G. Ansanay-alex, F. Babik, J. Latché, and D. Vola, An L2-stable approximation of the Navier-Stokes convection operator for low-order non-conforming finite elements, International Journal for Numerical Methods in Fluids, vol.17, issue.1, pp.555-580, 2011.
DOI : 10.1002/fld.2270

F. Archambeau, J. Hérard, and J. Laviéville, Comparative study of pressure-correction and Godunov-type schemes on unsteady compressible cases, Computers & Fluids, vol.38, issue.8, pp.1495-1509, 2009.
DOI : 10.1016/j.compfluid.2008.12.005

URL : https://hal.archives-ouvertes.fr/hal-01265395

R. Berry, Notes on the PCICE method: Simplification, generalization, and compressibility properties, Journal of Computational Physics, vol.215, issue.1, pp.6-11, 2006.
DOI : 10.1016/j.jcp.2005.11.008

H. Bijl and P. Wesseling, A Unified Method for Computing Incompressible and Compressible Flows in Boundary-Fitted Coordinates, Journal of Computational Physics, vol.141, issue.2, pp.153-173, 1998.
DOI : 10.1006/jcph.1998.5914

V. Casulli and D. Greenspan, Pressure method for the numerical solution of transient, compressible fluid flows, International Journal for Numerical Methods in Fluids, vol.116, issue.11, pp.1001-1012, 1984.
DOI : 10.1002/fld.1650041102

A. Chorin, Numerical solution of the Navier-Stokes equations, Mathematics of Computation, vol.22, issue.104, pp.745-762, 1968.
DOI : 10.1090/S0025-5718-1968-0242392-2

P. G. Ciarlet, Basic error estimates for elliptic problems, Handbook of Numerical Analysis, pp.17-351, 1991.
DOI : 10.1016/S1570-8659(05)80039-0

M. Crouzeix and P. Raviart, Conforming and nonconforming finite element methods for solving the stationary Stokes equations I, Revue fran??aise d'automatique informatique recherche op??rationnelle. Math??matique, vol.7, issue.R3, pp.33-75, 1973.
DOI : 10.1051/m2an/197307R300331

I. Demird?i´demird?i´c, M. Lilek, and . Peri´cperi´c, A collocated finite volume method for predicting flows at all speeds, International Journal for Numerical Methods in Fluids, vol.11, issue.12, pp.1029-1050, 1993.
DOI : 10.1002/fld.1650161202

R. Eymard, T. Gallouët, and R. Herbin, Finite volume methods, Handbook of Numerical Analysis, pp.713-1020, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00346077

R. Eymard, T. Gallouët, R. Herbin, and J. Latché, Convergence of the MAC Scheme for the Compressible Stokes Equations, SIAM Journal on Numerical Analysis, vol.48, issue.6, pp.2218-2246, 2010.
DOI : 10.1137/090779863

URL : https://hal.archives-ouvertes.fr/hal-00542676

T. Gallouët, L. Gastaldo, R. Herbin, and J. Latché, An unconditionally stable pressure correction scheme for the compressible barotropic Navier-Stokes equations, ESAIM: Mathematical Modelling and Numerical Analysis, vol.42, issue.2, pp.303-331, 2008.
DOI : 10.1051/m2an:2008005

L. Gastaldo, R. Herbin, W. Kheriji, C. Lapuerta, and J. Latché, Staggered discretizations, pressure correction schemes and all speed barotropic flows, Finite Volumes for Complex Applications VI -Problems and Perspectives -Prague, Czech Republic, pp.39-56, 2011.
DOI : 10.1007/978-3-642-20671-9_86

URL : https://hal.archives-ouvertes.fr/hal-00576246

L. Gastaldo, R. Herbin, and J. Latché, A discretization of the phase mass balance in fractional step algorithms for the drift-flux model, IMA Journal of Numerical Analysis, vol.31, issue.1, pp.116-146, 2011.
DOI : 10.1093/imanum/drp006

URL : https://hal.archives-ouvertes.fr/hal-00308838

L. Gastaldo, R. Herbin, J. Latché, and N. Therme, Explicit high order staggered schemes for the Euler equations. in preparation, 2014.

