Development of a Verified and Validated Computational Framework for Fluid-Structure Interaction: Investigating Lifting Operators and Numerical Stability

Abstract

Computational models of fluids, structures, and the interaction between them shows good promise in science and engineering, with nearly infinitely many applications. However, fluid-structure interaction (FSI) is poorly understood from a mathematical and computational stand point. The goal of this thesis was to develop a virtual framework for computational FSI problems using a monolithic scheme. The mathematics and physics that govern fluid and structures was introduces, and the necessary conditions to model FSI problems. The $\theta$-scheme was implemented in FEniCS because of its ability to uphold stability for long time FSI simulations. The code has been verified in parts using MMS.\newline The computational FSI solver was validated against the benchmark proposed by Hron and Turek 2010. Both the fluid and structure were validated separately, before addressing the FSI problem. Data was compared with contributions made by leading scientists in the field, and shown good agreement. In the fifth chapter of this thesis, the crucial choice of lifting is discussed for FSI problems with moderate to large deformations, and the need for long-term numerical stability schemes.