Control of transonic shock positions

Olivier Pironneau

ESAIM: Control, Optimisation and Calculus of Variations (2002)

  • 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 (2002): 907-914. <http://eudml.org/doc/244891>.

@article{Pironneau2002,
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},
language = {eng},
pages = {907-914},
publisher = {EDP-Sciences},
title = {Control of transonic shock positions},
url = {http://eudml.org/doc/244891},
volume = {8},
year = {2002},
}

TY - JOUR
AU - Pironneau, Olivier
TI - Control of transonic shock positions
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2002
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
UR - http://eudml.org/doc/244891
ER -

References

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  1. [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). Zbl1002.65127MR1879473
  2. [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. Zbl0912.35103MR1648240
  3. [3] J. Nečas, Écoulements de fluide : compacité par entropie. Masson, Paris (1989). Zbl0717.76002MR1269784
  4. [4] L. Landau and F. Lifschitz, Fluid mechanics. MIR Editions, Moscow (1956). 
  5. [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. Zbl0967.76079MR1819479
  6. [6] B. Mohammadi, Contrôle d’instationnarités en couplage fluide-structure. C. R. Acad. Sci. Sér. IIb Phys. Mécanique, astronomie 327 (1999) 115-118. Zbl0972.76088
  7. [7] N. Di Cesare and O. Pironneau, Shock sensitivity analysis. Comput. Fluid Dynam. J. 9 (2000) 1-15. 
  8. [8] R. Glowinski, Numerical methods for nonlinear variational problems. Springer-Verlag, New York (1984). Zbl0536.65054MR737005

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