. Un-exemple-d, solide : navigation d'un bateau Nous nous intéressons ici à l'exemple le plus naturel pour un écoulement présentant des interfaces fluide/fluide/solide : la navigation d'un bateau sur l'eau. Les masses volumiques sont ? air = 1.2kg/m 3 et ? eau = 1000kg

. Le, Le bateau a une longueur de 1 m avec une vitesse égale à 2 m/s . Le domaine étudié est D = [?4.2, 1.3] × [?0, Nous avons utilisé la méthode CSF présentée au chapitre 2, où l'interface est lissée sur 4 mailles. Finalement, afin d'éviter les trop forts nombres de Reynolds, nous avons utilisé des viscosités dix plus grandes que celles mentionnées ci-dessus

R. Abgrall, H. Beaugendre, and C. Dobrzynski, An immersed boundary method using unstructured anisotropic mesh adaptation combined with level-sets and penalization techniques, Journal of Computational Physics, vol.257, pp.83-101, 2014.
DOI : 10.1016/j.jcp.2013.08.052

URL : https://hal.archives-ouvertes.fr/hal-00940302

D. Adalsteinsson and J. A. Sethian, The Fast Construction of Extension Velocities in Level Set Methods, Journal of Computational Physics, vol.148, issue.1, pp.2-22, 1999.
DOI : 10.1006/jcph.1998.6090

S. Ahmed, S. Bak, J. Mclaughlin, and D. Renzi, A Third Order Accurate Fast Marching Method for the Eikonal Equation in Two Dimensions, SIAM Journal on Scientific Computing, vol.33, issue.5, pp.2402-2420, 2011.
DOI : 10.1137/10080258X

E. Akervik, G. Hoepffner, U. Ehrenstein, and D. S. , Optimal growth, model reduction and control in a separated boundary-layer flow using global eigenmodes, Journal of Fluid Mechanics, vol.579, pp.305-314, 2007.
DOI : 10.1017/S0022112007005496

URL : https://hal.archives-ouvertes.fr/hal-00211799

S. Alben, Simulating the dynamics of flexible bodies and vortex sheets, Journal of Computational Physics, vol.228, issue.7, pp.2587-2603, 2009.
DOI : 10.1016/j.jcp.2008.12.020

P. Angot, C. H. Bruneau, and P. , A penalization method to take into account obstacles in incompressible viscous flows, Numerische Mathematik, vol.81, issue.4, pp.497-520, 1999.
DOI : 10.1007/s002110050401

E. Arquis, Convection mixte dans une couche poreuse verticale non confinée. Application à l'isolation perméodynamique, Thèse de doctorat, 1984.

N. Aubry, P. Holmes, J. L. Lumley, and E. Stone, The dynamics of coherent structures in the wall region of a turbulent boundary layer, Journal of Fluid Mechanics, vol.15, issue.-1, pp.115-173, 1988.
DOI : 10.1146/annurev.fl.13.010181.002325

D. S. Barrett, M. S. Triantafyllou, D. K. Yue, M. A. Grosenbauch, and M. J. Wolfgang, Drag reduction in fish-like locomotion, Journal of Fluid Mechanics, vol.392, pp.182-212, 1999.
DOI : 10.1017/S0022112099005455

Y. Bazilevs, V. M. Calo, J. A. Cottrell, T. J. Hugues, A. Reali et al., Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.1-4, pp.173-201, 2007.
DOI : 10.1016/j.cma.2007.07.016

D. N. Beal, F. S. Hover, M. S. Triantafyllou, J. C. Liao, and G. V. Lauder, Passive propulsion in vortex wakes, Journal of Fluid Mechanics, vol.549, issue.-1, pp.385-402, 2006.
DOI : 10.1017/S0022112005007925

J. Benamou and Y. , A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem, Numerische Mathematik, vol.84, issue.3, pp.375-393, 2000.
DOI : 10.1007/s002110050002

M. Bergmann, Optimisation aérodynamique par réduction de modèle POD et contrôle optimal Application au sillage laminaire d'un cylindre circulaire, Thèse de doctorat, 2004.
DOI : 10.1051/meca:2007028

URL : https://hal.inria.fr/inria-00338832/document

M. Bergmann and C. H. Bruneau, Enablers for robust POD models, Journal of Computational Physics, vol.228, issue.2, pp.516-538, 2009.
DOI : 10.1016/j.jcp.2008.09.024

URL : https://hal.archives-ouvertes.fr/inria-00338203

M. Bergmann, T. Colin, A. Iollo, D. Lombardi, O. Saut et al., Reduced order models at work in aeronautics and medicine. Modeling, Simulation and Applications, 2013.

