T. Aslam, A partial differential equation approach to multidimensional extrapolation, J. Comput. Phys, vol.193, pp.349-355, 2004.

R. Borges, M. Carmona, B. Costa, and W. Et-don, An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws, J. Comput. Phys, vol.227, pp.3191-3211, 2008.

J. U. Brackbill, D. B. Kothe, and C. Et-zemach, A continuum method for modeling surface tension, J. Comput. Phys, vol.100, pp.335-354, 1992.

I. Chern, J. Glimm, O. Mcbryan, B. Plohr, and S. Et-yaniv, Front tracking for gas dynamics, J. Comput. Phys, vol.62, pp.83-110, 1986.

A. Chorin, A numerical method for solving incompressible viscous flow problems, J. Comput. Phys, vol.2, pp.12-26, 1967.

B. J. Daly, Numerical study of two fluid rayleigh-taylor instability, Phys. Fluids, vol.10, pp.297-307, 1967.

D. S. Dandy and L. G. Leal, Buoyancy-driven motion of a deformable drop through a quiescent liquid at intermediate reynolds numbers, J. Fluid Mech, vol.208, pp.161-192, 1989.

P. G. De-gennes, Wetting : statics and dynamics, Reviews of Modern Physics, vol.57, pp.827-863, 1985.

J. Dendy, Black box multigrid, J. Comput. Phys, vol.48, pp.366-386, 1982.

R. Fedkiw, T. Aslam, B. Merriman, and S. Et-osher, A non-oscillatory eulerian approach to interfaces in multimaterial flows (the ghost fluid method), J. Comput. Phys, vol.152, pp.457-492, 1999.

F. Gibou, R. Fedkiw, L. Cheng, and M. Kang, A second-order-accurate symmetric discretization of the poisson equation on irregular domains, J. Comput. Phys, vol.176, pp.205-227, 2002.

J. Glimm, C. Klingenberg, O. Mcbryan, B. Plohr, D. Sharp et al., Front tracking and two-dimensional riemann problems, Advances in Applied Mathematics, vol.6, pp.256-290, 1985.

D. Gueyffier, J. Li, A. Nadim, R. Scardovelli, and S. Et-zaleski, Volume-of-fluid interface tracking with smoothed surface stress methods for three-dimensional flows, J. Comput. Phys, vol.152, pp.423-456, 1999.

F. H. Harlow and J. E. Welch, Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. Fluids, vol.8, pp.2182-2189, 1965.

C. W. Hirt and B. D. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys, vol.39, pp.201-225, 1981.

M. Kang, R. Fedkiw, and X. Liu, A boundary condition capturing method for multiphase incompressible flow, J. Sci. Comput, vol.15, pp.323-360, 2000.

B. Lafaurie, C. Nardone, R. Scardovelli, S. Zaleski, and G. Et-zanetti, Modelling merging and fragmentation in multiphase flows with SURFER, J. Comput. Phys, vol.113, pp.134-147, 1994.

B. Lalanne, L. R. Villegas, S. Tanguy, and F. Et-risso, On the computation of viscous terms for incompressible two-phase flows with level set/ghost fluid method, J. Comput. Phys, vol.301, pp.289-307, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01308135

M. Lepilliez, Simulation numérique des ballotements d'ergols dans les réservoirs de satellites en microgravité et à faible nombre de Reynolds, 2015.

M. Lepilliez, E. R. Popescu, F. Gibou, and S. Et-tanguy, On two-phase flow solvers in irregular domains with contact line, J. Comput. Phys, vol.321, pp.1217-1251, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01349346

X. Liu, R. Fedkiw, and M. Et-kang, A boundary condition capturing method for poisson's equation on irregular domain, J. Comput. Phys, vol.160, pp.151-178, 2000.

S. Maclachlan, J. Tang, and C. Et-vuik, Fast and robust solvers for pressure-correction in bubbly flow problems, J. Comput. Phys, vol.227, pp.9742-9761, 2008.

Y. Ng, C. Min, and F. Et-gibou, An efficient fluid-solid coupling algorithm for single-phase flows, J. Comput. Phys, vol.228, pp.8807-8829, 2009.

W. F. Noh and P. Woodward, Slic (simple line interface calculation), Lecture Notes in Physics Proceedings of the Fifth International Conference on Numerical Methods in Fluid Dynamics, pp.330-340, 1976.

S. Osher and J. Et-sethian, Fronts propagating with curvature-dependent speed : algorithms based on hamilton-jacobi formulations, J. Comput. Phys, vol.79, pp.12-49, 1988.

