Petites perturbations et équations d'Euler pour l'aéroélasticité

C. Bardos; O. Pironneau

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1994)

  • Volume: 28, Issue: 4, page 463-497
  • ISSN: 0764-583X

How to cite

top

Bardos, C., and Pironneau, O.. "Petites perturbations et équations d'Euler pour l'aéroélasticité." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 28.4 (1994): 463-497. <http://eudml.org/doc/193748>.

@article{Bardos1994,
author = {Bardos, C., Pironneau, O.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Hadamard formula; equivalent boundary condition; frequency analysis; scattering formalism; resonancy; transfer matrix; asymptotic expansions; numerical methods; linearization},
language = {fre},
number = {4},
pages = {463-497},
publisher = {Dunod},
title = {Petites perturbations et équations d'Euler pour l'aéroélasticité},
url = {http://eudml.org/doc/193748},
volume = {28},
year = {1994},
}

TY - JOUR
AU - Bardos, C.
AU - Pironneau, O.
TI - Petites perturbations et équations d'Euler pour l'aéroélasticité
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1994
PB - Dunod
VL - 28
IS - 4
SP - 463
EP - 497
LA - fre
KW - Hadamard formula; equivalent boundary condition; frequency analysis; scattering formalism; resonancy; transfer matrix; asymptotic expansions; numerical methods; linearization
UR - http://eudml.org/doc/193748
ER -

