Monday 18-th November 2019- INRIA
Stefan Frei (University of Konstanz).

Title : A unified Nitsche approach for fluid-structure interactions with contact
(Joint work with E. Burman and M.A. Fernández)

In this talk we discuss fluid-structure interaction (FSI) problems with large structural deflections and the transition to contact between parts of the structure and an exterior wall. Several modelling issues arise when the fluid layer between structure and wall tends to vanish, including the well-known no-collision paradox related to the Navier-Stokes equations.

To tackle the equations numerically, we develop Nitsche-based formulations for both the FSI part and the contact model. Our numerical approach for contact is based on the works of Chouly and Hild [2] for contact problems in solid mechanics. We present two numerical approaches, both of them formulating the FSI interface and the contact conditions simultaneously in equation form on a joint interface-contact surface $\Gamma(t)$. The first approach uses a relaxation of the contact conditions to allow for a small mesh-dependent gap between solid and wall. The second alternative introduces an artificial fluid below the contact surface. The resulting system of equations can be included in a consistent fashion within a fully implicit monolithic variational formulation, which prevents the so-called “chattering” phenomenon [1].

To deal with the topology changes in the fluid domain at the time of impact, we use a fully Eulerian approach for the FSI problem [3,4]. We show a stability result and discuss the effect of slip and no-slip conditions. Finally, we illustrate the performance of the methods by means of detailed numerical investigations.

[1] E. Burman, M.A. Fernández, S. Frei: A Nitsche-based formulation for fluid-structure interactions
with contact, accepted at ESAIM M2AN (2019),
[2] F. Chouly, P. Hild. A Nitsche-based method for unilateral contact problems: Numerical analysis,
SIAM J Numer Anal 51(2):1295–1307 (2013)
[3] T. Dunne. An Eulerian approach to fluid-structure interaction and goal-oriented mesh refinement,
Int J Numer Methods Fluids 51:1017-1039 (2006)
[4] S. Frei. Eulerian finite element methods for interface problems and fluid-structure interactions,
Dissertation, Heidelberg University (2016)

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