M. Bergmann and L. Cordier, Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models, Journal of Computational Physics, vol.227, issue.16, pp.7813-7840, 2008.
DOI : 10.1016/j.jcp.2008.04.034

URL : https://hal.archives-ouvertes.fr/hal-00368500

M. Bergmann, L. Cordier, and J. Brancher, Optimal rotary control of the cylinder wake using POD Reduced Order Model, Phys. Fluids, vol.17, issue.9, pp.971011-971032, 2005.
URL : https://hal.archives-ouvertes.fr/inria-00338850

M. Bergmann, C. Galusinski, and A. Iollo, Weynans : Drag and drop simulations : form images to full 3d simulations, The Eigth International Conference on Computational Fluid Dynamics, 2014.

M. Bergmann and J. Hovnanian, Abstract, Communications in Computational Physics, vol.230, issue.05, pp.1266-1290, 2014.
DOI : 10.1002/fld.1281

M. Bergmann, Modeling and simulation of fish-like swimming, Journal of Computational Physics, vol.230, issue.2, pp.329-348, 2011.
DOI : 10.1016/j.jcp.2010.09.017

URL : https://hal.archives-ouvertes.fr/inria-00546358

M. Bergmann and A. Iollo, Numerical simulation of horizontal-axis wind turbine (hawt) The Seventh International Conference on Computational Fluid Dynamics, 2012.

M. Bergmann and F. Luddens, Weynans : A shrap cartesian method for the simulation of air water interface, The Eigth International Conference on Computational Fluid Dynamics, 2014.

M. Bergmann and H. Telib, Iollo : Implementation and validation of hybrid basis function rom method. Future fast aeroelastic simulation technologies, p.17, 2012.

M. Bergmann and H. Telib, Iollo : Implementation and validation of hybrid basis function rom method. Future fast aeroelastic simulation technologies, D2, 2012.

R. W. Blake, L. M. Chatters, and P. D. Domenici, Turning radius of yellowfin tuna (Thunnus albacares) in unsteady swimming manoeuvres, Journal of Fish Biology, vol.138, issue.3, pp.536-538, 1995.
DOI : 10.2307/1444198

I. Borazjani and F. Sotiropoulos, Numerical investigation of the hydrodynamics of carangiform swimming in the transitional and inertial flow regimes, Journal of Experimental Biology, vol.211, issue.10, pp.1541-1558, 2008.
DOI : 10.1242/jeb.015644

I. Borazjani and F. Sotiropoulos, Why don???t mackerels swim like eels? The role of form and kinematics on the hydrodynamics of undulatory swimming, Physics of Fluids, vol.21, issue.9, p.91109, 2009.
DOI : 10.1063/1.3205869.1

A. Bouharguane and A. Iollo, Weynans : Numerical solution of the monge-kantorovich problem by picard iterations, p.8477, 2014.

J. Brackbill, D. Kothe, and C. Zemach, A continuum method for modeling surface tension, Journal of Computational Physics, vol.100, issue.2, pp.335-354, 1992.
DOI : 10.1016/0021-9991(92)90240-Y

T. Braconnier, J. Ferrier, M. Jouhaud, P. Montagnac, and . Sagaut, Towards an adaptive POD/SVD surrogate model for aeronautic design, Computers & Fluids, vol.40, issue.1, pp.195-209, 2011.
DOI : 10.1016/j.compfluid.2010.09.002

URL : https://hal.archives-ouvertes.fr/hal-01298892

Y. Brenier, Polar factorization and monotone rearrangement of vector-valued functions, Communications on Pure and Applied Mathematics, vol.117, issue.4, pp.375-417, 1991.
DOI : 10.1002/cpa.3160440402

D. L. Brown, R. Cortez, and M. L. , Accurate Projection Methods for the Incompressible Navier???Stokes Equations, Journal of Computational Physics, vol.168, issue.2, pp.464-499, 2001.
DOI : 10.1006/jcph.2001.6715

