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The Discontinuous Galerkin Method for Convection-Diffusion Problems in Time-Dependent Domains

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • Václav Kučera

    (Charles University Prague, Faculty of Mathematics and Physics)

  • Miloslav Feistauer

    (Charles University Prague, Faculty of Mathematics and Physics)

  • Jaroslava Prokopov́

    (Charles University Prague, Faculty of Mathematics and Physics)

Abstract

This paper is concerned with the numerical treatment of convection-diffusion problems in time-dependent domains. A suitable formulation of the governing equations is derived using the Arbitrary Lagrangian–Eulerian (ALE) method. The equations are then discretized in space using the discontinuous Galerkin method. The resulting space-semidiscretization scheme is numerically tested on the compressible Navier–Stokes equations describing the flow of viscous gases. The particular form of these equations allows the use of a semi-implicit time discretization, which has already been extensively studied in the case of stationary computational domains.

Suggested Citation

  • Václav Kučera & Miloslav Feistauer & Jaroslava Prokopov́, 2010. "The Discontinuous Galerkin Method for Convection-Diffusion Problems in Time-Dependent Domains," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 551-559, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_59
    DOI: 10.1007/978-3-642-11795-4_59
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