R. Abgrall and S. Karni, Computations of Compressible Multifluids, Journal of Computational Physics, vol.169, issue.2, pp.594-623, 2001.
DOI : 10.1006/jcph.2000.6685

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.471.4035

G. Allaire, Analyse numérique et optimisation, une introduction à la modélisation mathématique et à la simulation numérique, École Polytechnique, issue.2, 2010.

A. S. Almgren, J. B. Bell, M. J. Lijewski, Z. Luki?, and E. Van-andel, Nyx: A MASSIVELY PARALLEL AMR CODE FOR COMPUTATIONAL COSMOLOGY, The Astrophysical Journal, vol.765, issue.1, p.39, 2013.
DOI : 10.1088/0004-637X/765/1/39

URL : http://arxiv.org/abs/1301.4498

A. S. Almgren, J. B. Bell, C. A. Rendleman, and M. Zingale, Low Mach Number Modeling of Type Ia Supernovae. I. Hydrodynamics, The Astrophysical Journal, vol.637, issue.2, p.922, 2006.
DOI : 10.1086/498426

A. Ambroso, C. Chalons, F. Coquel, and T. Galié, Relaxation and numerical approximation of a two-fluid twopressure diphasic model, ESAIM: Mathematical Modelling and Numerical Analysis, vol.436, pp.1063-1097, 2009.

G. M. Amdahl, Validity of the single processor approach to achieving large scale computing capabilities, spring joint computer conference, Proceedings of the, pp.483-485, 1967.

. Ph, J. Angot, K. Caltagirone, and . Khadra, Une méthode adaptative de raffinement local: la correction du flux à l'interface, Comptes rendus de l'Académie des sciences. Série 1, Mathématique 315, pp.739-745, 1992.

M. Anthonissen, Local defect correction techniques: analysis and application to combustion, 2001.
DOI : 10.1007/3-540-26825-1_15

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.6266

M. J. Anthonissen, R. M. Matthe?, J. H. Ten-th?e, and . Boonkkamp, Convergence analysis of the local defect correction method for diffusion equations, Numerische Mathematik, vol.95, issue.3, pp.401-425, 2003.
DOI : 10.1007/s00211-002-0451-8

K. Umminger, L. Dennhardt, S. Schollenberger, and B. Schoen, Integral Test Facility PKL: Experimental PWR Accident Investigation, Science and Technology of Nuclear Installations, vol.79, issue.8, 2012.
DOI : 10.1016/j.nucengdes.2007.10.002

URL : http://doi.org/10.1155/2012/891056

H. Askes and A. Rodríguez-ferran, A combined rh???adaptive scheme based on domain subdivision. Formulation and linear examples, International Journal for Numerical Methods in Engineering, vol.51, issue.3, pp.253-273, 2001.
DOI : 10.1002/nme.142

URL : http://upcommons.upc.edu/bitstream/2117/8259/5/2001-IJNME-AR-blanc.pdf

A. Badillo, Quantitative phase-field modeling for boiling phenomena, Physical Review E, vol.86, issue.4, p.41603, 2012.
DOI : 10.1016/0017-9310(69)90028-3

M. R. Baer and J. W. Nunziato, A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials, International Journal of Multiphase Flow, vol.12, issue.6, pp.861-889, 1986.
DOI : 10.1016/0301-9322(86)90033-9

S. Balay, W. D. Gropp, L. C. Mcinnes, and B. F. Smith, Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries, pp.163-202, 1997.
DOI : 10.1007/978-1-4612-1986-6_8

S. Balay, PETSc Users Manual ANL-95/11 ? Revision 3
DOI : 10.2172/1255238

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.457.6582

S. Balay, PETSc Web page, 2014.

L. Barbié, I. Ramière, and F. Lebon, Strategies involving the local defect correction multi-level refinement method for solving three-dimensional linear elastic problems, Computers & Structures, vol.130, pp.73-90, 2014.
DOI : 10.1016/j.compstruc.2013.10.008

F. B. Barros, S. P. Proenca, and C. S. De-barcellos, Generalized finite element method in structural nonlinear analysis?a p-adaptive strategy, Computational Mechanics, vol.332, issue.63, pp.95-107, 2004.

