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Error estimation and adaptive mesh refinement for aerodynamic flows
Hartmann, Ralf und Houston, Paul
(2010)
Error estimation and adaptive mesh refinement for aerodynamic flows.
In:
,Von Karman Institute for Fluid Dynamics, Rhode Saint Genese, Belgium.
ISBN 13 978-2-930389-98-2.
Vorschau |
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KurzfassungThis lecture course covers the theory of so-called duality-based a
posteriori error estimation of DG finite element methods. In
particular, we formulate consistent and adjoint consistent DG methods
for the numerical approximation of both the compressible Euler and
Navier-Stokes equations; in the latter case, the viscous terms are
discretized based on employing an interior penalty method. By
exploiting a duality argument, adjoint-based a posteriori error
indicators will be established. Moreover, application of these
computable bounds within automatic adaptive finite element algorithms
will be developed. Here, a variety of isotropic and anisotropic
adaptive strategies, as well as hp-mesh refinement will be
investigated.
The outline of these notes is as follows. In Section~2 we give an
introduction to the adjoint-based a posteriori error estimation and
mesh refinement for linear problems, and their subsequent exploitation
within an automatic adaptive finite element algorithms. Then, in
Section~3 we introduce both the compressible Euler and Navier-Stokes
equations and formulate DG numerical methods for their
discretization. In particular, here we will be concerned with the
derivation of so-called adjoint consistent methods, which ensure the
optimal approximation of target functionals of the underlying
solution. Section~4 is devoted to the derivation of adjoint-based a
posteriori error bounds for the computed error in a given target
functional of interest. Moreover, extensions to the case when there
are multiple quantities of interest will be considered. The practical
performance of these a posteriori error estimates within adaptive
finite element algorithms will be studied through a series of
numerical experiments. In Section~5 we consider the generalization of
the above ideas to the case when anisotropic mesh refinement is
permitted. In this setting, we derive both a priori and a posteriori
error bounds for the DG approximation of linear functionals of the
underlying analytical solution. The a priori analysis is fully
explicit in terms of the anisotropy of the underlying computational
mesh. Further, we introduce an anisotropic refinement algorithm, based
on choosing the most competitive subdivision of a given element from a
series of trial (Cartesian) refinements. The extension of these ideas
to general anisotropic hp-version DG finite element methods is
undertaken in Section~6. Finally, Section~7 is devoted to the
application of goal-oriented adaptive finite element algorithms to
complex aerodynamic flows, including three dimensional laminar flows
as well as two and three dimensional turbulent flows. elib-URL des Eintrags: | https://elib.dlr.de/61976/ |
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Dokumentart: | Beitrag im Sammelband |
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Titel: | Error estimation and adaptive mesh refinement for aerodynamic flows |
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Autoren: | Autoren | Institution oder E-Mail-Adresse | Autoren-ORCID-iD |
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Hartmann, Ralf | DLR | | Houston, Paul | University of Nottingham | |
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Datum: | 2010 |
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Open Access: | Ja |
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Gold Open Access: | Nein |
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In SCOPUS: | Nein |
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In ISI Web of Science: | Nein |
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Band: | 2010-0 |
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Herausgeber: | Herausgeber | Institution und/oder E-Mail-Adresse der Herausgeber | Herausgeber-ORCID-iD |
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Deconinck, Herman | VKI, Belgium | |
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Verlag: | ,Von Karman Institute for Fluid Dynamics, Rhode Saint Genese, Belgium |
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ISBN: | 13 978-2-930389-98-2 |
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Status: | veröffentlicht |
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Stichwörter: | Discontinuous Galerkin methods, error estimation, adjoint-based mesh refinement, anisotropic mesh refinement, hp refinement |
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HGF - Forschungsbereich: | Luftfahrt, Raumfahrt und Verkehr |
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HGF - Programm: | Luftfahrt |
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HGF - Programmthema: | Starrflügler (alt) |
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DLR - Schwerpunkt: | Luftfahrt |
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DLR - Forschungsgebiet: | L AR - Starrflüglerforschung |
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DLR - Teilgebiet (Projekt, Vorhaben): | L - Konzepte & Integration (alt) |
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Standort: |
Braunschweig
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Institute & Einrichtungen: | Institut für Aerodynamik und Strömungstechnik > CASE |
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Hinterlegt von: |
Hartmann, Dr.rer.nat. Ralf
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Hinterlegt am: | 05 Jan 2010 10:17 |
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Letzte Änderung: | 31 Jul 2019 19:26 |
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