S. Popinet, An accurate adaptive solver for surface-tension-driven interfacial flows, J. Comput. Phys, vol.228, pp.5838-5866, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01445445

E. G. Puckett, A. S. Almgren, J. B. Bell, D. L. Marcus, and W. J. Rider, A high-order projection method for tracking fluid interfaces in variable density incompressible flows, J. Comput. Phys, vol.130, pp.269-282, 1997.

W. J. Rider and D. B. Et-kothe, Reconstructing volume tracking, J. Comput. Phys, vol.141, pp.112-152, 1998.

G. Ryskin and L. G. Et-leal, Numerical solution of free-boundary problems in fluid mechanics. part 1. the finite-difference technique, J. Fluid Mech, vol.148, pp.1-17, 1984.

R. Scardovelli and S. Et-zaleski, Direct numerical simulation of free-surface and interfacial flow, Annu. Rev. Fluid Mech, vol.31, pp.567-603, 1999.

S. Sikalo, H. Wilhelm, I. V. Roisman, S. Jakirlic, and C. Et-tropea, Dynamic contact angle of spreading droplet : Experiments and simulations, Phys. Fluids, vol.17, p.62103, 2005.

J. H. Snoeijer and B. Et-andreotti, Moving contact lines : scales, regimes and dynamical transitions, Annu. Rev. Fluid Mech, vol.45, pp.269-292, 2013.

Y. Sui, H. Ding, and P. D. Et-spelt, Numerical simulations of flows with moving contact lines, Annu. Rev. Fluid Mech, vol.46, pp.97-119, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01296873

M. Sussman, P. Smereka, and S. Et-osher, A level set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys, vol.114, pp.146-159, 1994.

M. Sussman, K. Smith, M. Hussaini, M. Ohta, and R. Et-zhi-wei, A sharp interface method for incompressible two-phase flows, J. Comput. Phys, vol.221, pp.469-505, 2007.

S. O. Unverdi and G. Et-tryggvason, A front-tracking method for viscous, incompressible, multi-fluid flows, J. Comput. Phys, vol.100, pp.25-37, 1992.

D. L. Youngs, Time-dependent multimaterial flow with large fluid distortion, pp.273-285, 1982.

N. H. Abramson, The dynamic behaviour of liquids in moving containers, with applications to space vehicle technology, NASA SP, vol.106, 1967.

R. Borges, M. Carmona, B. Costa, and W. S. Don, An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws, J. Comput. Phys, vol.227, pp.3191-3211, 2008.

A. Chorin, A numerical method for solving incompressible viscous flow problems, J. Comput. Phys, vol.2, pp.12-26, 1967.

A. Dalmon, M. Lepilliez, S. Tanguy, B. Busset, H. Bavestrello et al., Mignot Figure 19. X-coordinate of the centre of mass of the fluids throughout time with ? f ill = 50%, for different Bo i and Bo c =

. Chapitre-3, . Simulation, . Du, and . Dans-un-réservoir,

A. Dalmon, M. Lepilliez, S. Tanguy, B. Busset, H. Bavestrello et al.,

J. E. Dendy, Black box multigrid, J. Comput. Phys, vol.48, pp.366-386, 1982.

F. T. Dodge, The new dynamic behaviour of liquids in moving containers, 2000.

O. M. Faltinsen, R. Firoozkoohi, and A. N. Timokha, Steady-state liquid sloshing in a rectangular tank with a slat-type screen in the middle: Quasilinear modal analysis and experiments, Phys. Fluids, vol.23, pp.42101-42120, 2011.

O. M. Faltinsen and A. N. Timokha, A multimodal method for liquid sloshing in a twodimensional circular tank, J. Fluid Mech, vol.665, pp.457-479, 2010.

O. M. Faltinsen and A. N. Timokha, Multimodal analysis of weakly nonlinear sloshing in a spherical tank, J. Fluid Mech, vol.719, pp.129-164, 2013.

R. Fedkiw, T. Aslam, B. Merriman, and S. Osher, A non-oscillatory eulerian approach to interfaces in multimaterial flows (the ghost fluid method), J. Comput. Phys, vol.152, pp.457-492, 1999.

F. Gibou, L. Cheng, D. Nguyen, and S. Banerjee, A level set based sharp interface method for the multiphase incompressible navier-stokes equations with phase change, J. Comput. Phys, vol.222, pp.536-555, 2007.

F. Gibou, R. Fedkiw, L. Cheng, and M. Kang, A second-order-accurate symmetric discretization of the poisson equation on irregular domains, J. Comput. Phys, vol.176, pp.205-227, 2002.

G. Huber, S. Tanguy, J. Bera, and B. Gilles, A time splitting projection scheme for compressible two-phase flows. application to the interaction of bubbles with ultrasound waves, J. Comput. Phys, vol.302, pp.439-468, 2015.