References

top
  1. J. L. AZEVEDO, Aeroelastic Analysis of Launch Vehicles in Transonic Flight, J. Spacecraft, vol. 26, n° 1, 14-23. 
  2. R. BANK, 1988, PTLMG User's guide, Dept of Math, UCSD tech. report. 
  3. J. BATINA, 1989, Unsteady Euler Algorithm with Unstructured Dynamic Mesh for Complex-Aircraft Aeroelastic Analysis, AIAA Paper 89-1189-CP. 
  4. M. BEYLISHER, Y. KURYLEV, 1991, Boundary Control, Wave Field Continuation and Inverse Problems for the Wave Equation, Computers Math. Applic., vol. 22, nos 4/5, 27-52. Zbl0768.35077MR1127213
  5. O. BENDLKSEN, K. KOUSEN, 1987, Transonic Flutter Analysis Using the Euler Equations, AIAA Paper 87-1238. 
  6. A. BESPALOV, Numerical solution of Maxwell equations by fictitious domains, INRIA Report. Zbl0896.76084
  7. J. BORIS, D. L. BOOK, 1976, Flux corrected transport, J. Comp. Phys., 20, 20, 397-431. Zbl0325.76037
  8. M. O. BRISTEAU, R. GLOWINSKI, J. PERIAUX, Solution of Helmoltz-Maxwell equations by Variational methods, INRIA Report (à paraître). Zbl0795.65038
  9. G. CHAVENT, G. JAFFRÉ, 1986, Mathematical methods and finite elements for reservoir simulations, North-Holland. Zbl0603.76101
  10. Y. CHOQUET-BRUHAT, 1969, Ondes Asymptotiques et approchées pour des systèmes d'équations aux dérivées partielles non linéaires, J. Math. Pures et Appliquées, 48, 117-158. Zbl0177.36404MR255964
  11. R. DAT, 1976, Détermination des caractéristiques numériques d'une structure par analyse de ses fonctions de transfert, Rev. Fr. de Mécanique, 59-69. 
  12. R. DAT, 1978, Vibrations aéroélastiques Cours à l'ENSAE (Sup Aéro), dept, Structures matériaux technologie. 
  13. A. DERVIEUX, 1985, Steady Euler simulations using unstructured meshes, Von Karman Lecture notes series 1884-04. 
  14. Ph. DESTUYNDER, B. QUINNEZ, Tendances actuelles dans les modélisations des phénomènes aéro-élastiques, Contrat CNES 2/91/004. 
  15. J. DONEA, 1984, A Taylor-Galerkin method for convective transport problems, J. Numer. Meth. Eng, 20, 101-120 (See also J. DONEA, L. QUARTAPELLE, V. SELMIN, 1987, An analysis of time discretization in the Finite Element Solution of Hyperbolic problems, J. Comp. Physics, 70, 2. Zbl0524.65071MR830474
  16. B. ENQUIST and A. MAJDA, 1979, Radiation Boundary Condition for Acoustic and elastic Wave Calculations, Comm. Pure. and Applied Math., 32, 313-357. Zbl0387.76070MR517938
  17. C. FARHAT, S. LANTERI, 1992, Substructure approach for transonic fluid-structure interaction (Thèse de S. Lanteri), University of Boulder Colorado. 
  18. A. FOURMAUX, A. LE MEUR, Computation of unsteady phenomena in transanic turbines, 4th Symp. on Unsteady Aerodynamics, Aachen, Sept. 1987. 
  19. K. FUNG, 1991, Prediction of flutter at transonic speed, Int Symp on CFD. 
  20. Y. FUNG, 1969, An introduction to the theory of Aeroelasticity, Dover Publication, New York. Zbl1156.74001
  21. J. GIBB, 1988, The cause and cure of periodic flow at transonic speed, ICAS paper 3.10.1. 
  22. J. GOODMAN, 1986, Non linear stability of viscous shock profiles for conservation laws, Arch. Rat. Mech. Anal., 95, 527-563. Zbl0631.35058MR853782
  23. J. GOODMAN, 1991, Remark on the stability of viscous shock waves, SIAM M. Shearer ed., 66-72. Zbl0825.76399MR1142641
  24. K. HALL, W. CLARK, Prediction of unsteady aerodynamics loads in cascades using the linearized Euler eqs on deforming grids, AiAA 91-3378. 
  25. K. C. HALL and E. F. CRAWLEY, 1989, Calculation of Unsteady Flows in Turbomachinery Using the Linearized Euler Equations, AIAA Journal, Vol. 2,AIAA Journal, Vol. 2, n° 6, 777-787. 
  26. K. C. HALL and J. M. VERDON, Gust Response of a Cascade Operating in a Nonuniform Mean Flow, presented at the AGARD Propulsion and Energetics Panel 74th Specialists' Meetings on 1, unsteady Aerodynamic Phenomena in Turbomachines, Kirchberg Plateau, Luxemburg, August 28-September 1. 
  27. L. HALPERN, 1982, Absorbing Boundary Conditions for the Discretisation Scheme of the one dimensional Wave Equation, Math. Comp., 38,415-429. Zbl0482.65053MR645659
  28. L. HALPERN and L. TREFETHEN, 1986, Well posedness of one Way Wave Equation and absorbing Boundary Conditions, Math. of Comp., 47, 176, 421-435. Zbl0618.65077MR856695
  29. R. HIGDON, 1986, Absorbing Boundary Conditions for difference approximation to multidimensionnal Wave Equation, Math. of Comp., 47, 176, 437-459. Zbl0609.35052MR856696
  30. T. J. R. HUGHES, M. MALLET, 1986, A new finite element formulation for computational fluid dynamics, Computer Meth. in Appl. Mech. and Eng., 54, 341-355. Zbl0622.76074MR836189
  31. J. HUNTER, A. MAJDA, R. ROSALES, 1986, Resonantly Interacting Weakly Non Linear Hyperbolic Waves II : Several Space Variables, Stud. Appl. Math., 75, 187-226. Zbl0657.35084MR867874
  32. A. JAMESON, 1978, Transonic flow calculations, Numerical methods in fluid mech. H. Wirz, J. Smolderen eds. McGraw-Hill, 1-87. 
  33. C. JOHNSON, A. SZEPESSY, 1987, On the convergence of streamline diffusion finite element methods for hyperbolic conservation laws, in Numerical methods for compressible flows, T. E. Tedzuyar ed. AMD-78. Zbl0634.65075