M. J. Berger and P. Collela, Local adaptive mesh refinement for shock hydrodynamics, Journal of Computational Physics, vol.82, issue.1, pp.64-84, 1989.
DOI : 10.1016/0021-9991(89)90035-1

M. J. Berger and J. Oliger, Adpative mesh refinement for hyperbolic partial equations, Journal of Computational Physics, vol.533, pp.484-512, 1984.
DOI : 10.1016/0021-9991(84)90073-1

URL : http://www.dtic.mil/get-tr-doc/pdf?AD=ADA121307

M. J. Berger and I. Rigoutsos, An algorithm for point clustering and grid generation, IEEE Transactions on Systems, Man, and Cybernetics, vol.21, issue.5, pp.1278-1286, 1991.
DOI : 10.1109/21.120081

M. Bernard, S. Dellacherie, G. Faccanoni, B. Grec, and O. Lafitte, Study of a low Mach nuclear core model for single-phase flows, ESAIM: Proceedings, vol.38, pp.118-134, 2012.
DOI : 10.1051/proc/201238007

URL : https://hal.archives-ouvertes.fr/hal-00662978

A. Bernard-champmartin and F. D. Vuyst, A low diffusive Lagrange-remap scheme for the simulation of violent air???water free-surface flows, Journal of Computational Physics, vol.274, pp.19-49, 2014.
DOI : 10.1016/j.jcp.2014.05.032

URL : https://hal.archives-ouvertes.fr/hal-00798783

R. A. Berry, J. W. Peterson, H. Zhang, R. C. Martineau, H. Zhao et al., Relap-7 theory manual, p.28
DOI : 10.2172/1262488

G. C. Bessette, E. B. Becker, L. M. Taylor, and D. L. Littlefield, Modeling of impact problems using an h-adaptive, explicit Lagrangian finite element method in three dimensions, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.13-14, pp.1649-1679, 2003.
DOI : 10.1016/S0045-7825(02)00657-6

D. Bestion, 4: Modèles à l'échelle 3D locale pour les écoulements bouillants et la prédiction du DNB " . INSTN course " Thermohydraulique diphasique dans les réacteurs, 2014.

D. Bestion, The physical closure laws in the CATHARE code, Nuclear Engineering and Design, vol.124, issue.3, pp.229-245, 1990.
DOI : 10.1016/0029-5493(90)90294-8

U. Bieder, V. Barthel, F. Ducros, P. Quéméré, and S. Vandroux, CFD calculations of wire wrapped fuel bundles: modeling and validation strategies, pp.4-7, 2010.

G. Bois, Heat and mass transfers at liquid/vapor interfaces with phase-change: proposal for a large-scale modeling of interfaces, pp.52-55, 2011.
URL : https://hal.archives-ouvertes.fr/tel-00627370

O. Botella and R. Peyret, Benchmark spectral results on the liddriven cavity flow, In: Computers & Fluids, vol.274, issue.151, pp.421-433, 1998.
DOI : 10.1016/s0045-7930(98)00002-4

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.454.2675

F. Boyer, C. Lapuerta, S. Minjeaud, and B. Piar, A local adaptive refinement method with multigrid preconditionning illustrated by multiphase flows simulations., ESAIM: Proceedings, vol.27, pp.15-53, 2009.
DOI : 10.1051/proc/2009018

URL : https://hal.archives-ouvertes.fr/hal-00307186

J. U. Brackbill, D. B. 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

M. J. Burwell, G. Lerchl, J. Miro, V. Teschendorff, and K. Wolfert, The thermalhydraulic code ATHLET for analysis of PWR and BWR systems " . In: Fourth international topical meeting on nuclear reactor thermal-hydraulics (NURETH-4), Proceedings, vol.2, 1989.

W. Cao, W. Huang, D. Robert, and . Russell, Comparison of two-dimensional r-adaptive finite element methods using various error indicators, Mathematics and Computers in Simulation, vol.56, issue.2, pp.127-143, 2001.
DOI : 10.1016/S0378-4754(01)00285-3

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.7266

A. Chaudhuri and A. Hadjadj, Ashwin Chinnayya and Sandrine Palerm Numerical study of compressible mixing layers using highorder WENO schemes, Journal of Scientific Computing, vol.472, pp.170-197, 2011.

L. David and . Chopp, Some improvements of the fast marching method, In: SIAM Journal on Scientific Computing, vol.231, pp.230-244, 2001.

