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Volumn 230, Issue 1, 2011, Pages 159-184

Reduced-order modeling of transonic flows around an airfoil submitted to small deformations

Author keywords

Hadamard formulation; Navier Stokes equations; Proper Orthogonal Decomposition; Reduced order modeling; Shape deformation; Transonic regime

Indexed keywords

AIRFOILS; FORECASTING; PRINCIPAL COMPONENT ANALYSIS; REYNOLDS NUMBER; TRANSONIC AERODYNAMICS; TRANSONIC FLOW; VISCOUS FLOW;

EID: 77958478968     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2010.09.019     Document Type: Article
Times cited : (59)

References (63)
  • 1
    • 0000325341 scopus 로고
    • On lines and planes of closest fit to systems of points in space
    • Pearson K. On lines and planes of closest fit to systems of points in space. Philos. Mag. 1901, 2:559-572.
    • (1901) Philos. Mag. , vol.2 , pp. 559-572
    • Pearson, K.1
  • 2
    • 0003319339 scopus 로고
    • Zur Spektraltheorie stochastischer Prozesse
    • Karhunen K. Zur Spektraltheorie stochastischer Prozesse. Ann. Acad. Sci. Fenn. A1 1946, 34.
    • (1946) Ann. Acad. Sci. Fenn. A1 , vol.34
    • Karhunen, K.1
  • 3
    • 85190077646 scopus 로고
    • in: A.M. Yaglom, V.I. Tatarski (Eds.), Atmospheric Turbulence and Radio Wave Propagation, Nauka, Moscow
    • J.L. Lumley, in: A.M. Yaglom, V.I. Tatarski (Eds.), Atmospheric Turbulence and Radio Wave Propagation, Nauka, Moscow, 1967.
    • (1967)
    • Lumley, J.L.1
  • 4
    • 0026067446 scopus 로고
    • Low-dimensional models for complex geometry flows: application to grooved channels and circular cylinders
    • Deane A., Kevrekidis I., Karniadakis G.E., Orszag S. Low-dimensional models for complex geometry flows: application to grooved channels and circular cylinders. Phys. Fluids A 1991, 3(10):2337-2354.
    • (1991) Phys. Fluids A , vol.3 , Issue.10 , pp. 2337-2354
    • Deane, A.1    Kevrekidis, I.2    Karniadakis, G.E.3    Orszag, S.4
  • 5
    • 0000878258 scopus 로고    scopus 로고
    • Proper orthogonal decomposition and low-dimensional models for driven cavity flows
    • Cazemier W., Verstappen R.W.C.P., Veldman A.E.P. Proper orthogonal decomposition and low-dimensional models for driven cavity flows. Phys. Fluids 1998, 10(7):1685-1699.
    • (1998) Phys. Fluids , vol.10 , Issue.7 , pp. 1685-1699
    • Cazemier, W.1    Verstappen, R.W.C.P.2    Veldman, A.E.P.3
  • 6
    • 0037053486 scopus 로고    scopus 로고
    • A low-dimensional model for simulating three-dimensional cylinder flow
    • Ma X., Karniadakis G.E. A low-dimensional model for simulating three-dimensional cylinder flow. J. Fluid Mech. 2002, 458:181-190.
    • (2002) J. Fluid Mech. , vol.458 , pp. 181-190
    • Ma, X.1    Karniadakis, G.E.2
  • 7
    • 0842279679 scopus 로고    scopus 로고
    • A hierarchy of low-dimensional models for the transient and post-transient cylinder wake
    • Noack B.R., Afanasiev K., Morzynski M., Tadmor G., Thiele F. A hierarchy of low-dimensional models for the transient and post-transient cylinder wake. J. Fluid Mech. 2003, 497:335-363.