  34. J. L. JOLY, G. METIVIER, J. RAUCH, Coherent and Focusing Multidimensional Nonlinear Geometric Optics, Prépublication n° 9205 Université de Bordeaux I, U.F.R. de Mathématiques et d'Informatique, 351 Cours de la Libération, 33405 Talence Cedex. Zbl0836.35087
  35. 1990, Formal and Rigourous Nonlinear High Frequency Hyperbolic Waves, in Proceedings of Varenna Conference on Nonlinear Hyperbolic Equations and Field Theory, M. K. Murthy, SD. Spagnolo eds., Pitman Research Note in Math. Series, 1992, 121-143. Zbl0824.35077MR1175206
  36. N. KIKUCHI, T. TORIGAKI, 1988, Adaptive finite element methods in computed aided engineering, Danmarks Tekniske HOJSKOLE, Matematisk report, 1988-09. 
  37. L. LANDAU, E. LIFSCHITZ, 1953, Mécanique des Fluides, MIR Moscou. 
  38. P. LAX, R. PHILLIPS, 1989, Scattering theory (revised ed.), Academic Press. Zbl0697.35004MR1037774
  39. J. LE BALLEUR, Ph. GIRODOUX, 1984, Méthode numérique semi-implicite et instationnaire d'interaction fluide visqueux-fluide parfait pour les écoulements décollés transsoniques, La Recherche Aérospatiale, French and Enghsh editions. Zbl0546.76023
  40. J. LE BALLEUR, Ph. GIRODOUX, 1985, Calculs d'aérodynamique instationnaire sur des configurations aéroélastiques 2D et 3D définies par l'AGARD, ONERA pub 1985. 
  41. A. LERAT, 1985, Implicit methods of second-order accuracy for the Euler equations, AIAA Paper 83-1925, AIAA Journal, vol. 23 33-40. Zbl0556.76054MR770080
  42. D. R. LINDQUIST and M. B. GILES, 1991, On the Validity of Linearized Unsteady Euler Equations with Shock Capturing, AIAA Paper 91-1598-CP, Honolulu, Hawai, June 24-27. Zbl0792.76036
  43. J. L. LIONS, 1989, la méthode HUM, Masson. 
  44. R. LOHNER, 1987, 3D grid generation by the advancing front method, in Laminar and turbulent flows, C. Taylor, W. C. Habashi, H. Hafez eds. Pinnendge press. 
  45. R. LOHNER, K. MORGAN, J. PERAIRE, O. C. ZIENKIEWICZ, Finite element methods for high speed flows, AIAA paper, 85, 1531. Zbl0606.76089
  46. A. MAJDA, Non linear Geometric Optic for Hyperbolic Systems of Conservation Laws, IMA. volume 2, Springer Verlag, New York, 115-1165. Zbl0622.65117
  47. G. MAJDA, W. STRAUSS et M. WEI, 1986. Imaginary poles of radial potentials, Tech. Report., Minneapolis MN55455. Zbl0641.35052MR902999
  48. A. MAJDA and R. ROSALES, 1984, Resonantly Interacting Weakly Non Linear Hyperbolic Waves I : a Single Space Variables, Stud. Appl. Math., 71, 149-179. Zbl0572.76066MR760229
  49. M. MALLET, 1985, A finite element method for computational fluid dynamics,Doctoral thesis, University of Stanford. 
  50. H. MORAND et R. OHAYON, Interactions Fluides-Structures RMA, 23, Masson. Zbl0754.73071MR1180076
  51. B. PALMERIO, V. BILLET, A. DERVIEUX, J. PERIAUX, 1985, Self adaptive mesh refinements and finite element methods for solving the Euler equations, Proceeding of the ICFD conf., Reading. Zbl0606.76076
  52. R. PEYRET, T. TAYLOR, 1985, Computational methods for fluid flows, Springer series in computational physics. Zbl0717.76003MR770204
  53. O. PIRONNEAU, 1983, Optimal shape design for elliptic Systems, Springer. Zbl0534.49001MR725856
  54. F. PLATZER, O. CARTA, 1987, Unsteady turbomachinery aerodynamics, vol. 1, AGARD-AG-298. 
  55. O. POISSON, 1993, Calcul des pôles de résonance associés a la diffraction d'ondes acoustiques et élastiques en dimension 2, Thèse Université de Paris Dauphine, UER Mathématiques de la décision. 
  56. Y. ROCARD, 1943, Dynamique Générale des vibrations, Masson. Zbl0061.41905MR29559
  57. Y. SAAD, 1981, Krylov subspace methods for solving unsymmetric linear Systems, Math of Comp., 37, 105-126. Zbl0474.65019MR616364
  58. E. SANCHEZ-PALENCIA, 1980, Non-Homogeneous Media and Vibration Theory, Lecture notes in physics, 127. Zbl0432.70002MR578345
  59. T. SHIEH, J. SCHOEN and K. FUNG, Techniques for Accurate, Efficient Computation of Unsteady Transonic Flow, AIAA 91-0597, 1-5. 
  60. C. SOIZE, 1990, Couplage fort fluide parfait, couche limite 2D compressible dans le cas des profils à bord d'attaque aigu. Cas Stationnaire, Rapport ONERA n. 42/1621 RY 093 R. 
  61. C. SOIZE, Couplage fort fluide parfait, couche limite 2D compressible dans le cas des profils à bord d'attaque aigu, cas instationnaire des profils isolés et cas stationnaire des grilles d'aubes, Rapport Onera n. 43/1621 RY 093 R, 006. 
  62. C. SOIZE, 1992, Strong coupling between inviscid fluid and boundary layer for airfoils with a sharp edge, II, 2D unsteady case for isilated airfoild and straight blade cascade, Rech. Aérosp., 3, 23-53. 
  63. B. STOUFFLET, J. PERIAUX, L. FEZOUI, A. DERVIEUX, 1987, Numerical simulations of 3D hypersonic Euler flows around space vehicles using adaptive finite elements, AIAA paper 8705660. 
  64. M. VAN DYKE, 1964, Perturbation Methods in Fluid Mechanics, Academic Press New York and London, 99-120. Zbl0136.45001MR176702
  65. V. VENKATAKRISHNAN and A. JAMESON, 1988, Computation of Unsteady Transonic Flows by the Solution of Euler Equations, AIAA Journal, vol. 26, n° 8, 974-981. MR965136

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.