Modeling of Fluid-Structure Interactions with the Least-Squares FEM

For years, the development and advancement of numerical methods for the calculation of physical phenomena has been the objective of numerous research. With the available computational capacity nowadays, the simulation of more complex problems such as fluid-structure interaction (FSI) is becoming increasingly demanded. FSI applications require not only the stable and accurate solution of the individual domains, but also the consideration of the interaction at the interface. Here, the least-squares finite element method (LSFEM) offers a possibility of monolithic coupling with inherent fulfillment of the interface conditions. The present work aims to investigate different approaches to solve FSI problems using the LSFEM. For this purpose, different formulations for the calculation of fluid flows based on the incompressible Navier-Stokes equations and for elastic solid deformations based on linear and hyperelastic material behavior are considered. A main focus is on the time discretization of these approaches including the application and analysis of high-order methods and adaptive time-stepping based on embedded Runge-Kutta methods. Another important aspect of investigation is the coupling of the presented least-squares formulations to solve FSI problems with large deformations, taking into account the fluid in an Arbitrary-Lagrangian-Eulerian (ALE) description, the hyperelastic solid formulation, and the deformation of the background mesh. Furthermore, different formulations for the calculation of flows of non-Newtonian fluids are investigated, which are, for example, suitable for the simulation of blood flows.


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