    • (2003) J. Fluid Mech. , vol.497 , pp. 335-363
    • Noack, B.R.1    Afanasiev, K.2    Morzynski, M.3    Tadmor, G.4    Thiele, F.5
  • 8
    • 1842688147 scopus 로고    scopus 로고
    • Low-order modelling of laminar flow regimes past a confined square cylinder
    • Galletti B., Bruneau C.H., Zannetti L., Iollo A. Low-order modelling of laminar flow regimes past a confined square cylinder. J. Fluid Mech. 2004, 503:161-170.
    • (2004) J. Fluid Mech. , vol.503 , pp. 161-170
    • Galletti, B.1    Bruneau, C.H.2    Zannetti, L.3    Iollo, A.4
  • 9
    • 13844250570 scopus 로고    scopus 로고
    • The need for a pressure-term representation in empirical Galerkin models of incompressible shear flows
    • Noack B., Papas P., Monkewitz P. The need for a pressure-term representation in empirical Galerkin models of incompressible shear flows. J. Fluid Mech. 2005, 523:339-365.
    • (2005) J. Fluid Mech. , vol.523 , pp. 339-365
    • Noack, B.1    Papas, P.2    Monkewitz, P.3
  • 10
    • 33751067802 scopus 로고    scopus 로고
    • Low-dimensional modelling of a confined three-dimensional wake flow
    • Buffoni M., Camarri S., Iollo A., Salvetti M.V. Low-dimensional modelling of a confined three-dimensional wake flow. J. Fluid Mech. 2006, 569:141-150.
    • (2006) J. Fluid Mech. , vol.569 , pp. 141-150
    • Buffoni, M.1    Camarri, S.2    Iollo, A.3    Salvetti, M.V.4
  • 11
    • 18344390422 scopus 로고    scopus 로고
    • Calibrated reduced-order POD-Galerkin system for fluid flow modelling
    • Couplet M., Basdevant C., Sagaut P. Calibrated reduced-order POD-Galerkin system for fluid flow modelling. J. Comput. Phys. 2005, 207:192-220.
    • (2005) J. Comput. Phys. , vol.207 , pp. 192-220
    • Couplet, M.1    Basdevant, C.2    Sagaut, P.3
  • 12
    • 65649118923 scopus 로고    scopus 로고
    • A generalized mean-field model of the natural and high-frequency actuated flow around a high-lift configuration
    • Luchtenburg D.M., Günter B., Noack B.R., King R., Tadmor G. A generalized mean-field model of the natural and high-frequency actuated flow around a high-lift configuration. J. Fluid Mech. 2009, 623:283-316.
    • (2009) J. Fluid Mech. , vol.623 , pp. 283-316
    • Luchtenburg, D.M.1    Günter, B.2    Noack, B.R.3    King, R.4    Tadmor, G.5
  • 13
    • 45449106388 scopus 로고    scopus 로고
    • Stochastic low-dimensional modelling of a random laminar wake past a circular cylinder
    • Venturi D., Wan X., Karniadakis G. Stochastic low-dimensional modelling of a random laminar wake past a circular cylinder. J. Fluid Mech. 2008, 606:339-367.
    • (2008) J. Fluid Mech. , vol.606 , pp. 339-367
    • Venturi, D.1    Wan, X.2    Karniadakis, G.3
  • 14
    • 0038346385 scopus 로고    scopus 로고
    • Projection methods for reduced order models of compressible flows
    • Lucia D.J., Beran P.S. Projection methods for reduced order models of compressible flows. J. Comput. Phys. 2003, 188:252-280.
    • (2003) J. Comput. Phys. , vol.188 , pp. 252-280
    • Lucia, D.J.1    Beran, P.S.2
  • 15
    • 0034298665 scopus 로고    scopus 로고
    • Proper orthogonal decomposition technique for transonic aerodynamic flows
    • Hall K., Thomas J., Dowell E. Proper orthogonal decomposition technique for transonic aerodynamic flows. AIAA J. 2000, 38(10):1853-1862.
