An asymptotic expansion for the solution of the generalized Riemann problem. Part 2 : application to the equations of gas dynamics

A. Bourgeade; Ph. Le Floch; P. A. Raviart

Annales de l'I.H.P. Analyse non linéaire (1989)

  • Volume: 6, Issue: 6, page 437-480
  • ISSN: 0294-1449

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Bourgeade, A., Le Floch, Ph., and 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 6.6 (1989): 437-480. <http://eudml.org/doc/78187>.

@article{Bourgeade1989,
author = {Bourgeade, A., Le Floch, Ph., Raviart, P. A.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {gas dynamics; Godunov method},
language = {eng},
number = {6},
pages = {437-480},
publisher = {Gauthier-Villars},
title = {An asymptotic expansion for the solution of the generalized Riemann problem. Part 2 : application to the equations of gas dynamics},
url = {http://eudml.org/doc/78187},
volume = {6},
year = {1989},
}

TY - JOUR
AU - Bourgeade, A.
AU - Le Floch, Ph.
AU - Raviart, P. A.
TI - An asymptotic expansion for the solution of the generalized Riemann problem. Part 2 : application to the equations of gas dynamics
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1989
PB - Gauthier-Villars
VL - 6
IS - 6
SP - 437
EP - 480
LA - eng
KW - gas dynamics; Godunov method
UR - http://eudml.org/doc/78187
ER -

References

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  1. sible Fluid Dynamics, J. Comp. Phys., Vol. 55, 1984, pp. 1-32. MR757422
  2. [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. Zbl0594.76057MR848562
  3. [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. Zbl0644.65059MR910100
  4. [4] R. Courant and K.O. Friedrichs, Supersonic Flows and Shock Waves, Interscience Pub.New York, Pure Appl. Math., Vol. 1, 1948. Zbl0041.11302MR29615
  5. [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. [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. Zbl0679.35064MR890629
  7. [7] Ph. Le Floch, Sur l'étude théorique et l'approximation numérique des systèmes hyperboliques non linéaires, Thèse, École Polytechnique, janvier 1988. 
  8. [8] Li Tatsien and Yu Wenci, Boundary Value Problem for Quasilinear Hyperbolic Systems, Duke Univ. Math. Series, 1985. MR823237
  9. [9] J. Smoller, Shock Waves and Reaction Diffusion Equations, Springer Verlag, New York, 1983. Zbl0508.35002MR688146
  10. [10] B. Van Leer, Toward the Ultimate Conservative Difference Scheme, V, J. Comp. Phys., Vol. 32, 1979, pp. 101-136. 

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