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Kinetic approximation of a boundary value problem for conservation laws

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Summary.

We design numerical schemes for systems of conservation laws with boundary conditions. These schemes are based on relaxation approximations taking the form of discrete BGK models with kinetic boundary conditions. The resulting schemes are Riemann solver free and easily extendable to higher order in time or in space. For scalar equations convergence is proved. We show numerical examples, including solutions of Euler equations.

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Authors and Affiliations

  1. Université Bordeaux 1, 351 cours de la Libération, 33405, Talence, France;

    Denise Aregba-Driollet

  2. Modelling and Scientific Computing Chair SB/IACS/CMCS Ecole Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland;

    Vuk Milišić

Authors
  1. Denise Aregba-Driollet
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  2. Vuk Milišić
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Correspondence to Denise Aregba-Driollet.

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Mathematics Subject Classification (2000): 65M06, 65M12, 76M20

Correspondence to: D. Aregba-Driollet

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Aregba-Driollet, D., Milišić, V. Kinetic approximation of a boundary value problem for conservation laws. Numer. Math. 97, 595–633 (2004). https://doi.org/10.1007/s00211-003-0514-5

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  • DOI: https://doi.org/10.1007/s00211-003-0514-5

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