Le Floch, Ph.; Raviart, P. A.
An asymptotic expansion for the solution of the generalized Riemann problem. Part I : general theory
Annales de l'I.H.P. Analyse non linéaire, Tome 5 (1988) no. 2 , p. 179-207
Zbl 0679.35064 | MR 954470 | 1 citation dans Numdam
⇒ partie suivante An asymptotic expansion for the solution of the generalized Riemann problem. Part 2 : application to the equations of gas dynamics
URL stable : http://www.numdam.org/item?id=AIHPC_1988__5_2_179_0

Bibliographie

[1] M. Ben-Artzi and J. Falcovitz, A Second Order Godunov-Type Scheme for Compressible Fluid Dynamics, J. Comp. Phys., Vol. 55, 1984, pp. 1-32. MR 757422 | Zbl 0535.76070

[2] M. Ben-Artzi and J. Falcovitz, An Upwind Second-Order Scheme for Compressible Duct Flows, S.I.A.M. J. Sci. Stat. Comp., Vol. 7, 1986, pp. 744-768. MR 848562 | Zbl 0594.76057

[3] A. Bourgeade, Ph. Le Floch and P.A. Raviart, Approximate Solution of the Generalized Riemann Problem and Applications, Actes du Congrès Hyperbolique of Saint-Etienne (France), January 1986, Springer-Verlag, 1988 (to appear). MR 910100 | Zbl 0644.65059

[4] A. Bourgeade, Ph. Le Floch and P.A. Raviart, An Asymptotic Expansion for the Solution of the Generalized Riemann Problem. Part. II: Application to the Gas Dynamics Equations (to appear). Numdam |

[5] J. Glimm, G. Marshall and B. Plohr, A Generalized Riemann Problem for Quasi-One-Dimensional Gas Flows, Adv. Appl. Maths., Vol. 5, 1984, pp. 1-30. MR 736548 | Zbl 0566.76056

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

[7] Ph. Le Floch and P.A. Raviart, Un développement asymptotique pour la solution d'un problème de Riemann généralisé, C.R. Acad. Sci. Paris, T. 304, Séries I, n° 4, 1987. MR 890629 | Zbl 0619.35074

[8] Li Tatsien and Yu Wenci, Boundary Value Problem for Quasilinear Hyperbolic Systems, Duke University Mathematics Series, 1985. MR 823237

[9] T.P. Liu, Quasilinear Hyperbolic Systems, Comm. Math. Phys., Vol. 68, 1979, pp. 141- 142. MR 543196 | Zbl 0435.35054

[10] J. Smoller, Shock waves and Reaction-Diffusion Equations, Springer-Verlag, New York, 1983. MR 688146 | Zbl 0508.35002

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