A. Chorin, A numerical method for solving incompressible viscous flow problems, Journal of Computational Physics, vol.2, issue.1, pp.12-26, 1967.
DOI : 10.1016/0021-9991(67)90037-X

A. Chorin, Numerical solution of the Navier-Stokes equations Mathematics of computation 22, pp.745-762, 1968.

R. Clift, J. R. Grace, and M. E. Weber, Bubbles, Drops, and Particles. 111 Fifth Avenue, 1978.

F. Coquel, J. Hérard, K. Saleh, and N. Seguin, A robust entropy???satisfying finite volume scheme for the isentropic Baer???Nunziato model, ESAIM: Mathematical Modelling and Numerical Analysis, vol.48, issue.1, pp.165-206, 2014.
DOI : 10.1051/m2an/2013101

URL : https://hal.archives-ouvertes.fr/hal-00795568

T. Cramer, D. Schmidl, M. Klemm, . Dieter, and . Mey, OpenMP Programming on Intel® Xeon Phi? Coprocessors: An Early Performance Comparison, 2012.

F. Dabbene, J. Brinster, D. Abdo, E. Porcheron, P. Lemaitre et al., Experimental Activities On Stratification And Mixing of a Gas Mixture under the Conditions of a Severe Accident with Intervention Of Mitigating Measures Performed in the ERCOSAM-SAMARA Projects, ICAPP 2015. ICAPP, 2015.

S. Dellacherie, K. Herilus, J. Jung, A. Mekkas, and A. Talpaert, Simulation numérique de systèmes de loi de conservation dans un environnement SALOME/C++ via la bibliothèque CDMATH, p.186

S. Dellacherie, Étude et discrétisation de modèles cinétiques et de modèles fluides à bas nombre de Mach " . Mémoire en vue d'obtenir l'Habilitation à Diriger des Recherches en Mathématiques, 2011.

S. Dellacherie, Numerical resolution of a potential diphasic low Mach number system, SMAI EDP Sciences, pp.487-514, 2007.
DOI : 10.1016/j.jcp.2006.09.009

S. Dellacherie, On a diphasic low mach number system, ESAIM: Mathematical Modelling and Numerical Analysis, vol.39, issue.3, pp.2-223, 2005.
DOI : 10.1051/m2an:2005020

S. Dellacherie, On a low Mach nuclear core model, ESAIM: Proceedings, vol.35, issue.129, pp.79-106, 2012.
DOI : 10.1051/proc/201235005

S. Dellacherie, G. Faccanoni, and B. Grec, Ethem Nayir and Yohan Penel 2D numerical simulation of a low Mach nuclear core model with stiffened gas using Freefem++, ESAIM: Proceedings and Surveys 45, pp.138-147, 2014.

S. Dellacherie and O. Lafitte, Existence et unicité d'une solution classique à un modèle abstrait de vibration de bulles de type hyperbolique-elliptique, p.51, 2005.

B. Després and F. Lagoutière, Contact Discontinuity Capturing Schemes for Linear Advection and Compressible Gas Dynamics, Journal of Scientific Computing, vol.164, issue.89, pp.479-524, 2002.

B. Després, F. Lagoutière, E. Labourasse, and I. Marmajou, An antidissipative transport scheme on unstructured meshes for multicomponent flows, The International Journal on Finite Volumes, pp.30-65, 2010.

D. Hachmi-ben, Problèmes mécaniques multi-échelles: la méthode Arlequin In: Comptes Rendus de l'Académie des Sciences-Series IIB-Mechanics-Physics-Astronomy 326, pp.899-904, 1998.

S. Delage-santacreu, S. Vincent, and J. Caltagirone, Tracking Fronts in One and Two-phase Incompressible Flows Using an Adaptive Mesh Refinement Approach, Journal of Scientific Computing, vol.33, issue.2, pp.221-237, 2009.
DOI : 10.1007/s10915-009-9294-0

URL : https://hal.archives-ouvertes.fr/hal-00395782

J. Dolbow, Level Sets I " . CEA-EDF-INRIA Numerical Analysis Summer School, p.55, 2014.

J. Dolbow, Level Sets II " . CEA-EDF-INRIA Numerical Analysis Summer School, 2014.

K. Domelevo and P. Omnes, A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids, ESAIM: Mathematical Modelling and Numerical Analysis, vol.39, issue.6, pp.6-1203, 2005.
DOI : 10.1051/m2an:2005047

J. Donea, A. Huerta, J. Ponthot, and A. Rodriguez-ferran, Encyclopedia of Computational Mechanics

&. Wiley and . Sons, 14: Arbitrary Lagrangian-Eulerian Methods (cit, p.62, 2004.

