Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
Volume 51, Issue 9-10, Pages 1131-1156Publisher
JOHN WILEY & SONS LTD
DOI: 10.1002/fld.1134
Keywords
finite element methods; discontinuous Galerkin methods; compressible Navier-Stokes equations; shock-capturing
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We present the Interior Penalty discontinuous Galerkin method for the compressible Navier-Stokes equations. Shock-capturing is used to reduce over-shoots at discontinuities and sharp gradients. This stabilization introduces artificial viscosity at places of large local residuals, but preserves conservation and Galerkin orthogonality of the DG method. Based on this discretization we derive a posteriori error estimates for the error measured in terms of arbitrary target functionals, like, e.g. the drag and lift coefficients of an airfoil immersed in a viscous or inviscid fluid. The performance of the nonlinear solution process, the a posteriori error estimation and an adaptive mesh refinement specially tailored for the accurate computation of the force coefficients are demonstrated for supersonic laminar flows around the NACA0012 airfoil. Copyright (c) 2005 John Wiley & Sons, Ltd.
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