The Institute of Mathematics of the Czech Academy of Sciences is organising a minisymposium in February 2018.
The core of the meeting will consist of a sequence of lectures of Professor Paolo Galdi (University of Pittsburg) who will deliver a series of lectures titled:
On the Motion of a Rigid Body with a Liquid-Filled Cavity: Mathematical Analysis
Abstract: Objective of this course is to provide a comprehensive analysis of the motion of the coupled system constituted by a rigid body containing an interior cavity that is entirely filled with a liquid. The main goal is to show how the presence of the liquid may dramatically influence the dynamics of the body. For this reason, we shall first briefly analyze the case when the cavity is empty and review classical results about the motion of a free or constrained rigid body, moving under the action of a given system of forces. Successively, in the second and more substantial part, we will focus on the case when the cavity is filled with a viscous liquid whose motion is governed by the Navier-Stokes equations. We will prove thus that then the liquid has always a stabilizing effect on the motion of the body and that the terminal state (as time goes to infinity) of the coupled system must be steady. The latter is, in general, a permanent rotation where the liquid is “frozen” inside the cavity and the coupled system moves as a single rigid body that, in some cases, can even reduce to rest. These results are also obtained via a “generalized principle of linearization” where one allows the spectrum of the linear operator to have a nonzero intersection with the imaginary axis.
An invited serie of lectures will be also delivered by Boris Muha (University of Zagreb). Its title is
The Fluid-Elastic Shell Interaction: Analysis, Numerics and Applications
Abstract: In this mini-course we will discuss questions of well-posedness, design of numerical schemes and application of fluid-structure interaction (FSI) problems. First, we will formulate a nonlinear fluid-elastic shell problem modeling the blood flow through medium to large artery. On this example we will explain the main challenges in design of numerical schemes for FSI problems. The emphasis will be on partitioned schemes where the structure and the fluid problem are solved with separate solvers. We will describe a partitioned scheme called "kinematically coupled scheme" and prove its stability and convergence. We will show how the ideas from numerics can be used to prove the existence of a weak solution. Finally, some extension of this ideas to different FSI problems will be discussed.
Miroslav Feistauer (Charles University in Prague) will present an invited talk:
On robust discontinuous Galerkin techniques for the simulation of interaction between compressible flow and nonlinear elasto-dynamic problems
Abstract: This lecture will be concerned with the numerical solution of compressible flow and dynamic elasticity by the discontinuous Galerkin (DG) method. We consider the linear case as well as the linear model, nonlinear St. Venant-Kirchhoff model and neo-Hookean model for the description of elastic dynamic deformations. The space discretization is carried out by the DG method. For the time discretization several techniques are applied and tested. The DG method is also applied to the solution of the compressible Navier-Stokes equations in time dependent domains. The dependence of the domain occupied by fluid on time is taken into account with the aid of the arbitrary Eulerian-Lagrangian (ALE) method. The applicability of the developed techniques is demonstrated by several numerical experiments and applied to the simulation of elastic bodies vibrations induced by compressible flow. Particularly the vocal fold vibrations induced by the air flow through vocal tract will be discussed. The results were obtained in cooperation with M. Balazsova, J. Cesenek, M. Hadrava, A. Kosik and J. Horacek.An invited talk will be presented also by Jaroslav Hron.
The event is intended for Ph.D. students and postdocs (presence of younger students is also encouraged). Each participant have a possibility to present his result in form of poster or short talk.