Optimal control as a tool for solving the stationnary Euler equation with periodic boundary conditions

  • T. Chacon
  • O. Pironneau
Conference paper
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 84)


We study the numerical resolution of the 3D stationnary Euler equation, in the unit cube with periodic boundary conditions.

A formulation of the problem as distributed parameters optimal control problem is first given. This problem is discretized by the Finite Elements Method and solved by conjugate gradient algorithms. In order to set rid of a quadratic state construit several different formulations of the optimal control problem are studied. A quasi-Newton method is also tested.


Finite Element Method Optimal Control Problem Periodic Boundary Condition Conjugate Gradient Conjugate Gradient Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    D. MCLAUGHLIN G. PAPANICOLAOU, O. PIRONNEAU, Convection of microstructures and related problems, SIAM S. Appl. Math., Vol.45, No. 5, Oct. 1985, pp.780–797.Google Scholar
  2. [2]
    M. HENON, Numerical exploration of Hamiltonian system (to appear).Google Scholar
  3. [3]
    C. BEGUE, Simulation numérique de la turbulence par méthode d'homogénérisation. Thèse 3ème Cycle, Univ. Paris VI, Déc. 1983.Google Scholar
  4. [4]
    T. CHACON, Etude d'un modèle pour la convection des microstructures. Thèse 3ème Cycle, Univ. Paris VI, April 1985.Google Scholar
  5. [5]
    T. CHACON, Contribucion al estudio del modelo M.P.P. de turbulencia. Tesis Doctoral Univ. Sevilla (Spain), Sept. 1984.Google Scholar
  6. [6]
    J.P. OLVER, A nonlinear Hamilton System structure for the Euler equations. Journal Math. Anal. Appl. 89, pp. 233–250 (1982).Google Scholar
  7. [7]
    T. CHACON, O. PIRONNEAU, On the mathematical foundations of the k-ɛ turbulent model (to appear).Google Scholar
  8. [8]
    C. BEGUE, O. PIRONNEAU, Hyperbolic systems with periodic boundary conditions, Comp. & Maths. with Appls., Vol.11, Nos. 1–3, pp. 113–128 (1985).Google Scholar
  9. [9]
    R. GLOWINSKI, B. MANTEL, J. PERIAUX, O. PIRONNEAU, A Finite Element Approximation of Navier-Stokes equations for incompressible viscous fluids. Computer Methods in Fluids. Pentech Press, New-York (1980).Google Scholar
  10. [10]
    A.J. SPENCER, Continuum Physics, Volume I. Academic Press, New-York and London, (1971).Google Scholar
  11. [11]
    A. BUCKLEY, A. LENIR, ON-Like variable storage conjugate gradients. Mathematical Programming 27, 2, pp. 155–175 (1983).Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • T. Chacon
    • 1
    • 2
  • O. Pironneau
    • 3
  1. 1.InriaLe ChesnayFrance
  2. 2.Facultad de MatematicasUniversidad de SevillaSevillaSpain
  3. 3.Université Paris 6 and InriaFrance

Personalised recommendations