Modelling and Simulation of Fluid-Structure Interactions with Contact and Multiple Scales in Time

Abstract

Fluid-structure interaction (FSI) describes the interplay of a flow and a solid mechanical system. Due to the many applications in industry, technology and science, FSI has been a very active field of research in recent decades, both from a mathematical and from an engineering perspective. Mathematically, the combination of fluid and solid mechanical equations poses several challenges, for example due to the different coordinate systems involved, time-dependent subdomains and interfaces and the different characters of the underlying partial differential equations. More recently, the additional difficulties that arise when the solid comes into contact with another solid or an exterior wall have been the subject of different publications. Among others, additional challenges are given by the resulting topology change in the fluid domain, the Navier-Stokes no-collision paradoxon and the nonlinearly changing interface conditions in the transition to contact. This habilitation thesis consists of nine journal articles [F1]-[F9] that deal with the modelling and simulation of fluid-structure interaction problems and contact [ F1]-[F3], the development and analysis of related discretisation techniques in space and time [F4]-[F7] and the efficient numerical simulation for FSI problems with multiple scales in time [F8, F9].