M. Buffoni, S. Camarri, A. Iollo, and M. V. , Low-dimensional modelling of a confined three-dimensional wake flow, Journal of Fluid Mechanics, vol.569, pp.141-150, 2006.
DOI : 10.1017/S0022112006002989

T. Bui-thanh, K. Willcox, O. Ghattas, B. Van-bloemen, and . Waander, Goal-oriented, model-constrained optimization for reduction of large-scale systems, Journal of Computational Physics, vol.224, issue.2, pp.880-896, 2007.
DOI : 10.1016/j.jcp.2006.10.026

J. Burkardt, M. D. Gunzburger, and H. , Lee : Centroidal Voronoi Tessellation-Based Reduced-Order Modeling of Complex Systems, 2004.

W. Cazemier, Proper Orthogonal Decomposition and low-dimensionnal models for turbulent flows, Thèse de doctorat, 1997.

W. Cazemier, R. W. Verstappen, and A. E. , Proper orthogonal decomposition and low-dimensional models for driven cavity flows, Physics of Fluids, vol.10, issue.7, pp.1685-1699, 1998.
DOI : 10.1063/1.869686

A. Chéné, C. Min, and F. Gibou, Second-Order Accurate Computation of Curvatures in a Level Set Framework Using Novel High-Order Reinitialization Schemes, Journal of Scientific Computing, vol.114, issue.2-3, pp.114-131, 2007.
DOI : 10.1007/s10915-007-9177-1

Y. Cheny and O. Botella, The LS-STAG method: A new immersed boundary/level-set method for the computation of incompressible viscous flows in complex moving geometries with good conservation properties, Journal of Computational Physics, vol.229, issue.4, pp.1043-1076, 2010.
DOI : 10.1016/j.jcp.2009.10.007

P. Cinnella, High-order residual-based compact schemes on overset grids, Workshops schémas aux différences, Méthodes cartésiennes, application en mécanique des fluides, 2013.

D. Clarke, H. Hassan, and M. Salas, Euler calculations for multielement airfoils using Cartesian grids, AIAA Journal, vol.24, issue.3, pp.353-358, 1986.
DOI : 10.2514/3.9273

R. Clift, J. R. Grace, and M. E. Weber, Bubbles, Drops, and Particles, 1978.

C. Conca, J. San-martin, and M. Tucsnak, Weak solutions of the equations modelling the motion of a rigid body in a viscous fluid, Comm. Partial Differential Equations, vol.25, pp.1019-1042, 2000.

M. Coquerelle and G. H. , A vortex level set method for the two-way coupling of an incompressible fluid with colliding rigid bodies, Journal of Computational Physics, vol.227, issue.21, pp.9121-9137, 2008.
DOI : 10.1016/j.jcp.2008.03.041

URL : https://hal.archives-ouvertes.fr/hal-00297673

L. Cordier and M. Bergmann, Proper Orthogonal Decomposition : an overview. In Lecture series 2002-04 on post-processing of experimental and numerical data. Von Kármán Institute for Fluid Dynamics, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00417819

L. Cordier and M. Bergmann, Two typical applications of POD : coherent structures eduction and reduced order modelling. In Lecture series 2002-04 on post-processing of experimental and numerical data. Von Kármán Institute for Fluid Dynamics, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00417833

F. Couderc, Développement d'un code de calcul pour la simulation d'écoulements de fluides non miscibles. Application à la désintégration assistée d'un jet liquide par un courant gazeux, Thèse de doctorat, 2007.

M. Couplet, C. Basdevant, and P. Sagaut, Calibrated reduced-order POD-Galerkin system for fluid flow modelling, Journal of Computational Physics, vol.207, issue.1, pp.192-220, 2005.
DOI : 10.1016/j.jcp.2005.01.008

R. G. Cox, The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow, Journal of Fluid Mechanics, vol.81, issue.-1, pp.169-194, 1986.
DOI : 10.1021/ie50320a024

J. O. Dabiri, S. P. Colin, J. H. Costello, and M. Gharib, Flow patterns generated by oblate medusan jellyfish: field measurements and laboratory analyses, Journal of Experimental Biology, vol.208, issue.7, pp.1257-1265, 2005.
DOI : 10.1242/jeb.01519

