Fluid Structure Interaction and Galilean Invariance.

LUCIANO GARELLI; RODRIGO R. PAZ; MARIO A. STORTI; LISANDRO D. DALCÍN

Computational Fluid Dynamics: Theory, Analysis and Applications

Nova Publisher

Lugar: New York; Año: 2010; p. 1 - 45

Multidisciplinary and Multiphysics coupled problems represent nowadays a challenging 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, compliance with the Discrete Geometric Conservation Law (DGCL), etc. Therefore, the aim of this chapter is to give an overview of the issues involved in the numerical 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 predictor schemes for the structural system and the influence of the partitioned coupling on stability are discussed. Another key point when solving FSI problems is the use of the Arbitrary Lagrangian Eulerian formulation" (ALE), which allows the use of moving meshes. As the ALE contributions aect the advective terms, some modications on the stabilizing and the shock-capturing terms, are needed. Also Dirichlet constraints at slip (or non-slip) walls must be modied when the ALE scheme is used. In this chapter the presented ALE formulation is invariant under Galilean transformations.