no. 6
An asymptotic expansion for the solution of the generalized Riemann problem. Part 2 : application to the equations of gas dynamics
Annales de l'I.H.P. Analyse non linéaire, Tome 6 (1989) no. 6, pp. 437-480
partie précédente An asymptotic expansion for the solution of the generalized Riemann problem. Part I : general theory 
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     title = {An asymptotic expansion for the solution of the generalized {Riemann} problem. {Part} 2 : application to the equations of gas dynamics},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {437--480},
     year = {1989},
     publisher = {Gauthier-Villars},
     volume = {6},
     number = {6},
     mrnumber = {1035338},
     zbl = {0703.35106},
     language = {en},
     url = {https://www.numdam.org/item/AIHPC_1989__6_6_437_0/}
}
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Bourgeade, A.; Le Floch, Ph.; Raviart, P. A. An asymptotic expansion for the solution of the generalized Riemann problem. Part 2 : application to the equations of gas dynamics. Annales de l'I.H.P. Analyse non linéaire, Tome 6 (1989) no. 6, pp. 437-480. https://www.numdam.org/item/AIHPC_1989__6_6_437_0/

sible Fluid Dynamics, J. Comp. Phys., Vol. 55, 1984, pp. 1-32. | MR

[2] M. Ben Artzi and J. Falcovitz, An Upwind Second-Order Scheme for Compressible Duct Flows, Siam J. Sci. Comp., Vol. 7, 1986, pp. 744-768. | Zbl | MR

[3] A. Bourgeade, Ph. Le Floch and P.A. Raviart, Approximate Solutions of the Generalized Riemann Problem and Applications, Proceedings of Saint-Étienne (France), 1986, Springer Verlag, No. 1270. | Zbl | MR

[4] R. Courant and K.O. Friedrichs, Supersonic Flows and Shock Waves, Interscience Pub. New York, Pure Appl. Math., Vol. 1, 1948. | Zbl | MR

[5] E. Harabetian, A Cauchy Kovalevska Theorem for Strictly Hyperbolic Systems of Conservation Laws with Piecewise Analytic Initial Data, Ph. D. dissertation, University of California, Los Angeles, 1984.

[6] Ph. Le Floch and P.A. Raviart, An Asymptotic Expansion for the Solution of the Generalized Riemann Problem. Part 1: General Theory, Ann. Inst. H. Poincaré, Nonlinear Analysis, vol. 5, n° 2 (1988), pp. 179-207; and Note aux C. R. Acad. Sci. Paris, T. 304, Série I, No. 4, 1987, pp. 119-222. | Zbl | MR | Numdam

[7] Ph. Le Floch, Sur l'étude théorique et l'approximation numérique des systèmes hyperboliques non linéaires, Thèse, École Polytechnique, janvier 1988.

[8] Li Tatsien and Yu Wenci, Boundary Value Problem for Quasilinear Hyperbolic Systems, Duke Univ. Math. Series, 1985. | MR

[9] J. Smoller, Shock Waves and Reaction Diffusion Equations, Springer Verlag, New York, 1983. | Zbl | MR

[10] B. Van Leer, Toward the Ultimate Conservative Difference Scheme, V, J. Comp. Phys., Vol. 32, 1979, pp. 101-136.