H. Dai, H. Luo, J. Ferreira-de-sousa, and J. Doyle, Thrust performance of a flexible low-aspect-ratio pitching plate, Physics of Fluids, vol.24, issue.10, p.101903, 2012.
DOI : 10.1063/1.4764047

B. J. Daly, Numerical Study of Two Fluid Rayleigh-Taylor Instability, Physics of Fluids, vol.10, issue.2, p.297, 1967.
DOI : 10.1063/1.1762109

B. J. Daly, Numerical Study of Density-Current Surges, Physics of Fluids, vol.11, issue.1, p.15, 1968.
DOI : 10.1063/1.1691748

A. E. Deane, I. G. Kevrekidis, G. E. Karniadakis, and S. A. , Low???dimensional models for complex geometry flows: Application to grooved channels and circular cylinders, Physics of Fluids A: Fluid Dynamics, vol.3, issue.10, pp.2337-2354, 1991.
DOI : 10.1063/1.857881

J. Delville, L. Ukeiley, L. Cordier, J. Bonnet, and M. Glauser, Examination of large-scale structures in a turbulent plane mixing layer. Part 1. Proper orthogonal decomposition, Journal of Fluid Mechanics, vol.391, pp.91-122, 1999.
DOI : 10.1017/S0022112099005200

J. Deng, X. M. Shao, and Z. S. Yu, Hydrodynamic studies on two traveling wavy foils in tandem arrangement, Physics of Fluids, vol.19, issue.11, p.113104, 2007.
DOI : 10.1063/1.2814259

P. D. Domenici and R. W. Blake, The kinematics and performance of the scape response in the angelfisf (pterophyllum eimekei), Canadian Journal of Zoology, vol.156, pp.187-205, 1991.

R. Fedkiw, T. Aslam, B. Merriman, and S. , A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method), Journal of Computational Physics, vol.152, issue.2, pp.457-492, 1999.
DOI : 10.1006/jcph.1999.6236

R. Fedkiw, T. Aslam, B. Merriman, and S. , A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method), Journal of Computational Physics, vol.152, issue.2, pp.457-492, 1999.
DOI : 10.1006/jcph.1999.6236

H. Fujita and N. Sauer, Construction of weak solutions of the Navier-Stokes equation in a noncylindrical domain, Bulletin of the American Mathematical Society, vol.75, issue.2, pp.465-468, 1969.
DOI : 10.1090/S0002-9904-1969-12224-X

B. Galletti, C. Bruneau, and L. Zannetti, Low-order modelling of laminar flow regimes past a confined square cylinder, Journal of Fluid Mechanics, vol.503, pp.161-170, 2004.
DOI : 10.1017/S0022112004007906

M. Gazzola, P. Chatelain, W. M. Van-rees, and P. Koumoutsakos, Accepted Manuscript, Journal of Computational Physics, pp.1-48, 2011.

R. Ghias and . Dong, A sharp interface immersed boundary method for compressible viscous flows, Journal of Computational Physics, vol.225, issue.1, pp.528-553, 2007.
DOI : 10.1016/j.jcp.2006.12.007

F. Gibou, R. Fedkiw, L. Cheng, and M. Kang, A Second-Order-Accurate Symmetric Discretization of the Poisson Equation on Irregular Domains, Journal of Computational Physics, vol.176, issue.1, pp.205-227, 2002.
DOI : 10.1006/jcph.2001.6977

R. Glowinski, T. Pan, T. I. Hesla, and D. D. Joseph, A Fictitious Domain Approach to the Direct Numerical Simulation of Incompressible Viscous Flow past Moving Rigid Bodies: Application to Particulate Flow, Journal of Computational Physics, vol.169, issue.2, pp.363-426, 2001.
DOI : 10.1006/jcph.2000.6542

K. Goda, A multistep technique with implicit difference schemes for calculating two- or three-dimensional cavity flows, Journal of Computational Physics, vol.30, issue.1, pp.76-95, 1979.
DOI : 10.1016/0021-9991(79)90088-3

S. Gottlieb and C. Shu, Total variation diminishing Runge-Kutta schemes Mathematics of Computation of the, pp.73-85, 1998.

