D. Amadori, L. Gosse, and G. Guerra, Godunov-type approximation for a general resonant balance law with large data, Journal of Differential Equations, vol.198, issue.2, pp.233-274, 2004.
DOI : 10.1016/j.jde.2003.10.004

A. Ambroso, C. Chalons, F. Coquel, and T. Galié, Relaxation and numerical approximation of a two-fluid two-pressure diphasic model, ESAIM: Mathematical Modelling and Numerical Analysis, vol.43, issue.6, pp.1063-1097, 2009.
DOI : 10.1051/m2an/2009038

N. Andrianov and G. Warnecke, On the solution to the Riemann problem for the compressible duct flow, SIAM J. Appl. Math, vol.64, issue.3, pp.878-901, 2004.

M. Ben-artzi and J. Falcovitz, An Upwind Second-Order Scheme for Compressible Duct Flows, SIAM Journal on Scientific and Statistical Computing, vol.7, issue.3, pp.744-768, 1986.
DOI : 10.1137/0907051

F. Bouchut, Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources, Frontiers in Mathematics, 2004.

F. Bouchut and F. James, Duality solutions for pressureless gases, monotone scalar conservation laws, and uniqueness, Comm. Partial Differential Equations, vol.24, pp.11-122173, 1999.

G. Chen and J. Glimm, Global solutions to the compressible Euler equations with geometrical structure, Communications in Mathematical Physics, vol.65, issue.1, pp.153-193, 1996.
DOI : 10.1007/BF02101185

A. Chinnayya, A. Leroux, and N. Seguin, A well-balanced numerical scheme for the approximation of the shallow-water equations with topography: the resonance phenomenon, Int. J. Finite Volumes, pp.1-33, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00017378

F. Coquel, E. Godlewski, B. Perthame, A. In, and P. Rascle, Some New Godunov and Relaxation Methods for Two-Phase Flow Problems, Godunov methods, pp.179-188, 1999.
DOI : 10.1007/978-1-4615-0663-8_18

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, 2013.
DOI : 10.1051/m2an/2013101

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

F. Coquel and B. Perthame, Relaxation of Energy and Approximate Riemann Solvers for General Pressure Laws in Fluid Dynamics, SIAM Journal on Numerical Analysis, vol.35, issue.6, pp.2223-2249, 1998.
DOI : 10.1137/S0036142997318528

T. Gallouët, J. Hérard, and N. Seguin, Some approximate Godunov schemes to compute shallow-water equations with topography, Computers & Fluids, vol.32, issue.4, pp.479-513, 2003.
DOI : 10.1016/S0045-7930(02)00011-7

T. Gallouët, J. Hérard, and N. Seguin, NUMERICAL MODELING OF TWO-PHASE FLOWS USING THE TWO-FLUID TWO-PRESSURE APPROACH, Mathematical Models and Methods in Applied Sciences, vol.14, issue.05, pp.663-700, 2004.
DOI : 10.1142/S0218202504003404

H. M. Glaz and T. Liu, The asymptotic analysis of wave interactions and numerical calculations of transonic nozzle flow, Advances in Applied Mathematics, vol.5, issue.2, pp.111-146, 1984.
DOI : 10.1016/0196-8858(84)90006-X

J. Glimm, G. Marshall, and B. Plohr, A generalized Riemann problem for quasi-one-dimensional gas flows, Advances in Applied Mathematics, vol.5, issue.1, pp.1-30, 1984.
DOI : 10.1016/0196-8858(84)90002-2

P. Goatin and P. G. Lefloch, The Riemann problem for a class of resonant hyperbolic systems of balance laws, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.21, issue.6, pp.881-902, 2004.
DOI : 10.1016/j.anihpc.2004.02.002

E. Godlewski and P. Raviart, Numerical approximation of hyperbolic systems of conservation laws, Applied Mathematical Sciences, vol.118, 1996.
DOI : 10.1007/978-1-4612-0713-9

L. Gosse, A WELL-BALANCED SCHEME USING NON-CONSERVATIVE PRODUCTS DESIGNED FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS WITH SOURCE TERMS, Mathematical Models and Methods in Applied Sciences, vol.11, issue.02, pp.339-365, 2001.
DOI : 10.1142/S021820250100088X

L. Gosse, Localization effects and measure source terms in numerical schemes for balance laws, Mathematics of Computation, vol.71, issue.238, pp.553-582, 2002.
DOI : 10.1090/S0025-5718-01-01354-0

L. Gosse and A. Leroux, Un schéma-équilibre adapté aux lois de conservation scalaires non-homogènes, C. R. Acad. Sci. Paris Sér. I Math, vol.323, issue.5, pp.543-546, 1996.
DOI : 10.1016/s0764-4442(99)80466-2

J. M. Greenberg and A. Leroux, A Well-Balanced Scheme for the Numerical Processing of Source Terms in Hyperbolic Equations, SIAM Journal on Numerical Analysis, vol.33, issue.1, pp.1-16, 1996.
DOI : 10.1137/0733001

E. Han, M. Hantke, and G. Warnecke, EXACT RIEMANN SOLUTIONS TO COMPRESSIBLE EULER EQUATIONS IN DUCTS WITH DISCONTINUOUS CROSS-SECTION, Journal of Hyperbolic Differential Equations, vol.09, issue.03, pp.9403-449, 2012.
DOI : 10.1142/S0219891612500130

A. Harten, P. D. Lax, and B. Van-leer, On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws, SIAM Review, vol.25, issue.1, pp.35-61, 1983.
DOI : 10.1137/1025002

J. Hong and B. Temple, The generic solution of the Riemann problem in a neighborhood of a point of resonance for systems of nonlinear balance laws, Methods Appl. Anal, vol.10, issue.2, pp.279-294, 2003.

J. M. Hong, An extension of Glimm's method to inhomogeneous strictly hyperbolic systems of conservation laws by ???weaker than weak??? solutions of the Riemann problem, Journal of Differential Equations, vol.222, issue.2, pp.515-549, 2006.
DOI : 10.1016/j.jde.2005.06.016

L. P. Huang and T. Liu, A conservative, piecewise-steady difference scheme for transonic nozzle flow, Hyperbolic partial differential equations, pp.377-388, 1986.
DOI : 10.1016/0898-1221(86)90170-7

E. Isaacson and B. Temple, Convergence of the $2 \times 2$ Godunov Method for a General Resonant Nonlinear Balance Law, SIAM Journal on Applied Mathematics, vol.55, issue.3, pp.625-640, 1995.
DOI : 10.1137/S0036139992240711

S. Jin and Z. P. Xin, The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications on Pure and Applied Mathematics, vol.54, issue.3, pp.235-276, 1995.
DOI : 10.1002/cpa.3160480303

P. G. Lefloch, Shock waves for nonlinear hyperbolic systems in non-conservative form, Institute for Math. Appl, 1991.

P. G. Lefloch and M. D. Thanh, The Riemann Problem for Fluid Flows in a Nozzle with Discontinuous Cross-Section, Communications in Mathematical Sciences, vol.1, issue.4, pp.763-797, 2003.
DOI : 10.4310/CMS.2003.v1.n4.a6

K. Saleh, Analyse et approximation numérique par relaxation d'écoulements diphasiques compressibles, 2012.

K. Saleh, Thorough numerical comparisons of approximate Riemann solvers for nozzle flows