G. Huber, S. Tanguy, M. Sagan, and C. Colin, Direct numerical simulation of nucleate pool boiling at large microscopic contact angle and moderate jakob number, Int. J. Heat Mass Transfer, vol.113, pp.662-682, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01552748

T. Ikeda, R. A. Ibrahim, Y. Harata, and T. Kuriyama, Nonlinear liquid sloshing in a square tank subjected to obliquely horizontal excitation, J. Fluid Mech, vol.700, pp.304-328, 2012.

M. Kang, R. Fedkiw, and X. Liu, A boundary condition capturing method for multiphase incompressible flow, J. Sci. Comput, vol.15, pp.323-360, 2000.

B. Lalanne, N. A. Chebel, J. Vejrazka, S. Tanguy, O. Masbernat et al., Non-linear shape oscillations of rising drops and bubbles: Experiments and simulations, Phys. of Fluids, p.27, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01308141

B. Lalanne, L. Villegas, . Rueda, S. Tanguy, and F. Risso, On the computation of viscous terms for incompressible two-phase flows with level set/ghost fluid method, J. Comput. Phys, vol.301, pp.289-307, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01308135

D. Langbein, Capillary surfaces: Shape Stability Dynamics, Particular Under Weightlessness, vol.178, 2002.

M. Lepilliez, Simulation numérique des ballotements d'ergols dans les réservoirs de satellites en microgravité età faible nombre de reynolds, 2015.

M. Lepilliez, E. R. Popescu, F. Gibou, and S. Tanguy, On two-phase flow solvers in irregular domains with contact line, J. Comput. Phys, vol.321, pp.1217-1251, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01349346

D. Liu and P. Lin, A numerical study of three-dimensional liquid sloshing in tanks, J. Comput. Phys, vol.227, pp.3921-3939, 2008.

X. Liu, R. Fedkiw, and M. Kang, A boundary condition capturing method for poissons equation on irregular domain, J. Comput. Phys, vol.160, pp.151-178, 2000.

S. P. Maclachlan, J. M. Tang, and C. Vuik, Fast and robust solvers for pressurecorrection in bubbly flow problems, J. Comput. Phys, vol.227, issue.23, pp.9742-9761, 2008.

J. Mignot, R. Pierre, M. Berhanu, B. Busset, R. Roumiguié et al., Fluid dynamic in space experiment, 68th International Astronautical Congress (IAC), 2017.

Y. T. Ng, C. Min, and F. Gibou, An efficient fluidsolid coupling algorithm for single-phase flows, J. Comput. Phys, vol.228, pp.8807-8829, 2009.

S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: algorithms based on hamiltonjacobi formulations, J. Comput. Phys, vol.79, pp.12-49, 1988.

J. Papac, . Gibou, and C. Ratsch, The dynamic behaviour of liquids in moving containers, SIMULATION NUMÉRIQUE DU BALLOTTEMENT DANS UN RÉSERVOIR References Abramson NH, vol.88, issue.3, p.106, 1967.

T. Aslam, A partial differential equation approach to multidimensional extrapolation, J Comput Phys, vol.193, pp.349-355, 2004.

A. Chorin, A numerical method for solving incompressible viscous flow problems, J Comput Phys, vol.2, pp.12-26, 1967.

J. Dendy, Black box multigrid, J Comput Phys, vol.48, pp.366-386, 1982.

F. T. Dodge, T. Aslam, B. Merriman, and S. Osher, A non-oscillatory eulerian approach to interfaces in multimaterial flows (the ghost fluid method), Texas Fedkiw R, vol.152, pp.457-492, 1999.

F. Gibou, R. Fedkiw, L. T. Cheng, and M. Kang, A second-orderaccurate symmetric discretization of the poisson equation on irregular domains, J Comput Phys, vol.176, pp.205-227, 2002.

F. Gibou, L. T. Cheng, D. Nguyen, and S. Banerjee, A level set based sharp interface method for the multiphase incompressible navierstokes equations with phase change, J Comput Phys, vol.222, pp.536-555, 2007.

G. Huber, S. Tanguy, J. Bera, and B. Gilles, A time splitting projection scheme for compressible two-phase flows. application to the interaction of bubbles with ultrasound waves, J Comput Phys, vol.302, pp.439-468, 2015.

G. Huber, S. Tanguy, M. Sagan, C. Colin, N. A. Chebel et al., Direct numerical simulation of nucleate pool boiling at large microscopic contact angle and moderate jakob number, Int J Heat Mass Transfer Lalanne B, vol.27, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01552748

M. Lepilliez, E. R. Popescu, F. Gibou, and S. Tanguy, Simulation numérique des ballotements d'ergols dans les réservoirs de satellites en microgravité età faible nombre de reynolds, J Comput Phys, vol.321, pp.1217-1251, 2015.

