The riemann problem for a class of resonant hyperbolic systems of balance laws

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 21, Issue 6, 2004, Pages 881-902

  Goatin, Paola ^a   LeFloch, Philippe G ^b  

^a UNIVERSITÉ DE TOULON   (France)

^b CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

Author keywords

Balance law; Entropy solution; Fluid flow; Hyperbolic conservation law; Nonconservatif; Nozzle; Resonant; Riemann problem; Shock wave

Indexed keywords

CONFORMAL MAPPING; FLOW OF FLUIDS; FUNCTIONS; MATHEMATICAL MODELS; RESONANCE; THEOREM PROVING;

BALANCE LAW; ENTROPY SOLUTIONS; HYPERBOLIC CONSERVATION LAW; NONCONSERVATIF; RIEMANN PROBLEMS;

PROBLEM SOLVING;

EID: 5744239576     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpc.2004.02.002     Document Type: Article

References (32)

1. D. Amadori, L. Gosse, G. Guerra, Global BV entropy solutions and uniqueness for hyperbolic systems of balance laws, Arch. Rational Mech. Anal. 162 (2002) 327-366.
2. D. Amadori, L. Gosse, G. Guerra, Godunov-type approximation for a general resonant balance law with large data, J. Differential Equations 198 (2004) 233-274.
3. N. Andrianov, G. Warnecke, The Riemann problem for the Baer-Nunziato model of two-phase flows, J. Comput. Phys., in press.
4. N. Andrianov, G. Warnecke, On the solution to the Riemann problem for the compressible duct flow, SIAM J. Appl. Math., in press.
5. N. Andrianov, R. Saurel, G. Warnecke, A simple method for compressible multiphase mixtures and interfaces, Int. J. Num. Meth. Fluids 41 (2003) 109-131.
6. F. Asakura, Global solutions with a single transonic shock wave for quasilinear hyperbolic systems, submitted for publication.
7. R. Botchorishvili, B. Perthame, A. Vasseur, Equilibrium schemes for scalar conservation laws with stiff sources, Math, of Comput. 72 (2003) 131-157.
8. F. Bouchut, An introduction to finite volume methods for hyperbolic systems of conservation laws with source, INRIA Rocquencourt Report, 2002.
9. G.-Q. Chen, J. Glimm, Global solutions to the compressible Euler equations with geometrical structure, Comm. Math. Phys. 180 (1996) 153-193.
10. F.H. Clarke, Optimization and Non-Smooth Analysis, Classics in Applied Mathematics, vol. 5, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1990.
11. R. Courant, K.O. Friedrichs, Supersonic Flow and Shock Waves, Wiley, New York, 1948.
12. G. Dal Maso, P.G. LeFloch, F. Murat, Definition and weak stability of nonconservative products, J. Math. Pures Appl. 74 (1995) 483-548.
13. P. Embid, J. Goodman, J. Majda, Multiple steady states for 1-D transonic flows, SIAM J. Sci. Stat. Comput. 5 (1984) 21-41.
14. J. Glimm, G. Marschall, B. Plohr, A generalized Riemann problem for quasi-one-dimensional gas flows, Adv. Appl. Math. 5 (1981) 1-30.
15. L. Gosse, A well-balanced scheme using non-conservative products designed for hyperbolic conservation laws with source-terms, Math. Model Methods Appl. Sci. 11 (2001) 339-365.
16. J.M. Greenberg, A.Y. Leroux, A well-balanced scheme for the numerical processing of source terms in hyperbolic equations, SIAM J. Numer. Anal. 33 (1996) 1-16.
17. P. Hartman, Ordinary Differential Equations, Wiley, New York, 1964.
18. E. Isaacson, B. Temple, Nonlinear resonance in systems of conservation laws, SIAM J. Appl. Math. 52 (1992) 1260-1278.
19. E. Isaacson, B. Temple, Convergence of the 2 × 2 Godunov method for a general resonant nonlinear balance law, SIAM J. Appl. Math. 55 (1995) 625-640.
20. S. Jin, X. Wen, An efficient method for computing hyperbolic systems with geometrical source terms having concentrations, J. Comp. Math. 2 (2004) 230-249.
21. S. Jin, X. Wen, Two interface numerical methods for computing hyperbolic systems with geometrical source terms having concentrations, SIAM J. Sci. Com., in press.
22. P.O. LeFloch, Entropy weak solutions to nonlinear hyperbolic systems in nonconservative form, Comm. Partial Differential Equations 13 (1988) 669-727.
23. P.G. LeFloch, Shock waves for nonlinear hyperbolic systems in nonconservative form, Institute for Math, and its Appl., Minneapolis, Preprint # 593, 1989.
24. P.O. LeFloch, An existence and uniqueness result for two nonstrictly hyperbolic systems, in: B.L. Keyfitz, M. Shearer (Eds.), Nonlinear Evolution Equations that Change Type, in: IMA Volumes in Math, and its Appl., vol. 27, Springer-Verlag, 1990, pp. 126-138.
25. P.O. LeFloch, Hyperbolic Systems of Conservation Laws: The Theory of Classical and Nonclassical Shock Waves, Lectures in Mathematics, ETH Zürich, Birkhäuser, 2002.
26. P.G. LeFloch, M.D. Thanh, The Riemann problem for fluid flows in a nozzle with discontinuous cross-section, Comm. Math. Sci. 1 (2003) 763-797.
27. W.C. Lien, Hyperbolic conservation laws with a moving source, Comm. Pure Appl. Math. 52 (1999) 1075-1098.
28. T.-P. Liu, Quasilinear hyperbolic systems, Comm. Math. Phys. 68 (1979) 141-172.
29. T.-P. Liu, Nonlinear stability and instability of transonic flows through a nozzle, Comm. Math. Phys. 83 (1982) 243-260.
30. T.-P. Liu, Nonlinear resonance for quasilinear hyperbolic equation, J. Math. Phys. 28 (1987) 2593-2602.
31. D. Marehesin, P.J. Paes-Leme, A Riemann problem in gas dynamics with bifurcation, PUC Report MAT 02/84, 1984.
32. D. Marehesin, B. Plohr, S. Schecter, An organizing center for wave bifurcation flow models, SIAM J. Appl. Math. 57 (1997) 1189-1215.