W. R. Graham, J. Peraire, and K. T. , Optimal control of vortex shedding using low-order models. Part II?model-based control, International Journal for Numerical Methods in Engineering, vol.44, issue.7, pp.973-990, 1999.
DOI : 10.1002/(SICI)1097-0207(19990310)44:7<973::AID-NME538>3.0.CO;2-F

F. Harlow and J. E. Welch, Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface, Physics of Fluids, vol.8, issue.12, p.2182, 1965.
DOI : 10.1063/1.1761178

A. Harten, B. Engquist, S. Osher, and S. R. Chakravarthy, Uniformly high order accurate essentially non-oscillatory schemes, III, Journal of Computational Physics, vol.71, issue.2, pp.231-303, 1987.
DOI : 10.1016/0021-9991(87)90031-3

J. Hovnanian, Méthode de Frontières Immergées pour la Mécanique des Fluides Application à la Simulation de la Nage, Thèse de doctorat, 2012.

T. J. Hugues, G. Feijóo, L. Mazzei, and J. B. Quincy, The variational multiscale method???a paradigm for computational mechanics, Computer Methods in Applied Mechanics and Engineering, vol.166, issue.1-2, pp.3-24, 1998.
DOI : 10.1016/S0045-7825(98)00079-6

A. Iollo, A. Dervieux, J. A. Désiéri, and S. Lanteri, Two stable POD-based approximations to the Navier???Stokes equations, Computing and Visualization in Science, vol.3, issue.1-2, pp.61-66, 2000.
DOI : 10.1007/s007910050052

A. Iollo, S. Lanteri, and J. A. , Stability Properties of POD-Galerkin Approximations for the Compressible Navier-Stokes Equations, Theoretical and Computational Fluid Dynamics, vol.13, issue.6, pp.377-393, 2000.
DOI : 10.1007/s001620050119

URL : https://hal.archives-ouvertes.fr/inria-00073091

K. Ito and S. S. , A Reduced-Order Method for Simulation and Control of Fluid Flows, Journal of Computational Physics, vol.143, issue.2, pp.403-425, 1998.
DOI : 10.1006/jcph.1998.5943

M. Jemison, E. Loch, M. Sussman, M. Shashkov, M. Arienti et al., A Coupled Level Set-Moment of Fluid Method for Incompressible Two-Phase Flows, Journal of Scientific Computing, vol.31, issue.2, pp.454-491, 2013.
DOI : 10.1007/s10915-012-9614-7

G. Jiang and D. Peng, Weighted ENO Schemes for Hamilton--Jacobi Equations, SIAM Journal on Scientific Computing, vol.21, issue.6, pp.2126-2143, 2000.
DOI : 10.1137/S106482759732455X

G. Jiang and C. Shu, Efficient Implementation of Weighted ENO Schemes, Journal of Computational Physics, vol.126, issue.1, pp.202-228, 1996.
DOI : 10.1006/jcph.1996.0130

G. Jin and M. Braza, A Nonreflecting Outlet Boundary Condition for Incompressible Unsteady Navier-Stokes Calculations, Journal of Computational Physics, vol.107, issue.2, pp.239-253, 1993.
DOI : 10.1006/jcph.1993.1140

X. Jin, B. Gaillardon, and M. Bergmann, Iollo : A simplified design tool for large wind turbine blades. The European Wind Energy Association conference, 2012.

V. L. Kalb and A. E. Deane, An intrinsic stabilization scheme for proper orthogonal decomposition based low-dimensional models, Physics of Fluids, vol.19, issue.5, p.54106, 2007.
DOI : 10.1063/1.2723149

M. Kang, R. Fedkiw, and X. Liu, A boundary condition capturing method for multiphase incompressible flow, Journal of Scientific Computing, vol.15, issue.3, pp.323-360, 2000.
DOI : 10.1023/A:1011178417620

G. S. Karamanos and G. E. , Karniadakis : A spectral vanishing viscosity method for Large Eddy Simulations, J. Comp. Phys, vol.162, pp.22-50, 2000.