D. Liu and P. Lin, A numerical study of three-dimensional liquid sloshing in tanks, J Comput Phys, vol.227, pp.3921-3939, 2008.

X. D. Liu, R. Fedkiw, and M. Kang, A boundary condition capturing method for poissons equation on irregular domain, J Comput Phys, vol.160, pp.151-178, 2000.

S. Maclachlan, J. Tang, and C. Vuik, Fast and robust solvers for pressure-correction in bubbly flow problems, Journal of Computational Physics, vol.227, issue.23, pp.9742-9761, 2008.

J. Mignot, R. Pierre, M. Berhanu, B. Busset, R. Roumigui et al., Fluid dynamic in space experiment, 68th International Astronautical Congress (IAC), 2017.

Y. Ng, C. Min, and F. Gibou, An efficient fluid-solid coupling algorithm for single-phase flows, J Comput Phys, vol.228, pp.8807-8829, 2009.

D. Q. Nguyen, R. P. Fedkiw, and M. Kang, A boundary condition capturing method for incompressible flame discontinuities, J Comput Phys, vol.172, pp.71-98, 2001.

S. Osher and J. Sethian, Fronts propagating with curvature-dependent speed: algorithms based on hamiltonjacobi formulations, J Comput Phys, vol.79, pp.12-49, 1988.

J. Papac, F. Gibou, and C. Ratsch, Efficient symmetric discretization for the poisson, heat and stefan-type problems with robin boundary conditions, J Comput Phys, vol.229, pp.875-889, 2010.

J. U. Brackbill, D. B. Kothe, and C. Et-zemach, A continuum method for modeling surface tension, J. Comput. Phys, vol.100, pp.335-354, 1992.

G. H. Cottet, M. Et, T. , and M. , Eulerian formulation and level set model for incompressible fluidstructure interaction, ESAIM : Mathematical Modelling and Numerical Analysis, vol.42, pp.471-492, 2008.

G. H. Cottet and E. Et-maitre, A level set method for fluid-structure interaction with immersed surfaces, Math. Model. Meth. Appl. Sci, vol.16, issue.3, pp.415-438, 2006.

C. D. Eggleton and A. S. Popel, Large deformation of red blood cell ghost in a simple shear flow, Phys. Fluids, vol.10, pp.1834-1845, 1998.

C. Farhat, K. G. Der-zee, and P. Et-geuzaine, Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity, Comput. Methods Appl. Mech. Engrg, vol.195, pp.1973-2001, 2006.

L. J. Fauci and C. S. Et-peskin, A computational model of aquatic animal locomotion, J. Comput. Phys, vol.77, pp.85-108, 1988.

R. Fedkiw, T. Aslam, B. Merriman, and S. Et-osher, A non-oscillatory eulerian approach to interfaces in multimaterial flows (the ghost fluid method), J. Comput. Phys, vol.152, pp.457-492, 1999.

Y. J. Ge and H. Tanaka, Aerodynamic flutter analysis of cable-supported bridges by multi-mode and full-mode approaches, Journal of wind engineering and industrial aerodynamics, vol.86, pp.123-153, 2000.

A. N. Gent and A. G. Thomas, Forms for the stored (strain) energy function for vulcanized rubber, J. of Polym. Sci, vol.28, pp.625-628, 1958.

G. Hou, J. Wang, and A. Et-layton, Numerical methods for fluid-structure interaction, Commun Comput. Phys, vol.12, pp.337-377, 2012.

S. Ii, X. Gong, K. Sugiyama, J. Wu, H. Huang et al., A full eulerian fluid-membrane coupling method with a smoothed volume-of-fluid approach, Commun Comput. Phys, vol.12, issue.2, pp.544-576, 2012.

R. Kamakoti and W. Et-shyy, Fluid-structure interaction for aeroelastic applications. Progress in Aerospace, Sciences, vol.40, pp.535-558, 2004.

M. Kang, R. Fedkiw, and X. Liu, A boundary condition capturing method for multiphase incompressible flow, J. Sci. Comput, vol.15, pp.323-360, 2000.

M. C. Lai and C. S. Et-peskin, An immersed boundary method with formal second-order accuracy and reduced numerical viscosity, J. Comput. Phys, vol.160, pp.705-719, 2000.

B. Lalanne, L. R. Villegas, S. Tanguy, and F. Et-risso, On the computation of viscous terms for incompressible two-phase flows with level set/ghost fluid method, J. Comput. Phys, vol.301, pp.289-307, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01308135

L. Lee and R. J. Et-leveque, An immersed interface method for incompressible navier-stokes equations, J. Sci. Comput, vol.25, pp.832-856, 2003.

R. J. Leveque and Z. Li, The immersed interface method for elliptic equations with discontinuous coefficient and singular sources, SIAM J. Numer. Anal, vol.31, issue.4, pp.1019-1044, 1994.

