Title: Mathematical and Computational Modeling of free boundary flows with strong interfacial effects


Abstract:

Free boundary flows involve the motion of a fluid in a region of space
which is not fixed but it evolves in time depending on the fluid flow
itself. In this talk, I will focus on fluid-structure interactions and
free capillary surface flows, with applications to biomedical and
engineering problems.

The main difficulties related to the mathematical and computational
modeling of free boundary flows are the following.  (1) The interface
deformation is coupled to the fluid flow both kinematically
(continuity of the velocities) and dynamically (balance of stresses),
and the coupling is nonlinear. This becomes a critical issue when the
interfacial effects dominate the flow (e.g. fluid-structure
interactions with fluid/solid density ratio approximately equal to one
and free capillary surface flows with small Capillary numbers) (2) The
coupled problem embodies a competition between hyperbolic effects
(e.g. fluid avdection, wave propagation in the solid,...) and
parabolic effects (e.g. viscous dissipation in the fluid, viscous
dissipation in the solid,...). A sophisticated combination of
hyperbolic and parabolic techniques is required for the analytical and
numerical study of the problem.

In this talk I will present some new ideas concerning the design of
efficient numerical algorithms for the solution of free surface flows
with strong interfacial effects, and I will discuss how the numerical
strategy is related to the mathematical features of the interfacial
nonlinearities arising through the conditions of continuity of
stresses and velocities. Applications related to blood flow
simulations and coating flows will be presented and numerical results
will be discussed.