E. , C. , O. C. Salome, and . Platform, Accessed: 2015-10-14, 2005.

D. Enright, R. Fedkiw, J. Ferziger, and I. Mitchell, A Hybrid Particle Level Set Method for Improved Interface Capturing, Journal of Computational Physics, vol.183, issue.1, pp.83-116, 2002.
DOI : 10.1006/jcph.2002.7166

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.15.910

G. Faccanoni, Étude d'un modèle fin de changement de phase liquide-vapeur. Contribution à l'étude de la crise d'ébullition " . Thèse en cotutelle entre l'École Polytechnique et l'Università di Trento, Italie, Thèse. École Polytechnique X, p.43, 2008.

J. J. Peter, A. A. Ferket, and . Reusken, A finite difference discretization method for elliptic problems on composite grids, Computing 56, pp.343-369, 1996.

J. J. Peter, A. A. Ferket, and . Reusken, Further analysis of the Local Defect Correction method, Computing 56, pp.117-139, 1996.

A. Fikl, Adaptive Mesh Refinement with p4est. Tech. rep. Digiteo Labs -bât. 565 -PC 190, CEA Saclay, 91191 Gif-sur-Yvette cedex: Sup Galilée, 2014.

J. Fish, The s-version of the finite element method, Computers & Structures, vol.43, issue.3, pp.539-547, 1992.
DOI : 10.1016/0045-7949(92)90287-A

A. Forestier, Cours sur les écoulements diphasiques, Troisième partie, p.2013

C. Fribourg, Réacteurs nucléaires de propulsion navale, 2002.

M. Billaud, F. , and S. Kokh, An anti-diffusive Lagrangeremap scheme for multi-material compressible flows with an arbitrary number of components, In: ESAIM: Proceedings, vol.35, pp.203-209, 2012.

J. Gerbeau, C. L. Bris, and T. Lelièvre, Mathematical methods for the Magnetohydrodynamics of liquid metals Chap. 5: Numerical simulation of two-fluid problems (cit, p.62, 2006.

]. U. Ghia, K. N. Ghia, and C. T. Shin, High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, Journal of Computational Physics, vol.48, issue.3, pp.387-411, 1982.
DOI : 10.1016/0021-9991(82)90058-4

S. Ghosh and S. K. Manna, R-adapted arbitrary lagrangian-eulerian finite-element method in metal-forming simulation, Journal of materials engineering and performance 2, pp.271-282, 1993.
DOI : 10.1007/BF02660296

H. Gittel, M. Günther, and G. Ströhmer, Remarks on a nonlinear transport problem, Journal of Differential Equations, vol.256, issue.3, pp.957-988, 2014.
DOI : 10.1016/j.jde.2013.10.002

W. Hackbusch, Local Defect Correction Method and Domain Decomposition Techniques, pp.89-113, 1984.
DOI : 10.1007/978-3-7091-7023-6_6

W. Hackbusch, Integral equations: theory and numerical treatment, Birkhäuser, vol.120, p.2012
DOI : 10.1007/978-3-0348-9215-5

M. Bernard, S. Dellacherie, and G. Faccanoni, Study of a low Mach nuclear core model for two-phase flows with phase transition I: stiffened gas law, ESAIM: Mathematical Modelling and Numerical Analysis, vol.48, issue.6, pp.1639-1679, 2014.
DOI : 10.1051/m2an/2014015

URL : https://hal.archives-ouvertes.fr/hal-00747616

H. Francis, J. E. Harlow, and . Welch, Numerical calculation of timedependent viscous incompressible flow of fluid with free surface, Physics of fluids, vol.812, p.2182, 1965.

A. Harten, B. Engquist, S. Osher, and S. 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

A. Harten and S. Osher, Uniformly High-Order Accurate Nonoscillatory Schemes. I, SIAM Journal on Numerical Analysis, vol.24, issue.2, pp.279-309, 1987.
DOI : 10.1137/0724022

URL : http://www.dtic.mil/get-tr-doc/pdf?AD=ADA158177

P. Helluy and N. Seguin, Relaxation models of phase transition flows, ESAIM: Mathematical Modelling and Numerical Analysis, vol.40, issue.2, pp.331-352, 2006.
DOI : 10.1051/m2an:2006015

URL : https://hal.archives-ouvertes.fr/hal-00139607

J. Hérard and J. Jung, An interface condition to compute compressible flows in variable cross section ducts, Comptes Rendus Mathematique, vol.354, issue.3, pp.323-327, 2016.
DOI : 10.1016/j.crma.2015.10.026

. Ikosaeder, Schematic description of PLIC reconstruction url: https://commons.wikimedia.org/wiki/File:Vof_scheme_ with_plic.png (cit, p.56, 2014.

