===== Fluid-structure coupling with overlapping fitted-unfitted fluid meshes ===== In this project, we aim to develop a Fluid-Structure Interaction solver by applying an overlapping fluid mesh technique. To do so, we introduce the multiscale Arlequin method [1], initially proposed and well developed in the Fracture Mechanics framework, into the Computational Fluid Mechanics context. The multiscale Arlequin method is based on three main ideas (see Fig. 1) [2,3]: • Superpose a discrete and suitable local model (Ω1) to a subregion of a global one (Ω0) where the global discretization is unsuitable for representing the localized effects;\\ • Define a distribution of energy between the models employing partition of unity weighting functions, ensuring the mechanical energy conservation;\\ • Couple the models in a subregion of the overlapping zone (Ωs), called gluing zone (Ωc). {{ :arlequin:arlequin.png?nolink&512 }}Figure 1 - Model superposition in the Arlequin Framework. To solve the fluid mechanics problem we employ a residual-based stabilized formulation and couple the domains by means of a Lagrange multiplier field, defined in the gluing zone. Following, some numerical examples are presented, but videos can be found on [[https://www.youtube.com/channel/UCUDQBJ4JNKeP2NFpvmEpH3Q/videos|https://www.youtube.com/channel/UCUDQBJ4JNKeP2NFpvmEpH3Q/videos]] {{ youtube>aoigCJBZZw4?large }}{{ youtube>IbYT7ct2LmE?large }}{{ youtube>_7wnjVkKcPo?large }}{{youtube>0HA2PaKmHEw?large}}{{youtube>nKO7xENw9Xw?large}}{{youtube>m3sc-tqbhU8?large}}{{youtube>jaUm6e3c75o?large }}{{youtube>698JMbIKGcQ?large }} ==== References ==== 1- Dhia, H. B. Multiscale mechanical problems: The arlequin method. Comptes Rendus Acad. Sci. Sér. Ilb., 326:899–904, 1998. 2- Dhia, H. B., Rateau, G.. The arlequin method as a flexible engineering design tool. International Journal for Numerical Methods in Engineering, 62(11):1442–1462, 2005. 3- H. B. Dhia. Further insights by theoretical investigations of the multiscale arlequin method. International Journal for Multiscale Computational Engineering, 6(3):215–232, 2008. ==== References ==== 1- Dhia, H. B. Multiscale mechanical problems: The arlequin method. Comptes Rendus Acad. Sci. Sér. Ilb., 326:899–904, 1998. 2- Dhia, H. B., Rateau, G.. The arlequin method as a flexible engineering design tool. International Journal for Numerical Methods in Engineering, 62(11):1442–1462, 2005. 3- H. B. Dhia. Further insights by theoretical investigations of the multiscale arlequin method. International Journal for Multiscale Computational Engineering, 6(3):215–232, 2008. Authors: Rodolfo A. K. Sanches Jeferson W. D. Fernandes Patricia Tonon