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Two-scale numerical simulation of the weakly compressible 1D isentropic Euler equations

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References

  1. Ailliot P., Frénod E. and Monbet V. (2006). Long term object drift in the ocean with tide and wind. Multiscale Modell. Simul. 5(2): 514–531

    Article  MATH  Google Scholar 

  2. Allaire G. (1992). Homogenization and two-scale convergence. SIAM J. Math. Anal. 23(6): 1482–1518

    Article  MATH  MathSciNet  Google Scholar 

  3. Fortenbach, R., Frénod, E., Klein, R., Munz, C.-D., Sonnendrücker, E.: Multiple scale consideration for sound generation in low Mach number flow. In: 8th DFG Workshop on French German Research Program Numerical Flow Simulation, Oct. 2001

  4. Frénod E., Raviart P.A. and Sonnendrücker E. (2001). Two-scale expansion of a singularly perturbed convection equation. J. Pure Appl. Math. 80(8): 815–843

    Article  MATH  Google Scholar 

  5. Frénod, E., Salvarani, F., Sonnendrücker, E.: Long time simulation of a beam in a periodic focusing channel via a two-scale PIC-method (in preparation)

  6. Frénod E. and Sonnendrücker E. (2000). Long time behavior of the Vlasov equation with a strong external magnetic field. Math. Models Methods Appl. Sci. 10(4): 539–553

    Article  MATH  MathSciNet  Google Scholar 

  7. Frénod E. and Sonnendrücker E. (2001). The finite Larmor radius approximation. SIAM J. Math. Anal. 32(6): 1227–1247

    Article  MATH  MathSciNet  Google Scholar 

  8. Godunov, S.-K.: A difference scheme for numerical solution of discontinuous solution of hydrodynamic equations. Math. Sbornik, vol. 47, pp.271–306 (1959). Translated US Joint Publ. Res. Service, JPRS 7226 (1969)

  9. Grenier E. (2001). Oscillatory pertubation of the Navier–Stokes equations. J. Math. Pure Appl. 76: 477–498

    MathSciNet  Google Scholar 

  10. Klainerman S. and Majda A. (1981). Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of the compressible fluids. Commun. Pure Appl. Math. 34(4): 481–524

    Article  MATH  MathSciNet  Google Scholar 

  11. Klainerman S. and Majda A. (1982). Compressible and imcompressible fluids. Commun. Pure Appl. Math. 35(5): 629–651

    Article  MATH  MathSciNet  Google Scholar 

  12. LeVeque, R.: Finite Volume Methods for Hyperbolic Problems. Cambridge Texts in Applied Mathematics. Cambridge University Press, London (2002)

  13. Lions J.-L. (1969). Quelques méthodes de résolution de problèmes aux limites non linéaires. Dunod, Gauthier-Villars

    MATH  Google Scholar 

  14. Majda A. (1984). Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables. Academic, New York

    MATH  Google Scholar 

  15. Marusic-Paloka E. and Piatnitski A. (2005). Homogenization of nonlinear convection-diffusion equation with rapidly oscillating coefficients and strong convection. J. Lond. Math. Soc. 72(2): 391–409

    Article  MATH  MathSciNet  Google Scholar 

  16. Métivier G. and Schochet S. (2001). The incompressible limit of the non-isotropic Euler equations. Arch. Ration. Mech. Anal. 158: 61–90

    Article  MATH  MathSciNet  Google Scholar 

  17. Munz, C.-D.: Computational fluid dynamics and aeroacoustics for low Mach number flow. Unpublished (personal communication)

  18. Nguetseng G. (1989). A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 20(3): 608–623

    Article  MATH  MathSciNet  Google Scholar 

  19. Roe P.-L. (1981). Approximate Riemann solvers, parameter vectors and difference schemes. J. Comput. Phys. 43: 357–372

    Article  MATH  MathSciNet  Google Scholar 

  20. Schochet S. (1988). Asymptotic for symmetric hyperbolic systems with a large parameter. J. Differ. Equ. 75: 1–27

    Article  MATH  MathSciNet  Google Scholar 

  21. Schochet S. (1994). Fast singular limit of hyperbolic pdes. J. Differ. Equ. 114: 476–512

    Article  MATH  MathSciNet  Google Scholar 

  22. Schochet S. (1986). Symmetric hyperbolic systems with a large parameter. Commun. PDE 11(15): 1627–1651

    Article  MATH  MathSciNet  Google Scholar 

  23. Schochet S. (1986). The compressible Euler equations in a bounded domain existence of solutions and the incompressible limit. Commun. Math. Phys. 104: 46–75

    Article  MathSciNet  Google Scholar 

  24. Serre D. (1999). Systems of Conservations Laws 1. Cambridge University Press, London

    Google Scholar 

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Authors and Affiliations

  1. LÉMEL & LMAM, Université Européenne de Bretagne, 56000, Vannes, France

    Emmanuel Frénod

  2. IRMA, Université Louis Pasteur, 67084, Strasbourg, France

    Alexandre Mouton & Eric Sonnendrücker

Authors
  1. Emmanuel Frénod
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  2. Alexandre Mouton
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  3. Eric Sonnendrücker
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Correspondence to Alexandre Mouton.

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Frénod, E., Mouton, A. & Sonnendrücker, E. Two-scale numerical simulation of the weakly compressible 1D isentropic Euler equations. Numer. Math. 108, 263–293 (2007). https://doi.org/10.1007/s00211-007-0116-8

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  • DOI: https://doi.org/10.1007/s00211-007-0116-8

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