Workshop on Numerical Methods and Analysis in CFD - Abstract

Vacca, Giuseppe

Virtual elements for a fluid-structure interaction problem (online talk)

In collaboration with L. Beirão da Veiga, C. Canuto, R. H. Nochetto

The Virtual Element Method (VEM) is a recent technology introduced in [Beirão da Veiga, Brezzi, Cangiani, Manzini, Marini, Russo, 2012, M3AS] for the discretization of partial differential equations.
The VEM can be interpreted as a novel approach that generalizes the classical Finite Element Method to arbitrary even non-convex element-geometry.
The present talk is both an introduction to the VEM for the Stokes equation, aiming at showing the main ideas of the method, and a brief look at some application to fluid-structure interaction problems.
In the first part part of the talk we will describe the basics of the divergence-free virtual elements for the Stokes equation.
In the second part, we will present a first application of VEM for a fluid structure interaction problem. We study, both theoretically and numerically, the equilibrium of a hinged rigid leaflet with an attached rotational spring, immersed in a stationary incompressible fluid within a rigid channel.