D. Liuzzi, Two-Phase Cavitation Modelling, 2012.

M. Frobenius, Numerische Simulation kavitierenden Stromungen in hydraulischen Stromungsmachinen, 2003.

I. Senoçak, Computational Methodology for the Simulation of Turbulent Cavitating Flows, 2002.

G. D. Ciocan and M. S. Iliescu, Vortex rope investigation by 3d-piv method, Proc. 2nd Int. Meeting of Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, 2007.

C. E. Brennen, Cavitation and Bubble Dynamics, 1995.
DOI : 10.1017/CBO9781107338760
URL : http://authors.library.caltech.edu/25017/1/cavbubdynam.pdf

J. Sauer, Instationar kavitierende StromungenEin neues Modell, basierend auf Front Capturing (VoF) und Blasendynamik, 2000.

Y. Chen and S. D. Heister, A Numerical Treatment for Attached Cavitation, Journal of Fluids Engineering, vol.116, issue.3, p.613618, 1994.
DOI : 10.1115/1.2910321

P. Dupont and F. Avellan, Numerical computation of a leading edge cavity, Proceedings of the Cavitation 91 Symposium. ASME-JSME, 1991.

V. Schütte, Modellierung und berechnung von blasenströmungen und kavitation in laufradkanälen von kreiselpumpen, Pumpentagung Karlsruhe '92, 1992.

R. Samulyak, Y. Prykarpatskyy, T. Lu, J. Glimm, Z. Xu et al., Comparison of Heterogeneous and Homogenized Numerical Models of Cavitation, International Journal for Multiscale Computational Engineering, vol.4, issue.3, p.377389, 2006.
DOI : 10.1615/IntJMultCompEng.v4.i3.70

T. Lu, R. Samulyak, and J. Glimm, Direct numerical simulation of bubbly ows and application to cavitation mitigation, Journal of Fluids Engineering, vol.129, p.595604, 2006.

A. Alajbegovic, G. Meister, D. Greif, and B. Basara, Three phase cavitating ows in high-pressure swirl injectors, Experimental Thermal and Fluid Science, vol.26, p.677681, 2002.
DOI : 10.1016/s0894-1777(02)00179-6

A. Kubota, H. Kato, and H. Yamaguchi, A new modelling of cavitating ows: a numerical study of unsteady cavitation on a hydrofoil section, Journal of Fluid Mechanics, vol.240, p.5996, 1992.

Y. Chen and S. D. Heister, Two-phase modeling of cavitated ows, Computers and Fluids, vol.24, issue.7, p.799809, 1995.

Y. Delannoy and J. L. Kueny, Cavity ow predictions based on the euler equation, ASME Cavitation and Multiphase Flow Forum, 1990.

O. Coutier-delgosha, S. Frikha, and J. A. , Inuence of the cavitation model on the simulation of cloud cavitation on 2d foil section, International Journal of Rotating Machinery, 2008.

J. L. Reboud, B. Stutz, and O. Coutier-delgosha, Two-phase ow structure of cavitation: Experiment and modeling of unsteady eects, Third International Symposium on Cavitation, 1998.

O. Coutier-delgosha, R. Fortes-patella, J. L. Reboud, N. Hakimi, and C. Hirsch, Numerical simulation of cavitating row in 2d and 3d inducer geometries, International Journal for Numerical Methods in Fluids, vol.48, p.135167, 2005.

D. P. Schmidt, C. J. Rutland, and M. L. Corradini, A numerical study of cavitating ow through various nozzle shapes, SAE Technical Paper. SAE International, 1997.

D. R. Van-der-heul, C. Vuik, and P. Wesseling, Ecient computation of ow with cavitation by compressible pressure correction, European Congress on Computational Methods in Applied Sciences and Engineering, 2000.

Y. Ventikos and G. Tzabiras, A numerical method for the simulation of steady and unsteady cavitating ows, Computers and Fluids, vol.29, p.6388, 2000.

E. Rapposelli and L. Agostino, A barotropic cavitation model with thermodynamic eects, Fifth International Symposium on Cavitation (cav2003), 2003.

E. Goncalvès and R. F. Patella, Numerical simulation of cavitating ows with homogeneous models. Computers and Fluids, p.16821696, 2009.

