BAIL 2006 Book of Abstracts - Institut für Numerische und ...

R. HARTMANN: Discontinuous Galerkin methods for compressible flows: higher order
accuracy, error estimation and adaptivity
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Discontinuous Galerkin methods for compressible flows:
higher order accuracy, error estimation and adaptivity
Ralf Hartmann
Institute of Aerodynamics and Flow Technology, German Aerospace Center (DLR),
Lilienthalplatz 7, 38108 Braunschweig, Germany
The Discontinuous Galerkin (DG) method for the compressible Euler equations is extended
to the symmetric interior penalty (SIP)DG method for the compressible Navier-Stokes equations,
see Hartmann & Houston [2]. Shock-capturing is used to avoid overshoots near shocks, see Hartmann
[1]. The nonlinear equations are solved using a fully implicit solver. We demonstrate the
accuracy of higher order DG discretizations with respect to the approximation of aerodynamical
force coefficients and to the approximation of viscous boundary layers, see Figure 1 and
Hartmann & Houston [2].
Finally, we demonstrate the use of a posteriori error estimation and goal-oriented (also
called weighted-residual-based or adjoint-based) adaptive mesh refinement for subsonic flows,
Hartmann & Houston [3], and for supersonic compressible flows, see Figure 2 and Hartmann [1].
References
[1] R. Hartmann. Adaptive discontinuous Galerkin methods with shock-capturing for the compressible
Navier-Stokes equations. Int. J. Numer. Meth. Fluids, 2006. To appear.
[2] R. Hartmann and P. Houston. Symmetric interior penalty DG methods for the compressible
Navier–Stokes equations I: Method formulation. Int. J. Num. Anal. Model., 3(1):1–20, 2006.
[3] R. Hartmann and P. Houston. Symmetric interior penalty DG methods for the compressible
Navier–Stokes equations II: Goal–oriented a posteriori error estimation. Int. J. Num. Anal.
Model., 3(2):141–162, 2006.
Speaker: HARTMANN, R. 22 BAIL 2006
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