This monograph discusses modeling, adaptive discretisation techniques and the numerical solution of fluid structure interaction. An emphasis in part I lies on innovative discretisation and advanced interface resolution techniques. The second part covers the efficient and robust numerical solution of fluid-structure interaction. In part III, recent advances in the application fields vascular flows, binary-fluid-solid interaction, and coupling to fractures in the solid part are presented. Moreover each chapter provides a comprehensive overview in the respective topics including many references to concurring state-of-the art work. Contents Part I: Modeling and discretization On the implementation and benchmarking of an extended ALE method for FSI problems The locally adapted parametric finite element method for interface problems on triangular meshes An accurate Eulerian approach for fluid-structure interactions Part II: Solvers Numerical methods for unsteady thermal fluid structure interaction Recent development of robust monolithic fluid-structure interaction solvers A monolithic FSI solver applied to the FSI 1,2,3 benchmarks Part III: Applications Fluid-structure interaction for vascular flows: From supercomputers to laptops Binary-fluid-solid interaction based on the Navier-Stokes-Cahn-Hilliard Equations Coupling fluid-structure interaction with phase-field fracture: Algorithmic details

Fluid-structure interaction problems arise in many application fields such as flows around elastic structures or blood flow problems in arteries. One method for solving such a problem is based on a reduction to an equation at the interface, involving the so-called Steklov-Poincare operators. This interface equation is solved by a Newton iteration for which directional derivatives with respect to the interface perturbation have to be evaluated appropriately. One step of the Newton iteration requires the solution of several decoupled linear sub-problems in the structure and the fluid domains. These sub-problems are spatially discretized by a finite element method on hybrid meshes containing different types of elements. For the time discretization implicit first order methods are used. The discretized equations are solved by algebraic multigrid methods for which a stabilized coarsening hierarchy is constructed in a proper way.