B. Charrière, J. Decaix, and E. Goncalvès, A comparative study of cavitation models in a venturi ow, European Journal of Mechanics B/Fluids, vol.49, p.287297, 2015.

C. L. Merkle, J. Feng, and P. E. Buelow, Computational modeling of dynamics of sheet cavitation, Third International Symposium on Cavitation, 1998.

N. Singhal, A. K. Vaidya, and A. D. Leonard, Multi-dimensional simulation of cavitating ows using a pdf model for phase change, ASME FED Meeting, 1997.

S. Gibelinga, T. R. Venkateswaranb, and . Govindan, A preconditioned navier-stokes method for two-phase ows with application to cavitation prediction, Computers and Fluids, vol.29, pp.849-875, 2000.

Y. Utturkar, Computational Modeling of Thermodynamic Eects in Cryogenic Cavitation, 2005.

A. Hosangadi, V. Ahuja, and R. Ungewitter, Simulations of Cavitating Cryogenic Inducers, 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 2004.
DOI : 10.2514/6.2004-4023

D. Dauby, P. Queutey, A. Leroyer, and M. Visonneau, Computation of 2d cavitating ows and tip vortex ows with an unstructured rans solver, 11èmes journé es de l'hydrodynamique Brest, 2007.

A. K. Singhal, L. Huiying, M. A. Mahesh, and Y. Jiang, Mathematical basis and validation of the full cavitation mode, Proceedings of ASME FEDSM'01. ASME, 2001.

M. Athavale and A. Singhal, Numerical analysis of cavitating ows in rocket turbopump elements, 37th Joint Propulsion Conference and Exhibit. Salt Lake City, 2001.

P. J. Zwart, A. G. Gerber, and T. Belamri, A two-phase ow model for predicting cavitation dynamics, International Conference on Multiphase Flow, 2004.

C. F. Delale, G. H. Schnerr, and J. Sauer, Quasi-one-dimensional steady-state cavitating nozzle ows, Journal of Fluid Mechanics, vol.427, p.167204, 2001.

T. Xing, Z. Li, and S. H. , Numerical simulation of vortex cavitation in a threedimensional submerged transitional jet, Journal of Fluids Engineering, vol.127, p.714725, 2005.

J. Zhu, Y. Chen, D. Zhao, and X. Zhang, Extension of the Schnerr???Sauer model for cryogenic cavitation, European Journal of Mechanics - B/Fluids, vol.52, p.110, 2015.
DOI : 10.1016/j.euromechflu.2015.01.008

A. šnidar£i£, R. Mettin, and M. Dular, Modeling cavitation in a rapidly changing pressure eld -application to a small ultrasonic horn, Ultrasonics Sonochemistry, vol.22, p.482492, 2015.

B. Stutz and J. L. Reboud, Two-phase ow structure of sheet cavitation, Physics of Fluids, vol.9, p.36783686, 1997.
DOI : 10.1063/1.869505

B. Stutz and J. L. Reboud, Experiments on unsteady cavitation, Experiments in Fluids, vol.22, issue.3, 1997.
DOI : 10.1007/s003480050037

B. Stutz and J. L. Reboud, Measurements within unsteady cavitation, Experiments in Fluids, vol.29, issue.6, p.545552, 2000.
DOI : 10.1007/s003480000122

Y. Kuhn-de-chizelle, S. L. Ceccio, and C. E. Brennen, Observations and scaling of traveling bubble cavitation, Journal of Fluid Mechanics, vol.293, p.96126, 1995.

C. Y. Li and S. L. Ceccio, Interaction of single travelling bubbles with the boundary layer and attached cavitation, Journal of Fluid Mechanics, vol.114, issue.-1, p.329353, 1996.
DOI : 10.1017/S0022112077002456

S. K. Wang, S. J. Lee, O. C. Jones, and R. T. Lahey, 3-d turbulence structure and phase distribution measurements in bubbly two-phase ow, International Journal of Multiphase Flow, vol.13, p.327343, 1987.
DOI : 10.1016/0301-9322(87)90052-8

M. Lance and J. Bataille, Turbulence in the liquid phase of a uniform bubbly air-water ow, Journal of Fluid Mechanics, vol.222, p.95118, 1991.

