Fluid structure interaction and Galilean invariance

Multidisciplinary and Multiphysics coupled problems represent nowadays a chal-lenging field when studying or analyzing even more complex phenomena that appear in nature and in new technologies (e.g. Magneto-Hydrodynamics, Micro-Electro-Mechanics, Thermo-Mechanics, Fluid-Structure Interaction, etc.). Particularly, when dealing with Fluid-Structure Interaction problems several questions arise, namely the coupling algorithm, the mesh moving strategy, the Galilean Invariance of the scheme, the compliance with the Discrete Geometric Conservation Law (DGCL), etc. There-fore, the aim of this chapter is to give an overview of the issues involved in the numer-ical solution of Fluid-Structure Interaction (FSI) problems. Regarding the coupling techniques, some results on the convergence of the strong coupling Gauss-Seidel iteration are presented. Also, the precision of different predic-tor schemes for the structural system and the influence of the partitioned coupling on stability are discussed. Another keypoint when solving FSI problems is the use of the "Arbitrary La-grangian Eulerian formulation" (ALE), which allows the use of moving meshes. As the ALE contributions affect the advective terms, some modifications on the stabiliz-ing and the shock-capturing terms,are needed. Also Dirichlet constraints at slip (ornon-slip) walls must be modified when the ALE scheme is used. In this chapter the presented ALE formulation is invariant under Galilean transformations.