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SIMUMAT (Summer School 2007): Numerical Analysis & Control in Fluids
Detalles
Fecha: 
07/16/2007 to 07/20/2007
Contacto: 

Carlos Castro (UPM)

Francisco Palacios (INTA)

Takéo Takahashi (INRIA)

Marius Tuscnak (UNancy)

Antonio Baeza (UAM)

Web: 
http://www.simumat.es/summer2007

COURSE: Numerical approximation and control in fluids problems

 

This course is a brief exposition of the main mathematical and computational tools in control problems in fluid dynamics and their numerical approximation. The course will focus on the following topics: fluid equations; conservations laws; weak solutions; conservative numerical methods; optimization; optimal design; finite differences and adjoint methods. 
     
The course will also have a practical scope in which the Euler equations in a sonic tube and a shape optimization problem will be solved and analyzed. In particular, participants will be guided to implement several numerical methods for linear and nonlinear scalar equations and the system of Euler equations in one dimension; including visualization techniques and simulations with MATLAB.  They will also experiment with an optimization method for the Euler equations already programmed, analyzing the results in different situations. Finally, we present the analysis and optimal design of a real-life, industrial aeronautical problem.

Instructors:

  • Carlos Castro, Universidad Politécnica de Madrid
  • Francisco Palacios, Instituto Nacional de Técnica Aeroespacial
  • Antonio Baeza, Universidad Autónoma de Madrid

 

COURSE: Fluid-structure interactions

 

In this type of problem, a system of PDE's modelling a fluid (Laplace equation, wave equation, Stokes or Navier-Stokes equations) is coupled to the equations modelling the motion of a portion of the boundary (this might be a rigid body motion or elastic vibrations). One of the difficulties raised by these problems is the occurrence of free boundaries. Our aim is to tackle various control problems by combining methods coming classical systems theory and methods coming from the modern theory of partial differential equations. Recent progress makes now possible the use of robust control techniques for partial differential equations modelling systems coming from hydraulics, acoustics, chemistry or optics.

 

Instructors:

  • Marius Tuscnak,  Université Henri Poincaré Nancy 1
  • Takéo Takahashi,  Université Henri Poincaré Nancy 1

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