J. Billard, P. Galivel, and D. H. Fruman, Eect of preturbulence on the cavitating bubble inception, Proceedings of ASME FED, 1993.

T. Baur and J. K. Ngeter, Measurements in the shear-layer behind a surface-mounted obstacle for the determination of coherent structures, Ninth Int. Symp. on Applications of Laser Techniques to Fluid Mechanics, 1998.

S. Gopalan, J. Katz, and O. Knio, The ow structure in the near eld of jets and its eects on cavitation inception, Journal of Fluid Mechanics, vol.398, p.143, 1999.

V. Aeschlimann, S. Barre, and H. Djeridi, Unsteady cavitation analysis using phase averaging and conditional approaches in a 2d venturi ow, Open Journal of Fluid Dynamics, vol.3, p.171183, 2013.

R. T. Knapp, Recent investigations of the mechanics of cavitation and cavitation damage, Transactions ASME, vol.77, p.10451054, 1955.

F. Joussellin, Y. Delannoy, E. Sauvage-boutar, and B. Goirand, Experimental investigations on unsteady attached cavities, Proceedings of ASME FED, 1991.

Q. Le, J. P. Franc, and J. M. Michel, Partial Cavities: Global Behavior and Mean Pressure Distribution, Journal of Fluids Engineering, vol.115, issue.2, p.243248, 1993.
DOI : 10.1115/1.2910131
URL : https://hal.archives-ouvertes.fr/hal-01133776

Y. Kawanami, H. Kato, M. Tanimura, and Y. Tagaya, Mechanism and Control of Cloud Cavitation, Journal of Fluids Engineering, vol.119, issue.4, p.788794, 1997.
DOI : 10.1115/1.2819499

M. Hofmann, H. Lohrberg, G. Ludwig, B. Stoel, J. L. Reboud et al., Numerical and experimental investigations on the self-oscillating behaviour of cloud cavitation -part i: Visualisation, Proceedings of ASME FEDSM, 1999.

A. Kubota, H. Kato, H. Yamaguchi, and M. Maeda, Unsteady Structure Measurement of Cloud Cavitation on a Foil Section Using Conditional Sampling Technique, Journal of Fluids Engineering, vol.111, issue.2, p.204210, 1989.
DOI : 10.1115/1.3243624

S. Gopalan and J. Katz, Flow structure and modeling issues in the closure region of attached cavitation, Physics of Fluids, vol.23, issue.11, 2000.
DOI : 10.1017/S0022112094002296

M. Callenaere, J. P. Franc, J. M. Michel, and M. Riondet, The cavitation instability induced by the development of a re-entrant jet, Journal of Fluid Mechanics, vol.444, p.223256, 2001.
DOI : 10.1017/S0022112001005420
URL : https://hal.archives-ouvertes.fr/hal-01134240

V. Aeschlimann, S. Barre, and H. Djeridi, Velocity eld analysis in an experimental cavitating mixing layer, Physics of Fluids, vol.23, p.280, 2011.
DOI : 10.1063/1.3592327
URL : https://hal.archives-ouvertes.fr/hal-00693944/document

V. Aeschlimann, S. Barre, and S. Legoupil, X-ray attenuation measurements in a cavitating mixing layer for instantaneous twodimensional void ratio determination, Physics of Fluids, vol.23, 2011.

O. Coutier-delgosha, M. Hocevar, I. Khlifa, and S. Fuzier, Velocity measurements in cavitating ows by fast x-ray, ISROMAC-14, 2012.

I. Khlifa, S. Fuzier, O. Roussette, A. Vabre, M. Ho£evar et al., Fast x-ray imaging of cavitating ows, Journal of Fluid Mechanics, 2017.

O. Coutier-delgosha, R. Fortes-patella, and J. L. Reboud, Evaluation of the turbulence model inuence on the numerical simulations of unsteady cavitation, Journal of Fluids Engineering, vol.125, p.3845, 2003.

M. Morgut, E. Nobile, and I. Bilu², Comparison of mass transfer models for the numerical prediction of sheet cavitation around a hydrofoil, International Journal of Multiphase Flow, vol.37, issue.6, p.620626, 2011.
DOI : 10.1016/j.ijmultiphaseflow.2011.03.005

O. Coutier-delgosha, Modélisation des écoulements cavitants : étude des comportements instationnaires et application tridimensionnelle aux turbomachines, 2001.

