Approximation of fluid-structure interaction problems with
Lagrange multiplier.
The Immersed Boundary Method (IBM) is a consolidated
technology for the approximation of problems involving the interaction
of fluids and solids. The Finite Element IBM (FE-IBM) provides an
efficient analysis for practical problems without the need of
approximating the Dirac delta function as in the original IBM. Within
this approach, semi-implicit time advancing schemes are stable if a
suitable CFL condition is satisfied.
A modification of the FE-IBM involves the introduction of a Lagrange
multiplier associated to a different approximation of the kinematic
condition. We called this formulation DLM-IBM, where DLM stands for
Distributed Lagrange Multiplier. In the case of solids of codimension
one, this new approach can be seen as a fictitious domain formulation.
It turns out that a semi-implicit time discretization of the coupled
system is unconditionally stable with respect to the time step size.
The stability of the fully discrete mixed problem is derived in terms
of an inf-sup condition which relates the solid and fluid meshes. Our
analysis leads to optimal convergence estimates.
11:00 a.m. to 12:00 p.m., Inria of Paris reseach center, building C, Jacques-Louis Lions lecture hall. Coffee from 10:45 a.m.