    • (2000) AIAA J. , vol.38 , Issue.10 , pp. 1853-1862
    • Hall, K.1    Thomas, J.2    Dowell, E.3
  • 16
    • 0035527633 scopus 로고    scopus 로고
    • Reduced-order models of unsteady viscous flows in turbomachinary using viscous-inviscid coupling
    • Epureanu B.I., Dowell E.H., Hall K.C. Reduced-order models of unsteady viscous flows in turbomachinary using viscous-inviscid coupling. J. Fluids Struct. 2001, 15:255-273.
    • (2001) J. Fluids Struct. , vol.15 , pp. 255-273
    • Epureanu, B.I.1    Dowell, E.H.2    Hall, K.C.3
  • 17
    • 0036557596 scopus 로고    scopus 로고
    • Application of model order reduction to compressor aeroelastic models
    • Willcox K., Peraire J., Paduano J. Application of model order reduction to compressor aeroelastic models. J. Eng. Gas Turb. Power 2002, 124(2):332-339.
    • (2002) J. Eng. Gas Turb. Power , vol.124 , Issue.2 , pp. 332-339
    • Willcox, K.1    Peraire, J.2    Paduano, J.3
  • 18
    • 0037866713 scopus 로고    scopus 로고
    • Three-dimensional transonic aeroelasticity using proper orthogonal decomposition-based reduced-order models
    • Thomas J., Dowell E., Hall K. Three-dimensional transonic aeroelasticity using proper orthogonal decomposition-based reduced-order models. J. Aircraft 2003, 40(3):544-551.
    • (2003) J. Aircraft , vol.40 , Issue.3 , pp. 544-551
    • Thomas, J.1    Dowell, E.2    Hall, K.3
  • 19
    • 34347218566 scopus 로고    scopus 로고
    • Adaptation of aeroelastic reduced-order models and application to an F-16 configuration
    • Lieu T., Farhat C. Adaptation of aeroelastic reduced-order models and application to an F-16 configuration. AIAA J. 2007, 45(6):1244-1257.
    • (2007) AIAA J. , vol.45 , Issue.6 , pp. 1244-1257
    • Lieu, T.1    Farhat, C.2
  • 20
    • 85190081781 scopus 로고    scopus 로고
    • Using automatic differentiation to create a nonlinear reduced order model of a computational fluid dynamic solver, AIAA Paper 7115, 2006.
    • J. Thomas, E. Dowell, K. Hall, Using automatic differentiation to create a nonlinear reduced order model of a computational fluid dynamic solver, AIAA Paper 7115, 2006.
    • (2006)
    • Thomas, J.1    Dowell E.Hall, K.2
  • 21
    • 0842343715 scopus 로고    scopus 로고
    • Model reduction for compressible flows using POD and Galerkin projection
    • Rowley C.W., Colonius T., Murray R.M. Model reduction for compressible flows using POD and Galerkin projection. Physica D 2004, 189(1-2):115-129.
    • (2004) Physica D , vol.189 , Issue.1-2 , pp. 115-129
    • Rowley, C.W.1    Colonius, T.2    Murray, R.M.3
  • 22
    • 36849079086 scopus 로고    scopus 로고
    • Extension of methods based on the proper orthogonal decomposition to the simulation of unsteady compressible Navier-Stokes flows, in: CFD'98, Proc. Fourth ECCOMAS Conf., Wiley
    • G. Vigo, A. Dervieux, M. Mallet, M. Ravachol, B. Stoufflet, Extension of methods based on the proper orthogonal decomposition to the simulation of unsteady compressible Navier-Stokes flows, in: CFD'98, Proc. Fourth ECCOMAS Conf., Wiley, 1998, pp. 648-653.
    • (1998) , pp. 648-653
    • Vigo, G.1    Dervieux, A.2    Mallet, M.3    Ravachol, M.4    Stoufflet, B.5
  • 23
    • 36849021426 scopus 로고    scopus 로고
    • Reduced-order modeling for unsteady transonic flows around an airfoil
    • Bourguet R., Braza M., Dervieux A. Reduced-order modeling for unsteady transonic flows around an airfoil. Phys. Fluids 2007, 19:111704.