R. E. Arndt, C. C. Song, M. Kjeldsen, J. He, and A. Keller, Instability of partial cavitation: A numerical/experimental approach, Twenty-Third Symposium on Naval Hydrodynamics, 2001.

N. Dittakavi, A. Chunekar, and S. Frankel, Large Eddy Simulation of Turbulent-Cavitation Interactions in a Venturi Nozzle, Journal of Fluids Engineering, vol.132, issue.12, 2010.
DOI : 10.1115/1.4001971

B. Ji and X. W. Luo, Three-dimensional large eddy simulation and vorticity analysis of unsteady cavitating ow around a twisted hydrofoil, Journal of Hydrodynamics, Ser. B, vol.25, p.510519, 2013.

K. Okabayashi, T. Kajishima, and T. Ohta, Dns and les of cavitating turbulent ow, Sixth International Symposium on Turbulence and Shear Flow Phenomena, 2009.

M. Mattson and K. Mahesh, Simulation of bubble migration in a turbulent boundary layer, Physics of Fluids, vol.23, issue.4, 2011.
DOI : 10.1002/zamm.19480281104

G. H. Oweis, I. E. Van-der-hout, C. Iyer, G. Tryggvason, and S. L. Ceccio, Capture and inception of bubbles near line vortices, Physics of Fluids, vol.100, issue.2, 2005.
DOI : 10.1017/S002211209900525X
URL : https://deepblue.lib.umich.edu/bitstream/2027.42/87832/2/022105_1.pdf

J. H. Seo, Y. J. Moon, and B. R. Shin, Prediction of cavitating ow noise by direct numerical simulation, Journal of Computational Physics, vol.227, p.65116531, 2008.
DOI : 10.1016/j.jcp.2008.03.016

Y. Bac, J. H. Sco, Y. J. Moon, and B. R. Shin, Direct Numerical Simulation of Cavitation Noise for a 3D Circular Cylinder Cross-Flow, p.605610, 2009.
DOI : 10.1007/978-3-642-01273-0_80

U. Piomelli, Large-eddy and direct simulation of turbulent fows, 2001.

M. Marquillie, U. Ehrenstein, and J. P. , Instability of streaks in wall turbulence with adverse pressure gradient, Journal of Fluid Mechanics, vol.21, p.205240, 2011.
DOI : 10.1017/S0022112098001323
URL : https://hal.archives-ouvertes.fr/hal-00611038

J. L. Guermond, P. Minev, and J. Shen, An overview of projection methods for incompressible ows, Comput. Methods Appl. Mech. Engrg, vol.195, p.60116045, 2006.

D. L. Brown, Accurate Projection Methods for the Incompressible Navier???Stokes Equations, Journal of Computational Physics, vol.168, issue.2, p.464499, 2001.
DOI : 10.1006/jcph.2001.6715

J. Kim and P. Moin, Application of a fractional-step method to incompressible Navier-Stokes equations, Journal of Computational Physics, vol.59, issue.2, p.308323, 1985.
DOI : 10.1016/0021-9991(85)90148-2

A. J. Chorin, Numerical solution of the Navier-Stokes equations, Mathematics of Computation, vol.22, issue.104, p.745762, 1968.
DOI : 10.1090/S0025-5718-1968-0242392-2

R. Temam, Sur l'approximation de la solution des equations de navier-stokes par la methode des pas fractionnaires ii, Arch. Ration. Mech. Anal, vol.33, p.377385, 1969.

P. Moin and K. Mahesh, DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research, Annual Review of Fluid Mechanics, vol.30, issue.1, p.539578, 1998.
DOI : 10.1146/annurev.fluid.30.1.539

S. Abide and S. Viazzo, A 2D compact fourth-order projection decomposition method, Journal of Computational Physics, vol.206, issue.1, p.252276, 2005.
DOI : 10.1016/j.jcp.2004.12.005

M. Marquillie and U. Ehrenstein, Numerical simulation of separating boundary-layer ow. Computers and Fluids, p.683693, 2002.
DOI : 10.1016/s0045-7930(01)00074-3

M. Marquillie, J. P. Laval, and R. Dolganov, Direct numerical simulation of a separated channel ow with a smooth prole, Journal of Turbulence, vol.9, p.123, 2008.

