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