    • (2007) Phys. Fluids , vol.19 , pp. 111704
    • Bourguet, R.1    Braza, M.2    Dervieux, A.3
  • 24
    • 0033540943 scopus 로고    scopus 로고
    • Optimal control of vortex shedding using low-order models, Part I - open-loop model development
    • Graham W.R., Peraire J., Tang K.Y. Optimal control of vortex shedding using low-order models, Part I - open-loop model development. Int. J. Numer. Methods Eng. 1999, 44(7):945-972.
    • (1999) Int. J. Numer. Methods Eng. , vol.44 , Issue.7 , pp. 945-972
    • Graham, W.R.1    Peraire, J.2    Tang, K.Y.3
  • 25
    • 0033540946 scopus 로고    scopus 로고
    • Optimal control of vortex shedding using low-order models, Part II - model-based control
    • Graham W.R., Peraire J., Tang K.Y. Optimal control of vortex shedding using low-order models, Part II - model-based control. Int. J. Numer. Methods Eng. 1999, 44(7):973-990.
    • (1999) Int. J. Numer. Methods Eng. , vol.44 , Issue.7 , pp. 973-990
    • Graham, W.R.1    Peraire, J.2    Tang, K.Y.3
  • 26
    • 0034327551 scopus 로고    scopus 로고
    • A reduced-order approach for optimal control of fluids using proper orthogonal decomposition
    • Ravindran S. A reduced-order approach for optimal control of fluids using proper orthogonal decomposition. Int. J. Numer. Methods Fluids 2000, 34:425-448.
    • (2000) Int. J. Numer. Methods Fluids , vol.34 , pp. 425-448
    • Ravindran, S.1
  • 27
    • 27144538190 scopus 로고    scopus 로고
    • Optimal rotary control of the cylinder wake using POD Reduced Order Model
    • Bergmann M., Cordier L., Brancher J.P. Optimal rotary control of the cylinder wake using POD Reduced Order Model. Phys. Fluids 2005, 3:1-21.
    • (2005) Phys. Fluids , vol.3 , pp. 1-21
    • Bergmann, M.1    Cordier, L.2    Brancher, J.P.3
  • 28
    • 85190081285 scopus 로고    scopus 로고
    • Investigation of non-linear projection for POD based reduced order models for aerodynamics, AIAA Paper 0926
    • P.A. Le Gresley, J.J. Alonso, Investigation of non-linear projection for POD based reduced order models for aerodynamics, AIAA Paper 0926, 2001.
    • (2001)
    • Le Gresley, P.A.1    Alonso, J.J.2
  • 29
    • 0141634354 scopus 로고    scopus 로고
    • POD-based reduced-order models with deforming grids
    • Anttonen J.S.R., King P.I., Beran P.S. POD-based reduced-order models with deforming grids. Math. Comput. Model. 2003, 38(1-2):41-62.
    • (2003) Math. Comput. Model. , vol.38 , Issue.1-2 , pp. 41-62
    • Anttonen, J.S.R.1    King, P.I.2    Beran, P.S.3
  • 30
    • 85190085553 scopus 로고    scopus 로고
    • Application of surface transpiration in computational aerodynamics, AIAA Paper 0511, 1986.
    • L.N. Sankar, S.Y. Ruo, J.B. Malone, Application of surface transpiration in computational aerodynamics, AIAA Paper 0511, 1986.
    • Sankar, L.N.1    Ruo, S.Y.2    Malone, J.B.3
  • 31
    • 4243114222 scopus 로고    scopus 로고
    • Multilevel optimisation of a supersonic aircraft
    • Vázquez M., Koobus B., Dervieux A. Multilevel optimisation of a supersonic aircraft. Finite Elem. Anal. Des. 2004, 40(15):2101-2124.
    • (2004) Finite Elem. Anal. Des. , vol.40 , Issue.15 , pp. 2101-2124
    • Vázquez, M.1    Koobus, B.2    Dervieux, A.3
  • 32
    • 85190081483 scopus 로고    scopus 로고
    • Reduced-order modeling for flutter prediction, AIAA Paper 1446
    • C.L. Pettit, P.S. Beran, Reduced-order modeling for flutter prediction, AIAA Paper 1446, 2000.