M. Marquillie and U. Ehrenstein, On the onset of nonlinear oscillations in a separating boundary-layer ow, Journal of Fluid Mechanics, vol.490, p.169188, 2003.

F. Gallaire, M. Marquillie, and U. Ehrenstein, Three-dimensional transverse instabilities in detached boundary layers, Journal of Fluid Mechanics, vol.571, p.221233, 2007.
DOI : 10.1017/S0022112006002898
URL : https://hal.archives-ouvertes.fr/hal-00211738

L. Kuban, J. P. Laval, W. Elsner, A. Tyliszczak, and M. Marquillie, Les modeling of converging-diverging turbulent channel ow, Journal of Turbulence, vol.13, issue.11, p.119, 2012.

S. K. Lele, Compact nite dierence schemes with spectral-like resolution, Journal of Computational Physics, vol.103, pp.1642-282, 1992.
DOI : 10.1016/0021-9991(92)90324-r

S. Nagarajan, S. Lele, and J. H. Ferziger, A robust high-order compact method for large eddy simulation, Journal of Computational Physics, vol.191, issue.2, p.392419, 2003.
DOI : 10.1016/S0021-9991(03)00322-X

R. K. Shukla and X. Zhong, Derivation of high-order compact nite dierence schemes for non-uniform grid using polynomial interpolation, Journal of Computational Physics, vol.204, p.404429, 2005.

L. Gamet, F. Ducros, F. Nicoud, and T. Poinsot, Compact nite dierence schemes on non-uniform meshes. application to direct numerical simulations of compressible ows, International Journal for Numerical Methods in Fluids, vol.29, p.159191, 1999.
DOI : 10.1002/(sici)1097-0363(19990130)29:2<159::aid-fld781>3.0.co;2-9

J. Jiménez and P. Moin, The minimal ow unit in near-wall turbulence, Journal of Fluid Mechanics, vol.225, p.213240, 1991.

J. C. Del-Álamo, J. Jiménez, P. Zandonade, and R. D. Moser, Scaling of the energy spectra of turbulent channels, Journal of Fluid Mechanics, vol.500, p.135144, 2004.
DOI : 10.1017/S002211200300733X

R. D. Moser, J. Kim, and N. N. Mansour, Direct numerical simulation of turbulent channel ow up to Re ? = 590, Physics of Fluids, vol.11, issue.4, p.943945, 1999.
DOI : 10.1063/1.869966

S. Hoyas and J. Jiménez, Scaling of the velocity uctuations in turbulent channels up to Re ? =, Physics of Fluids, vol.18, 2003.

M. Uhlmann and A. Sekimoto, Marginally turbulent ow in a square duct, Journal of Fluid Mechanics, 2007.

A. Huser, S. Biringen, and F. F. Hatay, Direct simulation of turbulent ow in a square duct: Reynolds-stress budgets, Physics of Fluids, vol.6, issue.9, p.31443152, 1994.

E. Vedy, S. Viazzo, and R. Schiestel, A high-order nite dierence method for incompressible uid turbulence simulations, International Journal for Numerical Methods in Fluids, vol.42, p.11551188, 2003.
DOI : 10.1002/fld.516

M. P. Simens, J. Jiménez, S. Hoyas, and Y. Mizuno, A high-resolution code for turbulent boundary layers, Journal of Computational Physics, vol.228, issue.11, p.42184231, 2009.
DOI : 10.1016/j.jcp.2009.02.031

U. Ehrenstein, M. Marquillie, and C. Eloy, Skin friction on a apping plate in uniform ow, Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, pp.372-2014, 2020.

G. A. Reis, I. V. Tasso, L. F. Souza, and J. A. Cuminato, A compact nite dierences exact projection method for the navier-stokes equations on a staggered grid with fourthorder spatial precision. Computers and Fluids, 1931.

