Radial basis functions for inter-grid interpolation and mesh motion in FSI problems

When addressing multi-domain/multi-physics problems, the correct exchange of mathematical information at subdomain interfaces is crucial. In this paper, such transfer is analyzed in the particular framework of a fluid-structure interaction (FSI) problem. A genuine FEM-FEM formulation is considered firstly, followed by a mixed FVM-FEM formulation. In both cases, we focus on two critical issues: how to interpolate numerical quantities at the interface, and how to achieve the property of conservation of energy transfer. In the second part of this work, we analyze the use of Radial Basis Functions (RBF) to handle both mesh motion and interpolation of numerical variables over non-matching interface grids. Different kinds of radial basis functions are considered and numerical tests comparing their performances in terms of accuracy and stability are presented and discussed.