Summer School

• Igor Aronson (Argonne National Lab, Chicago)
  Collective behavior in active systems.
  
  
  

  Abstract

  Lecture notes: Session1, Session 2, Session 3 & 4

  
  
• Didier Bresch (CNRS — LAMA, University of Savoie)
  Hierarchy of fluid models and environmental problem.
  
  
  

  Abstract An efficient interdisciplinary approach to study practical problems occurring in natural environmental media is important: geophysics, hydrology, ecology, sedimentation,….... It assumed the applied mathematicians have gained some knowledge of hierarchy of fluid models and that they know how such models are linked from one to the each other. During this lecture, we will present a hierarchy of different models, focus on some of their mathematical properties. We explain why it is important to understand mathematically the structure of such systems used in modelization and why the understanding of the continuous level may help to enrich the discrete level developed for numerics.

  Lecture notes: Part 1, Part 2, Part 3

• Alberto Figueroa (College of Engineering and Medical School, University of Michigan)
  Image-based modeling of the cardiovascular system
  
  
  
  

  Abstract Advances in numerical methods and 3D imaging techniques have enabled the quantification of hemodynamics in subject-specific anatomic and physiologic models. Patient-specific models are being used to guide cell culture and animal experiments and test hypotheses related to the role of biomechanical factors in vascular diseases. Furthermore, biomechanical models based on noninvasive medical imaging could provide invaluable data on the in vivo service environment where cardiovascular devices are employed and on the effect of the devices on physiologic function. Finally, the patient-specific modeling has enabled an entirely new application of cardiovascular mechanics, namely predicting outcomes of alternate therapeutic interventions for individual patients. In this lecture, we will review methods to create anatomic and physiologic models, obtain properties, assign boundary conditions, and solve the equations governing blood flow and vessel wall dynamics. Applications of patient-specific models of cardiovascular mechanics will also presented, followed by a discussion of the challenges and opportunities that lie ahead.

  Lecture notes: Part 1, Part 2, Part 3, Part 4,

• Céline Grandmont (Inria — LJLL, University of Paris VI)
  Fluid-Structure interaction.
  
  
  Abstract Many physical phenomena deal with a fluid interacting with a moving rigid or deformable structure. These kinds of problems have a lot of important applications, for instance, in aeroelasticity, biomechanics, hydroelasticity, sedimentation, etc. From the analytical point of view as well as from the numerical point of view they have been studied extensively over the past years. We will mainly focus on viscous fluid interacting with an elastic structure. The purpose of the present lecture is to present an overview of some of the numerical difficulties that may be encountered when dealing with fluid–structure interaction problems such as the geometrical nonlinearities or the added mass effect and how one can deal with these difficulties.
  
  

  Lecture notes: Notes

  Videos: Lecture 1, Lecture 2, Lecture 3, Lecture 4,

• Paul Vigneaux (ENS Lyon — UMPA)
  Small scale fluid dynamics, interfaces and numerics.
  
  
  Abstract This lecture is an overview on microfluidics and on the dynamics of fluid interfaces at small scales where surface tension has a leading influence. We will present the various models from particles to continuum approaches and hydrodynamic limits studies, as well as numerical methods for gas and fluids (DSMC, LBM, MD, DPD). As an illustration, we will talk about wall laws for liquids. We will then explore the dynamics of droplets at the microscale, which is of interest in life sciences. Numerical difficulties will be described and Level Set methods for evolving interfaces will be emphasized to treat these kind of problems.
  
  

  Lecture notes: Notes

Tentative schedule