C. A. Fletcher, Computational Techniques for Fluid Dynamics, Volumes I and II, 1991.

Y. Morinishi, T. S. Lund, O. V. Vasilyev, and P. Moin, Fully conservative higher order nite dierence schemes for incompressible ow, Journal of Computational Physics, vol.143, p.90124, 1998.
DOI : 10.1006/jcph.1998.5962
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.32.4898

Y. Morinishi, Skew-symmetric form of convective terms and fully conservative nite difference schemes for variable density low-mach number ows, Journal of Computational Physics, vol.229, p.276300, 2010.

P. Haldenwang, G. Labrosse, S. Abboudi, and M. Deville, Chebyshev 3-D spectral and 2-D pseudospectral solvers for the Helmholtz equation, Journal of Computational Physics, vol.55, issue.1, p.115128, 1984.
DOI : 10.1016/0021-9991(84)90018-4

G. Fontaine, S. Poncet, and E. Serre, Multidomain extension of a pseudospectral algorithm for the direct simulation of wall-conned rotating ows, Lecture Notes in Computational Science and Engineering, vol.95, p.261271, 2014.

G. Danabasoglu, S. Biringen, and C. L. Streett, Application of the Spectral Multidomain Method to the Navier-Stokes Equations, Journal of Computational Physics, vol.113, issue.2, p.155164, 1994.
DOI : 10.1006/jcph.1994.1127

H. Ganesh, Bubbly Shock Propagation as a Cause of Sheet to Cloud Transition of Partial Cavitation and Stationary Cavitation Bubbles Forming on a Delta Wing Vortex, 2015.

A. Gnanaskandan and K. Mahesh, A numerical method to simulate turbulent cavitating ows, International Journal of Multiphase Flow, vol.70, p.2234, 2015.
DOI : 10.1016/j.ijmultiphaseflow.2014.11.009

S. V. Patankar, Numerical heat transfer and uid ow, 1980.

C. Rezki, Simulation 2D et 3D des écoulements cavitants : d éveloppement d'un algorithme original dans Code Saturne et étude de l'inuence de la mod élisation de la turbulence, 2014.

C. D. Dimitropoulos and A. N. Beris, An ecient and robust spectral solver for nonseparable elliptic equations, Journal of Computational Physics, vol.133, p.186191, 1997.
DOI : 10.1006/jcph.1997.5661

R. J. Leveque, Finite dierence methods for dierential equations, 2005.

S. Abdallah, Numerical solutions for the pressure Poisson equation with Neumann boundary conditions using a non-staggered grid, I, Journal of Computational Physics, vol.70, issue.1, p.182192, 1987.
DOI : 10.1016/0021-9991(87)90008-8

M. L. Mansour and A. Hamed, Implicit solution of the lncompressible navier-stokes equations on a non-staggered grid, Journal of Computational Physics, vol.86, pp.147167-284, 1990.

Y. Li and L. Baldacchino, Accuracy and eciency of some higher-order schemes on nonuniform grids for uid ow problems, Twelfth Australian Fluid Mechanics Conference, 1995.

L. Eca and M. Hoekstra, Code vericaton of unsteady ow solvers with the method of the manufactures solutions, Proceedings of the Seventeenth International Oshore and Polar Engineering Conference. ISOPE, 2007.

K. Salari and P. Knupp, Code verication by the method of manufactured solutions, 2000.

L. Eça, G. Vaz, and M. Hoekstra, Code verication of refresco with a statistically periodic manufactured solution, Proceedings of ASME 33rd International Conference on Ocean, Oshore and Arctic Engineering, p.2014, 2014.

D. Pelletier, É. Turgeon, and D. Tremblay, Verication and validation of impinging round jet simulations using an adaptive fem, International Journal for Numerical Methods in Fluids, vol.44, p.737763, 2004.
DOI : 10.1002/fld.672

P. J. Roache, Code verication by the method of manufactured solutions, Journal of Fluids Engineering, vol.124, p.410, 2001.

F. Nicoud and F. Ducros, Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow, Turbulence and Combustion, p.183200, 1999.
URL : https://hal.archives-ouvertes.fr/hal-00910373

U. Ehrenstein and R. Peyret, A chebyshev collocation method for the navier-stokes equations with application to double-diusive convection, International Journal for Numerical Methods in Fluids, vol.9, p.427452, 1989.