Seminari Dipartimento di Matematica - Politecnico di Milano

Fluid–Structure Interaction (FSI) is of great relevance in many fields of engineering as well
is in the applied sciences and material forming with applications ranging from aerodynamics to
bioengineering and from automotive to civil engineering. There is an exigent need of robust high quality approaches for complex real industrial problems, i.e. approaches that have the potential to turn over from being a challenging and fascinating research topic to an advanced tool with real predictive capabilities. Usually when interaction effects are essential this comes along with large structural deformations and/or with turbulent flows.

However, many available approaches lack
robustness especially in these situations. One possible solution to that are fixed grid approaches and are available in the literature - but each have more or less severe drawbacks and therefore have problems to meet the challenges to become a real industrial tool.

In this paper, we propose a general new immersed stress method for solving rigid body motions in the incompressible Navier-Stokes flow. The proposed method is also developed in the
context of the monolithic formulation. It consists in considering a single grid and solving one set of equations with different material properties. A fast anisotropic mesh adaptation [1] algorithm based on the variations of the distance function is then applied to ensure an accurate capture of the discontinuities at the fluid-solid interface. Such strategy gives rise to an extra stress tensor in the Navier-Stokes equations coming from the presence of the structure in the fluid.
The system is solved using a finite element variational multiscale (VMS) method, which
consists in here of decomposition for both the velocity and the pressure fields into coarse/resolved scales and fine/unresolved scales. The distinctive feature of the proposed approach resides in the possible efficient enrichment of the extra constraint. This choice of decomposition is shown to be favourable for simulating multiphase flows at high Reynolds number [2].

REFERENCES
[1] T. Coupez, “Metric construction by length distribution tensor and edge based error for anisotropic
adaptive meshing”, J. Comp. Phys. In Press, DOI: 10.1016/j.jcp.2010.11.041. (2010)
[2]

REFERENCES

[1] T. Coupez, “Metric construction by length distribution tensor and edge based error for anisotropic adaptive meshing”, J. Comp. Phys. In Press, DOI: 10.1016/j.jcp.2010.11.041. (2010)

[2] E. Hachem, B. Rivaux, T. Kloczko, H. Digonnet and T. Coupez, “Stabilized finite element
method for incompressible flows with high Reynolds number”, J. Comp. Phys., Vol. 224, pp.
8643-8665, (2010).