Fluid flows in deformable domains occur in many applications in science, engineering and medicine. Examples include aeroelastic problems, fluttering of wings and structures, coating flows and, of course, blood flow in the cardiovascular system. The main difficulty in the analysis and simulation of the flow of a fluid in a deformable domain lies in the fact that the dynamics of the flow and the evolution of the domain are strongly coupled. The domain deforms under the action of the fluid stresses and, conversely, the fluid motion is modified by the displacement of the domain. Thus, the domain deformability introduces additional unknowns and nonlinearities in the problem, such as the shape of the domain and its evolution in time, that are not typically present in problems defined on fixed domains and bring new challenges from both the mathematical and computational viewpoints.
In this talk, we will review the basic principles underlying the mathematical formulation of the fluid flow in deformable domains as a system of nonlinear partial differential equations of mixed (hyperbolic/parabolic) type. We will discuss results concerning the well-posedeness of the system as well as numerical strategies to design stable algorithms by leveraging the hyperbolic/parabolic nature of the problem. Results will be presented in the context of blood flow applications.\
Coffee and Cookies will be served in Room 306 at 3:00pm.