Control of Transonic Shock Positions

Olivier Pironneau

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 8, page 907-914
  • ISSN: 1292-8119

Abstract

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We wish to show how the shock position in a nozzle could be controlled. Optimal control theory and algorithm is applied to the transonic equation. The difficulty is that the derivative with respect to the shock position involves a Dirac mass. The one dimensional case is solved, the two dimensional one is analyzed .

How to cite

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Pironneau, Olivier. "Control of Transonic Shock Positions." ESAIM: Control, Optimisation and Calculus of Variations 8 (2010): 907-914. <http://eudml.org/doc/90677>.

@article{Pironneau2010,
abstract = { We wish to show how the shock position in a nozzle could be controlled. Optimal control theory and algorithm is applied to the transonic equation. The difficulty is that the derivative with respect to the shock position involves a Dirac mass. The one dimensional case is solved, the two dimensional one is analyzed . },
author = {Pironneau, Olivier},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Partial differential equations; control; calculus of variation; nozzle flow; sensitivity; transonic equation.; transonic equation},
language = {eng},
month = {3},
pages = {907-914},
publisher = {EDP Sciences},
title = {Control of Transonic Shock Positions},
url = {http://eudml.org/doc/90677},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Pironneau, Olivier
TI - Control of Transonic Shock Positions
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 8
SP - 907
EP - 914
AB - We wish to show how the shock position in a nozzle could be controlled. Optimal control theory and algorithm is applied to the transonic equation. The difficulty is that the derivative with respect to the shock position involves a Dirac mass. The one dimensional case is solved, the two dimensional one is analyzed .
LA - eng
KW - Partial differential equations; control; calculus of variation; nozzle flow; sensitivity; transonic equation.; transonic equation
UR - http://eudml.org/doc/90677
ER -

References

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  1. F. Hecht, H. Kawarada, C. Bernardi, V. Girault and O. Pironneau, A finite element problem issued from fictitious domain techniques. East-West J. Appl. Math. (2002).  
  2. M. Olazabal, E. Godlewski and P.A. Raviart, On the linearization of hyperbolic systems of conservation laws. Application to stability, in Équations aux dérivées partielles et applications. Gauthier-Villars, Éd. Sci. Méd. Elsevier, Paris (1998) 549-570.  
  3. J. Necas, Écoulements de fluide : compacité par entropie. Masson, Paris (1989).  
  4. L. Landau and F. Lifschitz, Fluid mechanics. MIR Editions, Moscow (1956).  
  5. M.A. Giles and N.A. Pierce, Analytic adjoint solutions for the quasi-one-dimensional euler equations. J. Fluid Mech.426 (2001) 327-345.  
  6. B. Mohammadi, Contrôle d'instationnarités en couplage fluide-structure. C. R. Acad. Sci. Sér. IIb Phys. Mécanique, astronomie327 (1999) 115-118.  
  7. N. Di Cesare and O. Pironneau, Shock sensitivity analysis. Comput. Fluid Dynam. J.9 (2000) 1-15.  
  8. R. Glowinski, Numerical methods for nonlinear variational problems. Springer-Verlag, New York (1984).  

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