    • (2000)
    • Pettit, C.L.1    Beran, P.S.2
  • 33
    • 85190075462 scopus 로고    scopus 로고
    • A. Bouhadji, Analyse physique par simulation numérique de phénomènes de transition bi-et tridimensionnels dans l'écoulement compressible, visqueux autour d'une aile d'avion, Ph.D. Thesis, Institut National Polytechnique de Toulouse, 1998.
    • A. Bouhadji, Analyse physique par simulation numérique de phénomènes de transition bi-et tridimensionnels dans l'écoulement compressible, visqueux autour d'une aile d'avion, Ph.D. Thesis, Institut National Polytechnique de Toulouse, 1998.
  • 34
    • 0038138006 scopus 로고    scopus 로고
    • Organised modes and shock-vortex interaction in unsteady viscous transonic flows around an aerofoil, Part I
    • Bouhadji A., Braza M. Organised modes and shock-vortex interaction in unsteady viscous transonic flows around an aerofoil, Part I. Comput. Fluids 2003, 32(9):1233-1260.
    • (2003) Comput. Fluids , vol.32 , Issue.9 , pp. 1233-1260
    • Bouhadji, A.1    Braza, M.2
  • 35
    • 2942757053 scopus 로고
    • Approximate Riemann solvers, parameter vectors, and difference schemes
    • Roe P.L. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 1981, 43:357-372.
    • (1981) J. Comput. Phys. , vol.43 , pp. 357-372
    • Roe, P.L.1
  • 36
    • 2442433925 scopus 로고
    • Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
    • van Leer B. Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method. J. Comput. Phys. 1979, 32:101-136.
    • (1979) J. Comput. Phys. , vol.32 , pp. 101-136
    • van Leer, B.1
  • 38
    • 0037412229 scopus 로고    scopus 로고
    • Organised modes and shock-vortex interaction in unsteady viscous transonic flows around an aerofoil, Part II: Reynolds number effect
    • Bouhadji A., Braza M. Organised modes and shock-vortex interaction in unsteady viscous transonic flows around an aerofoil, Part II: Reynolds number effect. Comput. Fluids 2003, 32(9):1261-1281.
    • (2003) Comput. Fluids , vol.32 , Issue.9 , pp. 1261-1281
    • Bouhadji, A.1    Braza, M.2
  • 39
    • 0016951257 scopus 로고
    • Transonic flow about a thick circular-arc airfoil
    • McDevitt J.B., Levy L.L., Deiwert G.S. Transonic flow about a thick circular-arc airfoil. AIAA J. 1976, 14(5):606-613.
    • (1976) AIAA J. , vol.14 , Issue.5 , pp. 606-613
    • McDevitt, J.B.1    Levy, L.L.2    Deiwert, G.S.3
  • 40
    • 0018152408 scopus 로고
    • Steady and unsteady transonic flow
    • Seegmiller H.L., Marvin J.G., Levy L.L. Steady and unsteady transonic flow. AIAA J. 1978, 16(12):1262-1270.
    • (1978) AIAA J. , vol.16 , Issue.12 , pp. 1262-1270
    • Seegmiller, H.L.1    Marvin, J.G.2    Levy, L.L.3
  • 41
    • 12044259644 scopus 로고
    • The proper orthogonal decomposition in the analysis of turbulent flows
    • Berkooz G., Holmes P., Lumley J.L. The proper orthogonal decomposition in the analysis of turbulent flows. Ann. Rev. Fluid Mech. 1993, 25:539-575.
    • (1993) Ann. Rev. Fluid Mech. , vol.25 , pp. 539-575
    • Berkooz, G.1    Holmes, P.2    Lumley, J.L.3
  • 42
    • 0030822018 scopus 로고    scopus 로고
    • Low-dimensional models for flows with density fluctuations
    • Lumley J.L., Poje A. Low-dimensional models for flows with density fluctuations. Phys. Fluids 1997, 9(7):2023-2031.
