Discontinuous Galerkin Method – A Robust Solver for Compressible Flow

  • Miloslav Feistauer
  • Jan Česenek
  • Václav Kučera
Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design book series (NNFM, volume 120)

Abstract

The subject of the paper is the numerical simulation of inviscid and viscous compressible flow in time dependent domains. The motion of the boundary of the domain occupied by the fluid is taken into account with the aid of the ALE (Arbitrary Lagrangian-Eulerian) formulation of the Euler and Navier-Stokes equations describing compressible flow. They are discretized in space by the discontinuous Galerkin (DG) finite element method using piecewise polynomial discontinuous approximations. For the time discretization the BDF method or DG in time is used. Moreover, we use a special treatment of boundary conditions and shock capturing, allowing the solution of flow with a wide range of Mach numbers. As a result we get an efficient and robust numerical process. We show that the method allows to solve numerically the flow with a wide range of Mach numbers and it is applicable to the solution of practically relevant problems of flow induced airfoil vibrations.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Miloslav Feistauer
    • 1
  • Jan Česenek
    • 1
  • Václav Kučera
    • 1
  1. 1.Department of Numerical Mathematics, Faculty of Mathematics and PhysicsCharles UniversityPraha 8Czech Republic

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