9h30 - 10h30, C. Murea, Sensitivity and approximation of fluid-structure equations coupled by virtual control method
10h30 - 11h, Pause
11h - 12h, E. Maitre, A combined level-set
immersed boundary approach to describe the motion of an elastic curve in
a fluid. Application to cell dynamics.
14h30 -15h30, C. Grandmont, Some existence results for fluid-structure interaction problems.
15h30 - 16h, Pause
16h -17h, S. Piperno, Energy-conserving partitioned procedures
for the transient solution of coupled problems.
Friday, October 10,2003
9h-10h, J.-F. Gerbeau, Fluid-structure interaction problems in blood flows
10h - 10h30, Pause
10h30 - 11h30, J. Cagnol, Free boundary conditions associated with an intrinsic geometric shell model in the context of a structure-acoustic system
The list of abstracts is available on the bottom of this page!
You will find the campus map on the page
http://www.uha.fr/web/plan/mulhouse.jsp
Building no 21 on the map:
http://www.uha.fr/web/plan/mulhouse.jsp
Fax : 03 89 33 66 53
Speaker: E. Maitre, Laboratoire
de Modélisation et Calcul, IMAG, Grenoble
Titre: A combined level-set immersed boundary approach to describe
the motion of an elastic curve in a fluid. Application to cell dynamics.
Abstract: Cell shape deformation (in particular membrane protrusions)
and motion are routinely observed as spontaneous activity
or dynamic response to external stimuli (chemiotaxis). We are interested
in understanding what
are the driving mechanisms/parameters for these dynamics.
In that aim, we construct toy models, with minimal biochemistry and
fluid dynamics, capable to
reproduce observed behavior. The simplest model one can think of consists
in an elastic curve immersed in a fluid.
This is already a challenging fluid-structure model from the mathematical
and numerical point of view.
Whereas level set and immersed boundary technics are classical nowadays,
one originality of
our approach is to combine them into a synthetic model for which we
can obtain energy estimates.
These estimates bring us some confidence in the numerical simulations
that have beeen performed.
In this talk we introduce a model consisting in Navier-Stokes equations
coupled with a
transport equation of a fonction whose zero level set is the elastic
curve.
The elastic force exerced by the structure on the fluid is expressed
in a
level-set/immersed boundary framework. An energy estimate is proven
for this model, and
numerical simulations are presented. A modification of
this model to handle somehow the biomechanical behavior of the membrane
is proposed.
Speaker: Serge Piperno, CERMICS, INRIA, Sophia - Antipolis
Titre: Energy-conserving partitioned procedures
for the transient solution of coupled problems.
Abstract: In some cases, the conservation of a global energy
is
one of the key points for the accurate transient solution of
coupled systems. This is the case for instance for
fluid-structure interactions when a direct staggered time scheme
is used, or for the simulation in the time domain of the
propagation of acoustic or electromagnetic waves when the
geometrical domain in decomposed. The conservation of a global
energy is then seeked for, in order to ensure the global
stability of the algorithm or its accuracy for simulating
fluid-structure problems near critical conditions.
Speaker: J.-F. Gerbeau, INRIA, Rocquencourt
Title: Fluid-structure interaction problems in blood flows
Abstract: We will present some results in the numerical simulation
of the
mechanical interaction between the blood and the wall of large arteries.
In such problems, the overall stability strongly depends on the accuracy
of the resolution of a nonlinear equation raised on the fluid-structure
interface. Fixed point algorithms with relaxation are often used
to
solve this equation. We will show how to use simplified models in order
to design more efficient algorithms. The use of such simplified
models
in the parallelization in time will be also discussed.
Speaker: John Cagnol, Pole Universitaire Leonard de Vinci, Paris, France
Title: Free boundary conditions associated with an intrinsic
geometric
shell model in the context of a structure-acoustic system
Abstract: A wide variety of engineering and applied mathematics
problems can be modeled in the context of thin shells. Many problems
involve issues such as, for example, boundary feedback control, for
which sophisticated mathematical analysis have been developed in the
analogous plate case. The difficulty with adapting these techniques
to classical shell models is one motivating factor driving the
development of new modeling schemes. The technique proposed by
Michel
Delfour and Jean-Paul Zolesio and used here, takes advantage of the
intrinsic geometric properties of the shell. The model used in
this
presentation was introduced in a joint work by John Cagnol, Catherine
Lebiedzik, Irena Lasiecka and Jean-Paul Zolesio, where the Kirchhoff
hypothesis and shallowness assumption were used. In this talk
we
shall expand this shell model by formulating the associated 'free'
boundary conditions. We will present results obtained jointly
with
Catherine Lebiedzik where the shell is assumed to be clamped on a
portion of the boundary and free on the rest. We will also present
the control operator in the language of intrinsic modeling.
Speaker: C. Murea, Laboratoire de Mathématiques et Applications, Université de Haute-Alsace
Title: Sensitivity and approximation of fluid-structure equations coupled by virtual control method
Abstract: The formulation of a particular fluid-structure interaction
as an optimal
control problem is the departure point of this work. The analytic
expression for the gradient of the cost function is obtained in order
to
devise accurate numerical methods for the minimization problem.
Numerical simulations of blood flow in arteries are presented.