R. J. Leveque and Z. Li, Immersed interface methods for stokes flow with elastic boundaries or surface tension, J. Sci. Comput, vol.18, issue.3, pp.709-735, 1997.

Z. Li and M. C. Lai, The immersed interface method for the navier-stokes equations with singular forces, J. Comput. Phys, vol.171, pp.822-842, 2001.

W. K. Liu, Y. Liu, D. Farell, L. Zhang, X. S. Wang et al., Immersed finite element method and its applications to biological systems, Comput. Methods Appl. Mech. Engrg, vol.195, pp.1722-1749, 2006.

E. Longatte, Z. Bendjeddou, and M. Et-souli, Methods for numerical study of tube bundle vibrations in cross-flows, Journal of Fluids and Structures, vol.18, pp.513-528, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00139448

G. T. Mase and G. E. Et-mase, Continuum mechanics for engineers, 1999.

T. Milcent and E. Et-maitre, Eulerian model of immersed elastic surfaces with full membrane elasticity, Communications in Mathematical Sciences, vol.14, issue.3, pp.857-881, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01078869

C. Min, On reinitializing level set functions, J. Comput. Phys, vol.229, pp.2764-2772, 2010.

R. Mittal and G. Et-iaccarino, Immersed boundary methods, Annu. Rev. Fluid Mech, vol.37, pp.239-261, 2005.

M. Mooney, A theory of large elastic deformation, J. Appl. Phys, vol.11, pp.582-592, 1940.

R. W. Ogden, Large deformation isotropic elasticity -on the correlation of theory and experiment for incompressible rubberlike solids, Proc. R. Soc. Lond, vol.326, pp.565-584, 1972.

S. Osher and J. Et-sethian, Fronts propagating with curvature-dependent speed : algorithms based on hamilton-jacobi formulations, J. Comput. Phys, vol.79, pp.12-49, 1988.

C. S. Peskin, Flow patterns around heart valves : a numerical method, J. Comput. Phys, vol.10, pp.252-271, 1972.

C. S. Peskin, Numerical analysis of blood flow in the heart, J. Comput. Phys, vol.25, pp.220-252, 1977.

C. S. Peskin, The immersed boundary method, Acta Numerica, vol.11, pp.479-517, 2002.

E. M. Saiki and S. Et-biringen, Numerical simulation of a cylinder in uniform flow : application of a virtual boundary method, J. C, vol.123, pp.450-465, 1996.

R. Scardovelli and S. Et-zaleski, Direct numerical simulation of free-surface and interfacial flow, Annu. Rev. Fluid Mech, vol.31, pp.567-603, 1999.

J. Sigrist and D. Et-broc, Dynamic analysis of a tube bundle with fluid-structure interaction modelling using a homogenisation method, Comput. Methods Appl. Mech. Engrg, vol.197, pp.1080-1099, 2008.

K. Sugiyama, S. Ii, S. Takeuchi, S. Takagi, and Y. Et-matsumoto, A full eulerian finite difference approach for solving fluid-structure coupling problems, Journal of Computational Physics, vol.230, pp.596-627, 2011.

M. Sussman, P. Smereka, and S. Et-osher, A level set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys, vol.114, pp.146-159, 1994.

Z. Tan, D. V. Le, Z. Li, K. M. Lim, and B. C. Et-khoo, An immersed interface method for solving incompressible viscous flows with piecewise constant viscosity accross a moving elastic membrane, J. Comput. Phys, vol.227, pp.9955-9983, 2008.

Z. Tan, D. V. Le, K. M. Lim, and B. C. Et-khoo, An immersed interface method for the incompressible navier-stokes equations with discontinuous viscosity across the interface, J. Sci. Comput, vol.31, pp.1798-1819, 2009.

L. R. Treloar, The elasticity of a network of long chain molecules, Trans. Faraday Soc, vol.39, pp.36-41, 1943.

S. O. Unverdi and G. Et-tryggvason, A front-tracking method for viscous, incompressible, multi-fluid flows, J. Comput. Phys, vol.100, pp.25-37, 1992.

S. Xu and Z. J. Wang, Systematic derivation of jump conditions for the immersed interface method in three-dimensional flow simulation, J. Sci. Comput, vol.27, issue.6, pp.1948-1980, 2006.

. Yeoh, Characterization of elastic properties of carbon-black-filled rubber vulcanizates, Rubber Chemistry and Technology, vol.63, pp.792-805, 1990.