H. Kull, Theory of the Rayleigh-Taylor instability, Physics Reports, vol.206, issue.5, pp.197-325, 1991.
DOI : 10.1016/0370-1573(91)90153-D

J. Lee, J. Kim, H. Choi, and K. Yang, Sources of spurious force oscillations from an immersed boundary method for moving-body problems, Journal of Computational Physics, vol.230, issue.7, pp.2677-2695, 2011.
DOI : 10.1016/j.jcp.2011.01.004

G. Li and X. Lu, Force and power of flapping plates in a fluid, Journal of Fluid Mechanics, vol.200, pp.598-613, 2012.
DOI : 10.1017/S0022112010002387

J. C. Liao, D. N. Beal, G. V. Lauder, and M. S. , Fish Exploiting Vortices Decrease Muscle Activity, Science, vol.302, issue.5650, pp.1566-1569, 2003.
DOI : 10.1126/science.1088295

X. Liu, R. Fedkiw, and M. Kang, A Boundary Condition Capturing Method for Poisson's Equation on Irregular Domains, Journal of Computational Physics, vol.160, issue.1, pp.151-178, 2000.
DOI : 10.1006/jcph.2000.6444

X. Liu, S. Osher, and T. Chan, Weighted Essentially Non-oscillatory Schemes, Journal of Computational Physics, vol.115, issue.1, pp.200-212, 1994.
DOI : 10.1006/jcph.1994.1187

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.24.8744

E. Lombardi, M. Bergmann, and S. Camarri, Iollo : Low-order models : Optimal sampling and linearized control strategies, Journal Europeen des Systemes Automatises, vol.45, pp.7-10575, 2011.
DOI : 10.3166/jesa.45.575-593

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.366.8013

J. L. Lumley, Atmospheric Turbulence and Wave Propagation. The structure of inhomogeneous turbulence, pp.166-178, 1967.

X. Ma and G. E. , Karniadakis : A low-dimensional model for simulating three-dimensional cylinder flow, J. Fluid Mech, vol.458, pp.181-190, 2002.

O. Marsden, On the use of high-order explicit finite differences in bounded aeroacoustic computations, Workshops schémas aux différences, Méthodes cartésiennes, application en mécanique des fluides, 2013.

T. Mcmillen and P. Holmes, An elastic rod model for anguilliform swimming, Journal of Mathematical Biology, vol.17, issue.1, pp.843-886, 2006.
DOI : 10.1007/s00285-006-0036-8

R. Mittal, . Dong, F. Bozkurttas, . Najjar, and . Vargas, A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries, Journal of Computational Physics, vol.227, issue.10, pp.4825-4852, 2008.
DOI : 10.1016/j.jcp.2008.01.028

R. Mittal, IMMERSED BOUNDARY METHODS, Annual Review of Fluid Mechanics, vol.37, issue.1, pp.239-261, 2005.
DOI : 10.1146/annurev.fluid.37.061903.175743

G. Monge, Memoire sur la theorie des des déblais et des remblais, Histoire de l'Academie des Sciences de Paris, p.1781

?. Ne?asová, T. Takahashi, and M. Tucsnak, Weak Solutions for the Motion of a Self-propelled Deformable Structure in a Viscous Incompressible Fluid, Acta Applicandae Mathematicae, vol.24, issue.3, pp.329-352, 2011.
DOI : 10.1007/s10440-011-9646-2

B. R. Noack, K. Afanasiev, M. Morzy?ski, and G. Tadmor, A hierarchy of low-dimensional models for the transient and post-transient cylinder wake, Journal of Fluid Mechanics, vol.497, pp.335-363, 2003.
DOI : 10.1017/S0022112003006694

B. R. Noack and H. Eckelman, A low???dimensional Galerkin method for the three???dimensional flow around a circular cylinder, Physics of Fluids, vol.6, issue.1, pp.124-143, 1994.
DOI : 10.1063/1.868433

B. R. Noack, P. Papas, and P. A. , The need for a pressure-term representation in empirical Galerkin models of incompressible shear flows, Journal of Fluid Mechanics, vol.523, pp.339-365, 2005.
DOI : 10.1017/S0022112004002149

B. R. Noack, M. Schlegel, B. Ahlborn, G. Mutschke, M. Morzynski et al., Tadmor : A finite-time thermodynamics formalism for unsteady flows, J. Non-Equilib. Thermodyn, vol.3, issue.2, pp.103-148, 2008.

J. Nocedal and S. J. Wright, Numerical Optimization. Springer series in operations research, 1999.

S. Osher and J. A. , Sethian : Fronts propagating with curvature-dependent speed : Algorithms based on hamilton-jacobi formulations, J. Comput. Phys, issue.12, p.79, 1988.