D. Grapsas, R. Herbin, W. Kheriji, and J. Latché, An unconditionally stable staggered pressure correction scheme for the compressible Navier-Stokes equations, SMAI Journal of Computational Mathematics, vol.2, 2014.
DOI : 10.5802/smai-jcm.9

URL : https://hal.archives-ouvertes.fr/hal-01115250

J. Guermond, P. Minev, and J. Shen, An overview of projection methods for incompressible flows, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.44-47, pp.6011-6045, 2006.
DOI : 10.1016/j.cma.2005.10.010

J. Guermond and R. Pasquetti, Entropy-based nonlinear viscosity for Fourier approximations of conservation laws. Comptes Rendus de l'Académie des Sciences de Paris ? Série I ? Analyse Numérique, pp.801-806, 2008.

J. Guermond, R. Pasquetti, and B. Popov, Entropy viscosity method for nonlinear conservation laws, Journal of Computational Physics, vol.230, issue.11, pp.4248-4267, 2011.
DOI : 10.1016/j.jcp.2010.11.043

J. Guermond and L. Quartapelle, A Projection FEM for Variable Density Incompressible Flows, Journal of Computational Physics, vol.165, issue.1, pp.167-188, 2000.
DOI : 10.1006/jcph.2000.6609

F. Harlow and A. Amsden, Numerical calculation of almost incompressible flow, Journal of Computational Physics, vol.3, issue.1, pp.80-93, 1968.
DOI : 10.1016/0021-9991(68)90007-7

F. Harlow and A. Amsden, A numerical fluid dynamics calculation method for all flow speeds, Journal of Computational Physics, vol.8, issue.2, pp.197-213, 1971.
DOI : 10.1016/0021-9991(71)90002-7

F. Harlow and J. Welsh, Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface, Physics of Fluids, vol.8, issue.12, pp.2182-2189, 1965.
DOI : 10.1063/1.1761178

R. Herbin, W. Kheriji, and J. Latché, Staggered schemes for all speed flows, ESAIM Proceedings, pp.22-150, 2012.
DOI : 10.1051/proc/201235008

URL : https://hal.archives-ouvertes.fr/hal-00636173

R. Herbin, W. Kheriji, and J. Latché, Pressure correction staggered schemes for barotropic monophasic and two-phase flows, Computer and Fluids, vol.88, pp.524-542, 2013.

R. Herbin and J. Latché, Kinetic energy control in the MAC discretization of the compressible Navier-Stokes equations, International Journal of Finites Volumes, vol.7, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00477079

R. Herbin, J. Latché, and K. Mallem, Convergence of the MAC Scheme for the Steady-State Incompressible Navier-Stokes Equations on Non-uniform Grids, Proceedings of Finite Volumes for Complex Applications VII -Problems and Perspectives - Berlin, 2014.
DOI : 10.1007/978-3-319-05684-5_33

R. Herbin, J. Latché, and T. Nguyen, An explicit staggered scheme for the shallow water and Euler equations. submitted, 2013.

R. Herbin, J. Latché, and T. Nguyen, Explicit staggered schemes for the compressible euler equations, ESAIM: Proceedings, vol.40, pp.83-102, 2013.
DOI : 10.1051/proc/201340006

URL : https://hal.archives-ouvertes.fr/hal-00821069

B. Hjertager, Computer simulation of reactive gas dynamics. Modeling, Identification and Control, pp.211-236, 1985.

Y. Hou and K. Mahesh, A robust, colocated, implicit algorithm for direct numerical simulation of compressible, turbulent flows, Journal of Computational Physics, vol.205, issue.1, pp.205-221, 2005.
DOI : 10.1016/j.jcp.2004.10.039

R. Issa, Solution of the implicitly discretised fluid flow equations by operator-splitting, Journal of Computational Physics, vol.62, issue.1, pp.40-65, 1985.
DOI : 10.1016/0021-9991(86)90099-9

R. Issa, A. Gosman, and A. Watkins, The computation of compressible and incompressible recirculating flows by a non-iterative implicit scheme, Journal of Computational Physics, vol.62, issue.1, pp.66-82, 1986.
DOI : 10.1016/0021-9991(86)90100-2