. .. Algorithme-d'extension,

. .. Membrane-Étirée-dans-un-fluide, 141 6.2.2 Évolutions des rayons principaux et étude de convergence

. .. Membrane, 148 6.3.1 Saut de viscosité à la membrane

. .. Capsule, 152 6.4.3 Déformation de la membrane avec le temps

.. .. Conclusion,

A. Annexe, J. Comput. Phys, p.155, 2008.

.. .. Bibliographie,

, Dans un premier temps, l'algorithme d'extension est évalué pour montrer son efficacité à partir d'un champ scalaire quelconque avec et sans la résolution en sous maille. Ensuite, le cas-test de la membrane bidimensionnelle étirée et pressurisée est présenté. L'évolution des rayons principaux ainsi que les distributions de pression et vitesse sont évaluées et comparées aux résultats de la littérature, Les différents modèles et méthodes numériques décrits dans le chapitre précédent sont évalués sur des castests de la littérature

T. Aslam, A partial differential equation approach to multidimensional extrapolation, J. Comput. Phys, vol.193, pp.349-355, 2004.

D. Barthes-biesel, Capsule motion in flow : Deformation and membrane buckling, C. R. Physique, vol.10, pp.764-774, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00454462

D. Barthes-biesel and J. M. Et-rallison, The time-dependent deformation of a capsule freely suspended in a linear shear flow, J. Fluid Mech, vol.113, pp.251-267, 1981.

C. D. Eggleton and A. S. Popel, Large deformation of red blood cell ghost in a simple shear flow, Phys. Fluids, vol.10, pp.1834-1845, 1998.

L. Lac, D. Barthes-biesel, N. A. Pelekasis, and J. Et-tsamopoulos, Spherical capsules in threedimensional unbounded stokes flows : effect of the membrane constitutive law and onset of buckling, J. Fluid Mech, vol.516, pp.303-334, 2004.

L. Lee and R. J. Et-leveque, An immersed interface method for incompressible navier-stokes equations, J. Sci. Comput, vol.25, pp.832-856, 2003.

R. J. Leveque and Z. Li, Immersed interface methods for stokes flow with elastic boundaries or surface tension, J. Sci. Comput, vol.18, issue.3, pp.709-735, 1997.

C. Pozrikidis, Finite deformation of liquid capsules enclosed by elastic membranes in simple shear flow, J. Fluid Mech, vol.297, pp.123-152, 1995.

S. Ramanujan and C. Et-pozrikidis, Deformation of liquid capsule enclosed by elastic membranes in simple shear flow : large deformation and the effect of fluid viscosities, J. Fluid Mech, vol.361, pp.117-143, 1998.

Z. Tan, D. V. Le, Z. Li, K. M. Lim, and B. C. Et-khoo, An immersed interface method for solving incompressible viscous flows with piecewise constant viscosity accross a moving elastic membrane, J. Comput. Phys, vol.227, pp.9955-9983, 2008.

C. Tu and C. S. Et-peskin, Stability and instability in the computation of flows with moving immersed boundaries : a comparison of three methods, SIAM J. Sci. Stat. Comput, vol.13, issue.6, pp.1361-1376, 1992.

, Celui-ci contient une fine membrane hyperélastique d'une épaisseur de 0.2mm fixée à son diamètre, comme représentée sur la figure 7.1 à gauche. Ce nouveau réservoir va permettre d'obtenir des données inédites sur le ballottement dans les réservoirs à membrane. Les résultats nous permettront de choisir les modèles à implémenter au sein du code de calcul pour pouvoir approcher plus, phénomènes physiques pertinents, un nouveau réservoir sphérique va être envoyé début décembre 2018 à bord de l'ISS pour être intégré à l'expérience FLUIDICS

D. S. Airbus, Parmi ceux-ci, un réservoir contenant une baffle antiballottement sera envoyé en même temps que le réservoir à membrane à bord de l'ISS. Cette baffle prend la forme d'un anneau circulaire rigide inséré dans le réservoir, comme représentée par transparence sur la figure 7.1 à droite. Ce dispositif est utilisé afin d'atténuer le ballottement en servant d'obstacle solide à l'intérieur du réservoir. L'expérimentation en micro-gravité permettra de connaître plus en détail l'effet d'une baffle sur l'amortissement des fluides lors d'une manoeuvre et apportera des données originales, FLUIDICS pour tester de nouvelles technologies de réservoir et de systèmes capillaires en micro-gravité

T. Aslam, A partial differential equation approach to multidimensional extrapolation, J. Comput. Phys, vol.193, pp.349-355, 2004.

D. Barthes-biesel, Capsule motion in flow: Deformation and membrane buckling, C. R. Physique, vol.10, pp.764-774, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00454462

D. Barthes-biesel and J. M. Rallison, The time-dependent deformation of a capsule freely suspended in a linear shear flow, J. Fluid Mech, vol.113, pp.251-267, 1981.