    • (1997) Phys. Fluids , vol.9 , Issue.7 , pp. 2023-2031
    • Lumley, J.L.1    Poje, A.2
  • 43
    • 0000246863 scopus 로고
    • Turbulence and the dynamics of coherent structures, Part I-III
    • Sirovich L. Turbulence and the dynamics of coherent structures, Part I-III. Quart. Appl. Math. 1987, 45:561-590.
    • (1987) Quart. Appl. Math. , vol.45 , pp. 561-590
    • Sirovich, L.1
  • 44
    • 0034343536 scopus 로고    scopus 로고
    • On low-dimensional galerkin models for fluid flow
    • Rempfer D. On low-dimensional galerkin models for fluid flow. Theor. Comput. Fluid Dyn. 2000, 14(2):75-88.
    • (2000) Theor. Comput. Fluid Dyn. , vol.14 , Issue.2 , pp. 75-88
    • Rempfer, D.1
  • 45
    • 84972308308 scopus 로고
    • The dynamics of coherent structures in the wall region of a turbulent boundary layer
    • Aubry N., Holmes P., Lumley J.L., Stone E. The dynamics of coherent structures in the wall region of a turbulent boundary layer. J. Fluid Mech. 1988, 192:115-173.
    • (1988) J. Fluid Mech. , vol.192 , pp. 115-173
    • Aubry, N.1    Holmes, P.2    Lumley, J.L.3    Stone, E.4
  • 46
    • 0842333833 scopus 로고    scopus 로고
    • A spectral viscosity method for correcting the long-term behavior of POD model
    • Sirisup S., Karniadakis G.E. A spectral viscosity method for correcting the long-term behavior of POD model. J. Comput. Phys. 2004, 194:92-116.
    • (2004) J. Comput. Phys. , vol.194 , pp. 92-116
    • Sirisup, S.1    Karniadakis, G.E.2
  • 49
    • 77953224993 scopus 로고    scopus 로고
    • Calibration of POD reduced-order models by Tikhonov regularization
    • Cordier L., Abou El Majd B., Favier J. Calibration of POD reduced-order models by Tikhonov regularization. Int. J. Numer. Methods Fluids 2010, 63(2):269-296.
    • (2010) Int. J. Numer. Methods Fluids , vol.63 , Issue.2 , pp. 269-296
    • Cordier, L.1    Abou El Majd, B.2    Favier, J.3
  • 50
    • 70449579092 scopus 로고    scopus 로고
    • Capturing transition features around a wing by reduced-order modeling based on compressible Navier-Stokes equations
    • Bourguet R., Braza M., Sévrain A., Bouhadji A. Capturing transition features around a wing by reduced-order modeling based on compressible Navier-Stokes equations. Phys. Fluids 2009, 21:094104.
    • (2009) Phys. Fluids , vol.21 , pp. 094104
    • Bourguet, R.1    Braza, M.2    Sévrain, A.3    Bouhadji, A.4
  • 51
    • 26844463947 scopus 로고    scopus 로고
    • Applications of multi-POD to a pitching and plunging airfoil
    • Anttonen J.S.R., King P.I., Beran P.S. Applications of multi-POD to a pitching and plunging airfoil. Math. Comput. Model. 2005, 42(3-4):245-259.
    • (2005) Math. Comput. Model. , vol.42 , Issue.3-4 , pp. 245-259
    • Anttonen, J.S.R.1    King, P.I.2    Beran, P.S.3
  • 52
    • 85190075865 scopus 로고    scopus 로고
    • Generalized mean-field model with continuous mode interpolation for flow control, AIAA Paper 3488
    • M. Morzyński, W. Stankiewicz, B.R. Noack, F. Thiele, G. Tadmor, Generalized mean-field model with continuous mode interpolation for flow control, AIAA Paper 3488, 2006.
