSI becomes more important. For most FSI problems, analytical solutions to the model equations are impossible to obtain, whereas laboratory experiments are also limited in scope; thus to investigate the fundamental physics involved in the complex interaction between fluids and solids, mathematical modeling and numerical simulations become more necessary and promising. Because of the complexity of the underlying mathematical model of FSI problems, current solution techniques are still far from being satisfactory, and therefore more efficient and robust numerical techniques are urgently needed.While there is still a long way before such multiphysics FSI problems can be completely solved in an efficient and precise manner, this proposal will be devoted to the development of advanced modeling and novel numerical techniques for the following three methods: Arbitrary Lagrangian-Eulerian (ALE) method, fictitious domain method, and full Eulerian-phase field method. These methods still possess the problems of well-posedness, stability and/or convergence analysis, as well as a number of critical numerical difficulties caused by the mismatched grid on the interface, nonlinear coupling, and discontinuous/degenerate coefficients. The goal of this project is to address these difficulties, develop and analyze proper discretization schemes, robust iterative methods, and high performance computing techniques to solve the discretized system of FSI model in the sense of stable, fast and accurate convergence. The advanced and novel modeling and numerical techniques to be developed include: (1). A newly developed FSI model for a rotational and deformable elastic structure that is immersed in fluid, and its efficient numerical method with an ALE approach and method of characteristics (MOC). (2). A new fictitious domain method for FSI problem with incompressible fluid and compressible structure, and its well-posedness analysis. (3). A new stable implicit scheme for a full Eulerian FSI model with phase field formulation to deal with the degenerate structural momentum equation in Eulerian description. Newly developed numerical techniques will be immediately implemented to enrich our in-house codes and to validate our FSI model with the obtained numerical solutions. It is hoped that the effective numerical techniques developed in this proposed project will result in one to two orders of magnitude of improvement over current existing FSI solvers. Industrial applications are natural outcomes of this research because of its extensive applications in industry, and the close ties of my collaborators with engineers in the fields of hydrodynamics and bio-engineering.