D. Jamet and B. Mathieu, Simulation numérique directe des écoulements diphasiques " . INSTN course " Thermohydraulique diphasique dans les réacteurs nucléaires, 2014.

J. Jouhaud, Méthode d'adaptation de maillages structurés par enrichissement, application à la résolution des équations d'Euler et de Navier-Stokes, 1997.

D. Juric and G. Tryggvason, A Front-Tracking Method for Dendritic Solidification, Journal of Computational Physics, vol.123, issue.1, pp.127-148, 1996.
DOI : 10.1006/jcph.1996.0011

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.17.8419

R. E. Kelly, The stability of an unsteady Kelvin???Helmholtz flow, Journal of Fluid Mechanics, vol.165, issue.03, pp.3-547, 1965.
DOI : 10.1016/0021-8928(63)90062-5

K. Khadra, . Ph, J. P. Angot, P. Caltagirone, and . Morel, Concept de zoom adaptatif en architecture multigrille locale; étude comparative des méthodes LDC, FAC et FIC " . In: Modélisation mathématique et analyse numérique 30, pp.39-82, 1996.
DOI : 10.1051/m2an/1996300100391

K. Khadra, P. Angot, and J. Caltagirone, A comparison of locally adaptive multigrid methods: LDC, FAC AND FIC, 1993.

S. Kokh, Aspects numériques et théoriques de la modélisation des écoulements diphasiques compressibles par des méthodes de capture d'interface, 2001.

S. Kokh and G. Allaire, Numerical simulation of 2-D twophase flows with interface, pp.513-518, 2001.

S. Kokh and F. Lagoutière, An anti-diffusive numerical scheme for the simulation of interfaces between compressible fluids by means of a five-equation model, Journal of Computational Physics, vol.229, issue.8, pp.2773-2809, 2010.
DOI : 10.1016/j.jcp.2009.12.003

T. Kozlowski, A. Wysocki, I. Gajev, Y. Xu, T. Downar et al., Analysis of the OECD/NRC Oskarshamn-2 BWR stability benchmark, Annals of Nuclear Energy, vol.67, pp.4-12, 2014.
DOI : 10.1016/j.anucene.2013.09.028

A. Kudryavtsev and A. Hadjadj, Visualisation graphique en mécanique des fluides numérique In: CR de 9ème Colloque Francophone de Visualisation et de Traitement d'Images en Mécanique des Fluides ? FLUVISU, pp.55-62, 2001.

F. Lagoutière, Modélisation mathématique et résolution numérique de problèmes de fluides compressibles à plusieurs constituants " . Organisme d'accueil : Commissariat à l'Énergie Atomique, centre de Bruyères-le-Châtel, pp.55-90, 2000.

X. Liu, S. Osher, and T. Chan, Weigthed essentially non-oscillatory schemes, In: Journal of Computational Physics, vol.1151, issue.87, pp.200-212, 1994.
DOI : 10.1006/jcph.1994.1187

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

O. E. Livne, Clustering on Single Refinement Level: Berger-Rigoustos Algorithm. Tech. rep. UUSCI-2006-001. Scientific Computing and Imaging Institute, p.69, 2006.

O. E. Livne, Clustering Patches for Multi-Level Refined Grids: a Hierarchical Approach. Tech. rep. UUSCI-2006-004. Scientific Computing and Imaging Institute, 2006.

O. E. Livne, Efficient Update of Persistent Patches in the Berger Rigoutsous Algorithm. Tech. rep. UUSCI-2006-003. Scientific Computing and Imaging Institute, 2006.

O. E. Livne, Minimum and Maximum Patch Size Clustering on a Single Refinement Level. Tech. rep. UUSCI-2006-002. Scientific Computing and Imaging Institute, p.184, 2006.

A. Majda, Equations for low Mach number combustion. Tech. rep. 112, 1982.

F. Stephen and . Mccormick, Multilevel adaptive methods for partial differential equations, In: SIAM, vol.6, issue.101, p.74, 1989.

