An asymptotic expansion for the solution of the generalized Riemann problem. Part 2 : application to the equations of gas dynamics
Bourgeade, A. ; Le Floch, Ph. ; Raviart, P. A.
Annales de l'I.H.P. Analyse non linéaire, Tome S6 (1989), p. 437-480 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPC_1989__6_6_437_0,
     author = {Bourgeade, A. and Le Floch, Philippe and Raviart, P. A.},
     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},
     volume = {S6},
     year = {1989},
     pages = {437-480},
     mrnumber = {1035338},
     zbl = {0703.35106},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1989__6_6_437_0}
}

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 S6 (1989) pp. 437-480. http://gdmltest.u-ga.fr/item/AIHPC_1989__6_6_437_0/

sible Fluid Dynamics, J. Comp. Phys., Vol. 55, 1984, pp. 1-32. | MR 757422

[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. | MR 848562 | Zbl 0594.76057

[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. | MR 910100 | Zbl 0644.65059

[4] R. Courant and K.O. Friedrichs, Supersonic Flows and Shock Waves, Interscience Pub. New York, Pure Appl. Math., Vol. 1, 1948. | MR 29615 | Zbl 0041.11302

[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. | Numdam | MR 890629 | Zbl 0679.35064

[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 823237

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

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