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 (Ω_s), called gluing zone (Ω_c).

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

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.

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