S. Mccormick, Fast Adaptive Composite Grid (FAC) Methods: Theory for the Variational Case, pp.115-121, 1984.
DOI : 10.1007/978-3-7091-7023-6_7

S. Mccormick and J. Thomas, The fast adaptive composite grid (FAC) method for elliptic equations, Mathematics of Computation, vol.46, issue.174, pp.439-456, 1986.
DOI : 10.1090/S0025-5718-1986-0829618-X

A. Mekkas, C. , and O. Ma, Résolution numérique d'un modèle de vibration de bulle abstraite, 2008.

V. Menier, 3D Parallel Anisotropic Unsteady Mesh Adaptation for the High-Fidelity Prediction of Bubble Motion, ESAIM: Proceedings and Surveys 50, pp.169-188, 2015.
DOI : 10.1051/proc/201550009

S. Minjeaud, F. Boyer, C. Lapuerta, and B. Piar, Local refinement and multigrid preconditioning for a ternary Cahn- Hilliard/Navier-Stokes model. Poster at the CANUM 2014 Congress in Carry-Le-Rouet, p.67, 2014.

E. Gordon and . Moore, Cramming more components onto integrated circuits, Proceedings of the IEEE, vol.86, issue.1, pp.82-85, 1998.

F. William, P. Noh, and . Woodward, SLIC (Simple Line Interface Calculation), Proceedings of the Fifth International Conference on Numerical Methods in Fluid Dynamics, pp.330-340, 1976.

P. Obry, J. L. Cheissoux, M. Grandotto, J. P. Gaillard, E. De-langre et al., An advanced steam generator design 3D code, Thermal Hydraulics of Advanced Heat Exchangers, Proceedings of the 1990 ASME Winter Annual Meeting, pp.15-21, 1990.

S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.12-49, 1988.
DOI : 10.1016/0021-9991(88)90002-2

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.413.5254

M. E. Pasquini, Experimental study of vapor bubble dynamics, 2015.
URL : https://hal.archives-ouvertes.fr/tel-01208170

M. E. Pasquini, B. Cariteau, C. Josserand, and P. Salvatore, Experimental study on subcooled nucleate boiling from a single artificial cavity, International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, p.2014

Y. Penel, Étude théorique et numérique de la déformation d'une interface séparant deux fluides non-miscibles à bas nombre de Mach " . Organisme d'accueil : Commissariat à l'Énergie Atomique, centre de Saclay, Thèse. Université Paris 13, 2010.

Y. Penel, Well-posedness of a low Mach number system, Comptes Rendus Mathematique, vol.350, issue.1-2, pp.51-55, 2012.
DOI : 10.1016/j.crma.2011.12.009

Y. Penel, S. Dellacherie, and O. Lafitte, Theoretical Study of an Abstract Bubble Vibration Model, Zeitschrift f??r Analysis und ihre Anwendungen, vol.32, issue.1, pp.19-36, 2013.
DOI : 10.4171/ZAA/1472

URL : https://hal.archives-ouvertes.fr/hal-00655568

Y. Penel, A. Mekkas, S. Dellacherie, J. Ryan, and M. Borrel, Application of an AMR Strategy to an Abstract Bubble Vibration Model, 19th AIAA Computational Fluid Dynamics, 2009.
DOI : 10.2514/6.2009-3891

M. Pérache, Contribution à l'élaboration d'environnements de programmation dédiés au calcul scientifique hautes performances, 2006.

G. Prigent, Modélisation et simulation numérique d'écoulements diphasiques pour la microfluidique, 2013.

J. William, D. B. Rider, and . Kothe, Reconstructing volume tracking, Journal of Computational Physics, vol.141, issue.84, pp.112-152, 1998.

L. Philip and . Roe, Some contributions to the modelling of discontinuous flows In: Large-scale computations in fluid mechanics, pp.163-193, 1985.

Y. Sato and B. Ni?eno, A conservative local interface sharpening scheme for the constrained interpolation profile method, International Journal for Numerical Methods in Fluids, vol.65, issue.4, pp.441-467, 2012.
DOI : 10.1002/fld.2695

P. Thomas, A. H. Scholcz, H. Van-zu?len, and . B?l, A multi-model incremental adaptive strategy to accelerate partitioned fluid-structure algorithms using space-mapping, Coupled Problems 2011: Proceedings of the 4th International Conference on Computational Methods for Coupled Problems in Science and Engineering, pp.20-22, 2011.