J. and P. Velandia, Modélisation et simulation à l'échelle du pore de la récupération assistée des hydrocarbures par injection de polymers, Thèse de doctorat, 2012.

B. Podvin and J. Lumley, A low-dimensional approach for the minimal flow unit, Journal of Fluid Mechanics, vol.362, pp.121-151, 1998.
DOI : 10.1017/S0022112098008854

R. D. Prabhu, S. S. Collis, and Y. Chang, The influence of control on proper orthogonal decomposition of wall-bounded turbulent flows, Physics of Fluids, vol.13, issue.2, pp.520-537, 2001.
DOI : 10.1063/1.1333038

D. Rempfer, Investigations of boundary layer transition via Galerkin projections on empirical eigenfunctions, Physics of Fluids, vol.8, issue.1, pp.175-188, 1996.
DOI : 10.1063/1.868825

D. Rempfer, On Low-Dimensional Galerkin Models for Fluid Flow, Theoretical and Computational Fluid Dynamics, vol.14, issue.2, pp.75-88, 2000.
DOI : 10.1007/s001620050131

D. Rempfer and H. F. , Evolution of three-dimensional coherent structures in a flat-plate boundary layer, Journal of Fluid Mechanics, vol.104, issue.-1, pp.351-375, 1994.
DOI : 10.1063/1.857573

C. M. Rhie and W. L. , Numerical study of the turbulent flow past an airfoil with trailing edge separation, AIAA Journal, vol.21, issue.11, pp.1525-1532, 1983.
DOI : 10.2514/3.8284

G. Russo and P. , A Remark on Computing Distance Functions, Journal of Computational Physics, vol.163, issue.1, pp.51-67, 2000.
DOI : 10.1006/jcph.2000.6553

Y. Saad and M. H. Schultz, GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems, SIAM Journal on Scientific and Statistical Computing, vol.7, issue.3, pp.856-869, 1986.
DOI : 10.1137/0907058

P. Sagaut, Large Eddy Simulation for Incompressible Flows. An Introduction, Measurement Science and Technology, vol.12, issue.10, 2005.
DOI : 10.1088/0957-0233/12/10/707

J. San-martin, J. Scheid, T. Takahashi, and M. , An Initial and Boundary Value Problem Modeling of Fish-like Swimming, Archive for Rational Mechanics and Analysis, vol.272, issue.3, pp.429-455, 2008.
DOI : 10.1007/s00205-007-0092-2

J. , S. Martin, and V. Starovoitov, Global weak solutions for the two dimensional motion of several rigid bodies in an incompressible viscous fluid. Archive for Rational Mechanics and Analysis, pp.113-147, 2002.

M. Sfatiotakis, D. M. Lane, and D. J. Bruce, Review of fish swimming modes for aquatic locomotion, IEEE Journal of Oceanic Engineering, vol.24, issue.2, pp.237-252, 1999.
DOI : 10.1109/48.757275

C. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes, Journal of Computational Physics, vol.77, issue.2, pp.439-471, 1988.
DOI : 10.1016/0021-9991(88)90177-5

S. Sirisup and G. E. , A spectral viscosity method for correcting the long-term behavior of POD models, Journal of Computational Physics, vol.194, issue.1, pp.92-116, 2004.
DOI : 10.1016/j.jcp.2003.08.021

S. Sirisup, G. E. Karniadakis, D. Xiu, and I. G. , Equation-free/Galerkin-free POD-assisted computation of incompressible flows, Journal of Computational Physics, vol.207, issue.2, pp.568-587, 2005.
DOI : 10.1016/j.jcp.2005.01.024

L. Sirovich, Turbulence and the dynamics of coherent structures, Quarterly of Applied Mathematics XLV, issue.3, pp.561-590, 1987.