    • (2006)
    • Morzyński, M.1    Stankiewicz, W.2    Noack, B.R.3    Thiele, F.4    Tadmor, G.5
  • 53
    • 33751544551 scopus 로고    scopus 로고
    • The immersed boundary method
    • Peskin C.S. The immersed boundary method. Acta Numer. 2002, 11:479-517.
    • (2002) Acta Numer. , vol.11 , pp. 479-517
    • Peskin, C.S.1
  • 54
    • 85190078409 scopus 로고
    • Perturbation deséquations d'équilibre d'un plasma confiné: comportement de la frontère libre,étude des branches de solutions, R.R. INRIA 0018
    • A. Dervieux, Perturbation deséquations d'équilibre d'un plasma confiné: comportement de la frontère libre,étude des branches de solutions, R.R. INRIA 0018, 1980.
    • (1980)
    • Dervieux, A.1
  • 55
    • 0027007641 scopus 로고
    • Extract-gradient shape optimization of a 2D Euler flow
    • Beux F., Dervieux A. Extract-gradient shape optimization of a 2D Euler flow. Finite Elem. Anal. Des. 1992, 12:281-302.
    • (1992) Finite Elem. Anal. Des. , vol.12 , pp. 281-302
    • Beux, F.1    Dervieux, A.2
  • 56
    • 85190085861 scopus 로고    scopus 로고
    • Calculs de sensibilité par différentation pour l'aérodynamique, in: ESAIM: Proceedings
    • A. Dervieux, Y. Mesri, F. Courty, L. Hascoet, B. Koobus, M. Vazquez, Calculs de sensibilité par différentation pour l'aérodynamique, in: ESAIM: Proceedings, vol. 22, 2007, pp. 181-189.
    • (2007) , vol.22 , pp. 181-189
    • Dervieux, A.1    Mesri, Y.2    Courty, F.3    Hascoet L.Koobus, B.4    Vazquez, M.5
  • 59
    • 85190086841 scopus 로고    scopus 로고
    • Trust-region proper orthogonal decomposition for flow control, Icase Report 25
    • E. Arian, M. Fahl, E.W. Sachs, Trust-region proper orthogonal decomposition for flow control, Icase Report 25, 2000.
    • (2000)
    • Arian E.Fahl, M.1    Sachs, E.W.2
  • 60
    • 47749108243 scopus 로고    scopus 로고
    • Interpolation method for adapting reduced-order models and application to aeroelasticity
    • Amsallem D., Farhat C. Interpolation method for adapting reduced-order models and application to aeroelasticity. AIAA J. 2008, 46(7):1803-1813.
    • (2008) AIAA J. , vol.46 , Issue.7 , pp. 1803-1813
    • Amsallem, D.1    Farhat, C.2
  • 61
    • 45849126783 scopus 로고    scopus 로고
    • Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models
    • Bergmann M., Cordier L. Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models. J. Comput. Phys. 2008, 227:7813-7840.
    • (2008) J. Comput. Phys. , vol.227 , pp. 7813-7840
    • Bergmann, M.1    Cordier, L.2
  • 62
    • 51749091330 scopus 로고    scopus 로고
    • Input separation methods for reduced-order model-based feedback flow control
    • Caraballo E., Kasnakoĝlu C., Serrani A., Samimy M. Input separation methods for reduced-order model-based feedback flow control. AIAA J. 2008, 46(9):2306-2322.
    • (2008) AIAA J. , vol.46 , Issue.9 , pp. 2306-2322
    • Caraballo, E.1    Kasnakoĝlu, C.2    Serrani, A.3    Samimy, M.4
  • 63
    • 46349087113 scopus 로고    scopus 로고
    • Control input separation by actuation mode expansion for flow control problems
    • Kasnakoĝlu C., Serrani A., Efe M.O. Control input separation by actuation mode expansion for flow control problems. Int. J. Control 2008, 81(9):1475-1492.
    • (2008) Int. J. Control , vol.81 , Issue.9 , pp. 1475-1492
    • Kasnakoĝlu, C.1    Serrani, A.2    Efe, M.O.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.