R. Borges, M. Carmona, B. Costa, and W. Don, An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws, J. Comput. Phys, vol.227, pp.3191-3211, 2008.

A. Chorin, A numerical method for solving incompressible viscous flow problems, J. Comput. Phys, vol.2, pp.12-26, 1967.

M. Cisternino and L. Weynans, A Parallel Second Order Cartesian Method for Elliptic Interface Problems, Commun Comput. Phys, vol.12, issue.5, pp.1562-1587, 2012.
URL : https://hal.archives-ouvertes.fr/inria-00577874

G. H. Cottet and E. Maitre, A level set method for fluid-structure interaction with immersed surfaces, Math. Model. Meth. Appl. Sci, vol.16, issue.3, pp.415-438, 2006.

A. Dalmon, M. Lepilliez, S. Tanguy, A. Pedrono, B. Busset et al., Direct Numerical Simulation of a bubble motion in a spherical tank under external forces and microgravity conditions, J. Fluid Mech, vol.849, pp.467-497, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01831710

J. Dendy, Black box multigrid, J. Comput. Phys, vol.48, pp.366-386, 1982.

C. D. Eggleton and A. S. Popel, Large deformation of red blood cell ghost in a simple shear flow, Phys. Fluids, vol.10, issue.8, pp.1834-1845, 1998.

R. Fedkiw, T. Aslam, B. Merriman, and S. Osher, A non-oscillatory Eulerian approach to interfaces in multimaterial flows (The Ghost Fluid Method), J. Comput. Phys, vol.152, pp.457-492, 1999.

A. N. Gent and A. G. Thomas, Forms for the stored (strain) energy function for vulcanized rubber, J. of Polym. Sci, vol.28, pp.625-628, 1958.

F. Gibou, R. Fedkiw, L. Cheng, and M. Kang, A second-order-accurate symmetric discretization of the Poisson equation on irregular domains, J. Comput. Phys, vol.176, pp.205-227, 2002.

A. Guittet, M. Lepilliez, S. Tanguy, and F. Gibou, Solving elliptic problems with discontinuities on irregular domains -the Voronoi Interface Method, J. Comput. Phys, vol.298, pp.747-765, 2015.

C. W. Hirt and B. D. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys, vol.39, pp.201-225, 1981.

S. Hou and X. Liu, A numerical method for solving variable coefficient elliptic equation with interfaces, J. Comput. Phys, vol.202, pp.411-445, 2005.

G. Huber, S. Tanguy, J. Bera, and B. Gilles, A time splitting projection scheme for compressible two-phase flows. Application to the interaction of bubbles with ultrasound waves, J. Comput. Phys, vol.302, pp.439-468, 2015.

S. Ii, X. Gong, K. Sugiyama, J. Wu, H. Huang et al., A full eulerian fluid-membrane coupling method with a smoothed volume-of-fluid approach, Commun Comput. Phys, vol.12, issue.2, pp.544-576, 2012.

M. Kang, R. Fedkiw, and X. Liu, A boundary condition capturing method for multiphase incompressible flow, J. Sci. Comput, vol.15, pp.323-360, 2000.

L. Lac, D. Barthes-biesel, N. A. Pelekasis, and J. Tsamopoulos, Spherical capsules in three-dimensional unbounded Stokes flows: effect of the membrane constitutive law and onset of buckling, J. Fluid Mech, vol.516, pp.303-334, 2004.

B. Lalanne, L. R. Villegas, S. Tanguy, and F. Risso, On the computation of viscous terms for incompressible two-phase flows with Level Set/Ghost Fluid Method, J. Comput. Phys, vol.301, pp.289-307, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01308135

L. Lee and R. J. Leveque, An immersed interface method for incompressible Navier-Stokes equations, J. Sci. Comput, vol.25, issue.3, pp.832-856, 2003.

M. Lepilliez, E. R. Popescu, F. Gibou, and S. Tanguy, On two-phase flow solvers in irregular domains with contact line, J. Comput. Phys, vol.321, pp.1217-1251, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01349346

R. J. Leveque and Z. Li, The immersed interface method for elliptic equations with discontinuous coefficient and singular sources, SIAM J. Numer. Anal, vol.31, issue.4, pp.1019-1044, 1994.

R. J. Leveque and Z. Li, Immersed interface methods for Stokes flow with elastic boundaries or surface tension, J. Sci. Comput, vol.18, issue.3, pp.709-735, 1997.

Z. Li and M. C. Lai, The immersed interface method for the Navier-Stokes equations with singular forces, J. Comput. Phys, vol.171, pp.822-842, 2001.

X. Liu, R. Fedkiw, and M. Kang, A boundary condition capturing method for Poisson's equation on irregular domain, J. Comput. Phys, vol.160, pp.151-178, 2000.