H. David and . Sharp, An overview of Rayleigh-Taylor instability, Physica D: Non-linear Phenomena, vol.121, pp.3-18, 1984.

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

URL : http://www.dtic.mil/get-tr-doc/pdf?AD=ADA189392

C. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes, II, Journal of Computational Physics, vol.83, issue.1, pp.32-78, 1989.
DOI : 10.1016/0021-9991(89)90222-2

M. Sussman, K. M. Smith, M. Hussaini, R. Ohta, and . Zhi-wei, A sharp interface method for incompressible two-phase flows, Journal of Computational Physics, vol.221, issue.2, pp.469-505, 2007.
DOI : 10.1016/j.jcp.2006.06.020

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.413.7193

A. Talpaert, Analysis of interfacial forces on the physics of twophase flow and hyperbolicity of the two-fluid model, 2013.

A. Talpaert and G. Allaire, Stéphane Dellacherie and Anouar Mekkas Direct Numerical Simulation of bubbles using Adaptive Mesh Refinement on parallel architecture. Poster at the CEA-GAMNI seminar at IHP in Paris, 2015.

A. Talpaert, S. Dellacherie, and A. Mekkas, Analysis of the efficiency and relevance of patch creation algorithms in the case of AMR of thin flagged areas. Poster at the CANUM 2014 Congress in Carry-Le-Rouet, 2014.

R. Temam, Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires (I) . In: Archive for Rational Mechanics and Analysis 32, pp.135-153, 1969.

R. Temam, Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires (II) . In: Archive for Rational Mechanics and Analysis 33, pp.377-385, 1969.

. S. Abhijat and . Tilak, A Pressure Based Unstructured Grid Method for Fluid Flow and Heat Transfer, Eleventh annual conference of the CFD Society of Canada (CFD 2003). Proceedings, 2003.

I. Tkatschenko, E. Studer, J. Magnaud, L. Blumenfeld, H. Simon et al., Status of the MISTRA programme for the validation of containment thermal-hydraulic codes, 2005.

E. Neil, . Todreas, S. Mujid, and . Kazimi, Nuclear systems: thermal hydraulic fundamentals, 2012.

F. Eleuterio and . Toro, Riemann solvers and numerical methods for fluid dynamics: a practical introduction, p.90, 2009.

I. Toumi, A. Bergeron, D. Gallo, E. Royer, and D. Caruge, FLICA-4: a three-dimensional two-phase flow computer code with advanced numerical methods for nuclear applications, Nuclear Engineering and Design, vol.200, issue.1-2, pp.139-155, 2000.
DOI : 10.1016/S0029-5493(99)00332-5

G. Tryggvason, A. Esmaeeli, J. Lu, and S. Biswas, Direct numerical simulations of gas/liquid multiphase flows, Fluid dynamics research, pp.660-681, 2006.
DOI : 10.1016/j.fluiddyn.2005.08.006

G. Tryggvason, R. Scardovelli, and S. Zaleski, Direct numerical simulations of gas?liquid multiphase flows, 2011.

S. Ozen, U. , and G. Tryggvason, A front-tracking method for viscous, incompressible, multi-fluid flows, Journal of computational physics, vol.1001, pp.25-37, 1992.

J. Valenciano and R. G. Owens, An h???p adaptive spectral element method for Stokes flow, Applied Numerical Mathematics, vol.33, issue.1-4, pp.365-371, 2000.
DOI : 10.1016/S0168-9274(99)00103-8

M. Viellieber and A. G. Class, Sub channel scale resolution in homogenization codes by the Coarse-Grid-CFD, THINS 2014 International Workshop. THINS, 2014.

J. Vila, High-order schemes and entropy condition for nonlinear hyperbolic systems of conservation laws, Mathematics of computation 50, pp.53-73, 1988.
DOI : 10.1090/S0025-5718-1988-0917818-1

C. Workgroup, CDMATH source repository url: https://github.com/PROJECT-CDMATH/CDMATH (cit, pp.33-186, 2016.

S. Zaleski, J. Li, and S. Succi, Two-Dimensional Navier-Stokes Simulation of Deformation and Breakup of Liquid Patches, Physical review letters 75, p.244, 1995.
DOI : 10.1103/PhysRevLett.75.244

D. Zuzio and J. L. Estivalezes, An efficient block parallel AMR method for two phase interfacial flow simulations, Computers & Fluids, vol.44, issue.1, pp.339-357, 2011.
DOI : 10.1016/j.compfluid.2011.01.035