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===== 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 (Ω<sub>1</sub>) to a subregion of a global one (Ω<sub>0</sub>) 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 (Ω<sub>s</sub>), called gluing zone (Ω<sub>c</sub>).

{{  :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]]

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==== 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