R. Issa and M. Javareshkian, Pressure-Based Compressible Calculation Method Utilizing Total Variation Diminishing Schemes, AIAA Journal, vol.36, issue.9, pp.1652-1657, 1998.
DOI : 10.2514/2.567

S. Kadioglu, M. Sussman, S. Osher, J. Wright, and M. Kang, A second order primitive preconditioner for solving all speed multi-phase flows, Journal of Computational Physics, vol.209, issue.2, pp.477-503, 2005.
DOI : 10.1016/j.jcp.2005.03.020

K. Karki and S. Patankar, A pressure based calculation procedure for viscous flows at all speeds in arbitrary configurations, 26th Aerospace Sciences Meeting, pp.1167-1174, 1989.
DOI : 10.2514/6.1988-58

M. Kobayashi and J. Pereira, Characteristic-based pressure correction at all speeds, AIAA Journal, vol.34, issue.2, pp.272-280, 1996.
DOI : 10.2514/3.13061

A. Kurganov and Y. Liu, New adaptive artificial viscosity method for hyperbolic systems of conservation laws, Journal of Computational Physics, vol.231, issue.24, pp.8114-8132, 2012.
DOI : 10.1016/j.jcp.2012.07.040

N. Kwatra, J. Su, J. Grétarsson, and R. Fedkiw, A method for avoiding the acoustic time step restriction in compressible flow, Journal of Computational Physics, vol.228, issue.11, pp.4146-4161, 2009.
DOI : 10.1016/j.jcp.2009.02.027

J. Latché and K. Saleh, A convergent staggered scheme for variable density incompressible Navier-Stokes equations. submitted, 2014.

F. Lien, A pressure-based unstructured grid method for all-speed flows, International Journal for Numerical Methods in Fluids, vol.114, issue.3, pp.355-374, 2000.
DOI : 10.1002/1097-0363(20000615)33:3<355::AID-FLD12>3.0.CO;2-X

A. Majda and J. Sethian, The Derivation and Numerical Solution of the Equations for Zero Mach Number Combustion, Combustion Science and Technology, vol.6, issue.3-4, pp.185-205, 1985.
DOI : 10.1080/00102208508960376

R. Martineau and R. Berry, The pressure-corrected ICE finite element method for compressible flows on unstructured meshes, Journal of Computational Physics, vol.198, issue.2, pp.659-685, 2004.
DOI : 10.1016/j.jcp.2004.01.034

J. Mcguirk and G. Page, Shock capturing using a pressure-correction method, AIAA Journal, vol.28, issue.10, pp.1751-1757, 1990.
DOI : 10.2514/3.10470

F. Moukalled and M. Darwish, A High-Resolution Pressure-Based Algorithm for Fluid Flow at All Speeds, Journal of Computational Physics, vol.168, issue.1, pp.101-133, 2001.
DOI : 10.1006/jcph.2000.6683

V. Moureau, C. Bérat, and H. Pitsch, An efficient semi-implicit compressible solver for large-eddy simulations, Journal of Computational Physics, vol.226, issue.2, pp.1256-1270, 2007.
DOI : 10.1016/j.jcp.2007.05.035

K. Nerinckx, J. Vierendeels, and E. Dick, Mach-uniformity through the coupled pressure and temperature correction algorithm, Journal of Computational Physics, vol.206, issue.2, pp.597-623, 2005.
DOI : 10.1016/j.jcp.2004.12.019

K. Nerinckx, J. Vierendeels, and E. Dick, A Mach-uniform algorithm: Coupled versus segregated approach, Journal of Computational Physics, vol.224, issue.1, pp.314-331, 2007.
DOI : 10.1016/j.jcp.2007.02.008

P. Nithiarasu, R. Codina, and O. Zienkiewicz, The Characteristic-Based Split (CBS) scheme???a unified approach to fluid dynamics, International Journal for Numerical Methods in Engineering, vol.33, issue.10, pp.1514-1546, 2006.
DOI : 10.1002/nme.1698

G. Patnaik, R. Guirguis, J. Boris, and E. Oran, A barely implicit correction for flux-corrected transport, Journal of Computational Physics, vol.71, issue.1, pp.1-20, 1987.
DOI : 10.1016/0021-9991(87)90016-7

