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Lagrangian Gas Dynamics in Two Dimensions and Lagrangian systems

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Abstract

We propose a new and canonical way of writing the equations of gas dynamics in Lagrangian coordinates in two dimensions as a weakly hyperbolic system of conservation laws. One part of the system is called the physical part and contains physical variables; the other part is the geometrical part. We show that the physical part is symmetrizable. We show that the weak hyperbolicity is due to shear contact discontinuities. Free divergence constraints play an important role in the system. We prove the L 2 stability of the physical part of the system. Based on this formulation, we derive a new conservative and entropy-consistent finite-volume numerical scheme. We prove the stability of the numerical scheme. Numerical results show the potential interest of this approach. Various examples (Born-Infeld, MHD, 3D lagrangian gas dynamics) can be written using the same abstract formalism.

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Authors and Affiliations

  1. Laboratoire Jacques Louis Lions, 175 rue du Chevaleret, Université de Paris VI, 75013, Paris, France

    Bruno Després

  2. DSSI, Commissariat à l'Energie Atomique, 91680, Bruyères-le-Châtel; BP 12, France

    Constant Mazeran

Authors
  1. Bruno Després
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  2. Constant Mazeran
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Correspondence to Bruno Després.

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Communicated by Y. Brenier

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Després, B., Mazeran, C. Lagrangian Gas Dynamics in Two Dimensions and Lagrangian systems. Arch. Rational Mech. Anal. 178, 327–372 (2005). https://doi.org/10.1007/s00205-005-0375-4

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  • DOI: https://doi.org/10.1007/s00205-005-0375-4

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