J. N. Sørensen, Aerodynamic Aspects of Wind Energy Conversion, Annual Review of Fluid Mechanics, vol.43, issue.1, pp.427-448, 2011.
DOI : 10.1146/annurev-fluid-122109-160801

S. Stöcker and D. Weihs, Optimization of energetic advantages of burst swimming of fish, Mathematical Methods in the Applied Sciences, vol.27, issue.2, pp.1387-1400, 2001.
DOI : 10.1002/mma.187

M. Sussman, A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles, Journal of Computational Physics, vol.187, issue.1, pp.110-136, 2003.
DOI : 10.1016/S0021-9991(03)00087-1

M. Sussman and E. Fatemi, An Efficient, Interface-Preserving Level Set Redistancing Algorithm and Its Application to Interfacial Incompressible Fluid Flow, SIAM Journal on Scientific Computing, vol.20, issue.4, pp.1165-1191, 1999.
DOI : 10.1137/S1064827596298245

M. Sussman and E. G. Puckett, A Coupled Level Set and Volume-of-Fluid Method for Computing 3D and Axisymmetric Incompressible Two-Phase Flows, Journal of Computational Physics, vol.162, issue.2, pp.301-337, 2000.
DOI : 10.1006/jcph.2000.6537

M. Sussman, P. Smereka, and S. Osher, A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow, Journal of Computational Physics, vol.114, issue.1, pp.146-159, 1994.
DOI : 10.1006/jcph.1994.1155

S. Tancogne, Calcul numérique et stabilité d'écoulements diphasiques tridimensionnels en microfluidique, Thèse de doctorat, 2007.

R. Temam, Sur l'approximation de la solution des equations de navier-stokes par la méthode des pas fractionnaires ii, Archiv. Rat. Mech. Anal, vol.32, pp.377-385, 1969.

L. J. Timmermans, P. D. Minev, and F. N. , AN APPROXIMATE PROJECTION SCHEME FOR INCOMPRESSIBLE FLOW USING SPECTRAL ELEMENTS, International Journal for Numerical Methods in Fluids, vol.17, issue.7, pp.673-688, 1996.
DOI : 10.1002/(SICI)1097-0363(19960415)22:7<673::AID-FLD373>3.0.CO;2-O

J. J. Videler and D. Weihs, Energetic advantages of burst-and-coast swimming of fish at high speeds, J. exp. Biol, vol.97, pp.169-178, 1982.

G. Vigo, The Proper Orthogonal Decomposition applied to unsteady compressible Navier-Stokes equation, 1998.

C. Villani, Topics in optimal transportation, 2003.
DOI : 10.1090/gsm/058

C. Villani, Optimal Transport, old and new, 2009.

A. Von-loebbecke, R. Mittal, F. Fish, and R. Mark, Propulsive Efficiency of the Underwater Dolphin Kick in Humans, Journal of Biomechanical Engineering, vol.131, issue.5, p.54504, 2009.
DOI : 10.1115/1.3116150

P. W. Webb, Body Form, Locomotion and Foraging in Aquatic Vertebrates, American Zoologist, vol.24, issue.1, pp.107-120, 1984.
DOI : 10.1093/icb/24.1.107

P. W. Webb and R. S. Keyes, Division of labour between median fins in swimming dolphins (pisces : Coryphaeidae ). Copiea, pp.901-904, 1981.

D. Weihs, Energetic advantages of burst swimming of fish, Journal of Theoretical Biology, vol.48, issue.1, pp.215-229, 1974.
DOI : 10.1016/0022-5193(74)90192-1

D. Weihs and P. W. Webb, Optimization of locomotion, 1983.

K. Willcox and J. Peraire, Balanced Model Reduction via the Proper Orthogonal Decomposition, AIAA Journal, vol.40, issue.11, pp.2323-2330, 2002.
DOI : 10.2514/2.1570

T. Ye, R. Mittal, H. S. Udaykumar, and W. Shyy, An Accurate Cartesian Grid Method for Viscous Incompressible Flows with Complex Immersed Boundaries, Journal of Computational Physics, vol.156, issue.2, pp.209-240, 1999.
DOI : 10.1006/jcph.1999.6356

C. Yu, S. Ting, M. Yeh, and J. Yang, Three-dimensional numerical simulation of hydrodynamic interactions between pectoral-fin vortices and body undulation in a swimming fish, Physics of Fluids, vol.23, issue.9, p.91901, 2011.
DOI : 10.1063/1.3640080

Q. Zhu, M. J. Wolfgang, D. K. Yue, and M. S. Triantafyllou, Three-dimensional flow structures and vorticity control in fish-like swimming, Journal of Fluid Mechanics, vol.468, pp.1-28, 2002.
DOI : 10.1017/S002211200200143X