S. Maclachlan, J. Tang, and C. Vuik, Fast and robust solvers for pressure-correction in bubbly flow problems, Journal of Computational Physics, vol.227, issue.23, pp.21-9991, 2008.

J. Mignot, R. Pierre, M. Berhanu, B. Busset, R. Roumigui et al., Fluid dynamic in space experiment, 68th International Astronautical Congress (IAC)

C. Min, On reinitializing level set functions, J. Comput. Phys, vol.229, pp.2764-2772, 2010.

C. Min and F. Gibou, A second order accurate level set method on non-graded adaptive cartesian grids, J. Comput. Phys, vol.225, pp.300-321, 2007.

M. Mooney, A theory of large elastic deformation, J. Appl. Phys, vol.11, pp.582-592, 1940.

Y. Ng, C. Min, and F. Gibou, An efficient fluid-solid coupling algorithm for single-phase flows, J. Comput. Phys, vol.228, pp.8807-8829, 2009.

R. W. Ogden, Large deformation isotropic elasticity -On the correlation of theory and experiment for incompressible rubberlike solids, Proc. R. Soc. Lond, vol.326, pp.565-584, 1972.

S. Osher and J. Sethian, Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys, vol.79, pp.12-49, 1988.

C. S. Peskin, Flow patterns around heart valves: a numerical method, J. Comput. Phys, vol.10, pp.252-271, 1972.

C. S. Peskin, Numerical analysis of blood flow in the heart, J. Comput. Phys, vol.25, pp.220-252, 1977.

C. S. Peskin, The immersed boundary method, Acta Numerica, vol.11, pp.479-517, 2002.

C. Pozrikidis, Finite deformation of liquid capsules enclosed by elastic membranes in simple shear flow, J. Fluid Mech, vol.297, pp.123-152, 1995.

S. Ramanujan and C. Pozrikidis, Deformation of liquid capsule enclosed by elastic membranes in simple shear flow: large deformation and the effect of fluid viscosities, J. Fluid Mech, vol.361, pp.117-143, 1998.

L. Villegas, R. Alis, M. Lepilliez, and S. Tanguy, A Ghost Fluid/Level Set Method for boiling flows and liquid evaporation: Application to the Leidenfrost effect, J. Comput. Phys, vol.316, pp.789-813, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01407719

R. Scardovelli and S. Zaleski, Direct Numerical Simulation of free-surface and interfacial flow, Annu. Rev. Fluid Mech, vol.31, pp.567-603, 1999.

K. Sugiyama, S. Ii, S. Takeuchi, S. Takagi, and Y. Matsumoto, A full Eulerian finite difference approach for solving fluid-structure coupling problems, Journal of Computational Physics, vol.230, pp.596-627, 2011.

M. Sussman, P. Smereka, and S. Osher, A Level Set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys, vol.114, pp.146-159, 1994.

M. Sussman, K. Smith, M. Hussaini, M. Ohta, and R. Zhi-wei, A sharp interface method for incompressible two-phase flows, J. Comput. Phys, vol.221, pp.469-505, 2007.

Z. Tan, D. V. Le, Z. Li, K. M. Lim, and B. C. Khoo, An immersed interface method for solving incompressible viscous flows with piecewise constant viscosity accross a moving elastic membrane, J. Comput. Phys, vol.227, pp.9955-9983, 2008.

Z. Tan, D. V. Le, K. M. Lim, and B. C. Khoo, An immersed interface method for the incompressible Navier-Stokes equations with discontinuous viscosity across the interface, J. Sci. Comput, vol.31, issue.3, pp.1798-1819, 2009.

S. Tanguy, T. Menard, and A. Berlemont, A level set method for vaporizing two-phase flows, J. Comput. Phys, vol.221, pp.837-853, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00649783

S. Tanguy, M. Sagan, B. Lalanne, F. Couderc, and C. Colin, Benchmarks and numerical methods for the simulation of boiling flows, J. Comput. Phys, vol.264, pp.1-22, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00973210

L. R. Treloar, The elasticity of a network of long chain molecules, Trans. Faraday Soc, vol.39, pp.36-41, 1943.

C. Tu and C. S. Peskin, Stability and instability in the computation of flows with moving immersed boundaries: a comparison of three methods, SIAM J. Sci. Stat. Comput, vol.13, issue.6, pp.1361-1376, 1992.

S. Xu and Z. J. Wang, Systematic derivation of jump conditions for the immersed interface method in three-dimensional flow simulation, J. Sci. Comput, vol.27, issue.6, pp.1948-1980, 2006.

. Yeoh, Characterization of Elastic Properties of Carbon-Black-Filled Rubber Vulcanizates, Rubber Chemistry and Technology, vol.63, issue.5, pp.792-805, 1990.