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Discontinuous Galerkin methods for compressible flows: higher order accuracy, error estimation and adaptivity

Hartmann, Ralf (2006) Discontinuous Galerkin methods for compressible flows: higher order accuracy, error estimation and adaptivity. In: VKI Lecture Series, 2006-0. pp. 1-50.

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Abstract

1) Introduction<br></br> 2) The Discontinuous Galerkin discretization of hyperbolic conservation equations<br></br> 2.1) Hyperbolic conservation equations<br></br> 2.2) Scalar hyperbolic problem<br></br> 2.3) The compressible Euler equations<br></br> 2.4) The Discontinuous Galerkin discretization<br></br> 2.5) DG for scalar hyperbolic problems<br></br> 2.6) DG for scalar hyperbolic problems: <em>A priori</em> error estimates<br></br> 3) Higher order convergence of the DG method for the 2d compressible Euler equations<br></br> 3.1) The Ringleb flow problem<br></br> 4) A Discontinuous Galerkin discretization of the compressible Navier-Stokes equations<br></br> 4.1) The compressible Navier-Stokes equations<br></br> 4.2) The Interior Penalty Discontinuous Galerkin discretization<br></br> 5) Newton--GMRES algorithm<br></br> 5.1) Jacobians of boundary terms<br></br> 5.2) Jacobians of numerical flux functions<br></br> 5.3) Numerical performance of the Newton iteration<br></br> 6) Higher order convergence of the DG method for the 2d compressible Navier-Stokes equations<br></br> 6.1) Subsonic flow around an airfoil: Convergence of force coefficients<br></br> 6.2) Flow over a flat plate<br></br> 7) Shock-capturing<br></br> 7.1) Introduction<br></br> 7.2) Shock-capturing for the compressible Navier-Stokes equations<br></br> 7.3) The Jacobian of the shock-capturing term<br></br> 7.4) Numerical results<br></br> 7.4.1) Supersonic flow past a wedge<br></br> 7.4.2) Supersonic flow around an airfoil<br></br> 8) Error estimation and adaptivity<br></br> 8.1) Introduction<br></br> 8.2) The dual (adjoint) problem<br></br> 8.3) Adjoint problems for scalar hyperbolic problems<br></br> 8.4) Error estimation<br></br> 8.5) Adaptive mesh refinement<br></br> 8.6) Numerical examples<br></br> 8.6.1) Ringleb flow problem<br></br> 8.6.2) Supersonic flow past a wedge<br></br> 8.6.3) Supersonic flow around an airfoil<br></br> 9) Acknowledgements

Item URL in elib:https://elib.dlr.de/44203/
Document Type:Contribution to a Collection
Title:Discontinuous Galerkin methods for compressible flows: higher order accuracy, error estimation and adaptivity
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Hartmann, RalfUNSPECIFIEDUNSPECIFIED
Date:2006
Open Access:Yes
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Volume:2006-0
Page Range:pp. 1-50
Editors:
EditorsEmail
Deconinck, H.UNSPECIFIED
Ricchiuto, M.UNSPECIFIED
Series Name:VKI Lecture Series
Status:Published
Keywords:discontinuous Galerkin discretization, compressible Euler equations, compressible Navier-Stokes equations, a posteriori error estimation
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:Aircraft Research (old)
DLR - Research area:Aeronautics
DLR - Program:L AR - Aircraft Research
DLR - Research theme (Project):L - Concepts & Integration (old)
Location: Braunschweig
Institutes and Institutions:Institute of Aerodynamics and Flow Technology > CASE
Deposited By: Hartmann, Dr.rer.nat. Ralf
Deposited On:21 Jul 2006
Last Modified:31 Jul 2019 19:17

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