L. Piar, F. Babik, R. Herbin, and J. Latché, A formally second-order cell centred scheme for convection-diffusion equations on general grids, International Journal for Numerical Methods in Fluids, vol.228, issue.7, pp.873-890, 2013.
DOI : 10.1002/fld.3688

E. Politis and K. Giannakoglou, A PRESSURE-BASED ALGORITHM FOR HIGH-SPEED TURBOMACHINERY FLOWS, International Journal for Numerical Methods in Fluids, vol.4, issue.1, pp.63-80, 1997.
DOI : 10.1002/(SICI)1097-0363(19970715)25:1<63::AID-FLD539>3.0.CO;2-A

R. Rannacher and S. Turek, Simple nonconforming quadrilateral Stokes element, Numerical Methods for Partial Differential Equations, vol.2, issue.2, pp.97-111, 1992.
DOI : 10.1002/num.1690080202

E. Sewall and D. Tafti, A time-accurate variable property algorithm for calculating flows with large temperature variations, Computers & Fluids, vol.37, issue.1, pp.51-63, 2008.
DOI : 10.1016/j.compfluid.2007.04.001

R. Temam, Sur l'approximation de la solution deséquationsdeséquations de Navier-Stokes par la méthode des pas fractionnaires II, Arch. Rat. Mech. Anal, vol.33, pp.377-385, 1969.

S. Thakur and J. Wright, A multiblock operator-splitting algorithm for unsteady flows at all speeds in complex geometries, International Journal for Numerical Methods in Fluids, vol.46, issue.4, pp.383-413, 2004.
DOI : 10.1002/fld.763

N. Therme and Z. Chady, Comparison of consistent explicit schemes on staggered and colocated meshes. in preparation, 2014.

E. Toro, Riemann solvers and numerical methods for fluid dynamics ? A practical introduction, 2009.

D. Van-der-heul, C. Vuik, and P. Wesseling, Stability analysis of segregated solution methods for compressible flow, Applied Numerical Mathematics, vol.38, issue.3, pp.257-274, 2001.
DOI : 10.1016/S0168-9274(01)00028-9

D. Van-der-heul, C. Vuik, and P. Wesseling, A conservative pressure-correction method for flow at all speeds, Computers & Fluids, vol.32, issue.8, pp.1113-1132, 2003.
DOI : 10.1016/S0045-7930(02)00086-5

J. Van-dormaal, G. Raithby, and B. Mcdonald, The segregated approach to predicting viscous compressible fluid flows, Transactions of the ASME, vol.109, pp.268-277, 1987.

D. Vidovi´cvidovi´c, A. Segal, and P. Wesseling, A superlinearly convergent Mach-uniform finite volume method for the Euler equations on staggered unstructured grids, Journal of Computational Physics, vol.217, issue.2, pp.277-294, 2006.
DOI : 10.1016/j.jcp.2006.01.031

C. Wall, C. Pierce, and P. Moin, A Semi-implicit Method for Resolution of Acoustic Waves in Low Mach Number Flows, Journal of Computational Physics, vol.181, issue.2, pp.545-563, 2002.
DOI : 10.1006/jcph.2002.7141

I. Wenneker, A. Segal, and P. Wesseling, A Mach-uniform unstructured staggered grid method, International Journal for Numerical Methods in Fluids, vol.31, issue.9, pp.1209-1235, 2002.
DOI : 10.1002/fld.417

C. Xisto, J. Páscoa, P. Oliveira, and D. Nicolini, A hybrid pressure-density-based algorithm for the Euler equations at all Mach number regimes, International Journal for Numerical Methods in Fluids, vol.41, issue.1, 2011.
DOI : 10.1002/fld.2722

S. Yoon and T. Yabe, The unified simulation for incompressible and compressible flow by the predictor-corrector scheme based on the CIP method, Computer Physics Communications, vol.119, issue.2-3, pp.149-158, 1999.
DOI : 10.1016/S0010-4655(99)00192-7

O. Zienkiewicz and R. Codina, A general algorithm for compressible and incompressible flow???Part I. the split, characteristic-based scheme, International Journal for Numerical Methods in Fluids, vol.20, issue.8-9, pp.869-885, 1995.
DOI : 10.1002/fld.1650200812