This book starts by introducing the fundamental concepts of mathematical continuum mechanics for fluids and solids and their coupling. Special attention is given to the derivation of variational formulations for the subproblems describing fluid- and solid-mechanics as well as the coupled fluid-structure interaction problem. Two monolithic formulations for fluid-structure interactions are described in detail: the well-established ALE formulation and the modern Fully Eulerian formulation, which can effectively deal with problems featuring large deformation and contact. Further, the book provides details on state-of-the-art discretization schemes for fluid- and solid-mechanics and considers the special needs of coupled problems with interface-tracking and interface-capturing techniques. Lastly, advanced topics like goal-oriented error estimation, multigrid solution and gradient-based optimization schemes are discussed in the context of fluid-structure interaction problems.
Part I Fundamentals.- Introduction.- Models.- Coupled Fluid -Structure Interactions.- Discretization.- Part II Numerical Realization.- ALE Formulation for Fluid-Structure Interactions.- Fully Eulerian Formulation for Fluid-Structure Interactions.- Linear Solvers for Fluid-Structure Interactions.- Error Estimation and Adaptivity.- Part III Applications.- Optimization with fluid-structure interactions .- Mechano-chemical fluid-structure interactions and active materials.- Non-Stationary Dynamics and Coupled Oscillations.- Fluid-Structure Interaction with contact.- References.- Index