Hartmann, Ralf und Leicht, Tobias (2014) Higher order and adaptive DG methods for compressible flows. In: 37th Advanced CFD Lecture Series: Recent developments in higher order methods and industrial application in aeronautics VKI lecture series, 2014 (3). Von Karman Institute for Fluid Dynamics. Seiten 1-156. ISBN ISBN-13978-2-87516-065-2.
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Kurzfassung
In this work, we introduce the consistency and adjoint consistency analysis of
discontinuous Galerkin discretizations (Section 2). In particular, we give a
general framework for analyzing the consistency and adjoint consistency of DG
discretizations for linear problems with inhomogeneous boundary conditions
(Section 2.1). This includes the derivation of continuous adjoint problems
associated to specific target quantities J(·), the derivation of primal and
adjoint residual forms of the discretizations and the discussion whether the
discretizations of the primal equations in combination with the
discretizations of the target quantities, J_h(·), are adjoint consistent or
not. This analysis is then extended to nonlinear problems (Section 2.2).
In subsequent sections, we consider DG discretizations of scalar model problems,
• the linear advection(-reaction) equation (Section 3), and
• Poisson’s equation (Section 4),
and of compressible flow problems governed by
• the compressible Euler equations (Section 5),
• the compressible Navier-Stokes equations (Section 6), and
• the Reynolds-averaged Navier-Stokes (RANS) equations and the k-ω turbulence
model equations (Section 7).
Each of these discretizations will be analyzed with respect to consistency,
adjoint consistency, and global and local conservation
properties. Furthermore, for the DG discretizations of the scalar model
problems we discuss stability properties and give a priori estimates of the
discretization error measured in terms of related DG-norms, in terms of the
L2-norm as well as in terms of target quantities J(·), (Sections 3 and
4). Furthermore, some of the theoretical results, in particular the a priori
error estimates in L2 and J(·), are supported by experimental measurements of
the order of convergence (Sections 4.9 and 4.11). For the compressible flow
problems, for which no a priori error estimates are available, we provide
numerical results and experimental measurements of the order of convergence
for inviscid and viscous laminar flows (Sections 5.8 and 6.8). Then, Section
8 is devoted to the derivation of adjoint-based a posteriori estimates of the
discretization error in computed target quantity values J_h(u_h) like
aerodynamic force coefficients. These estimates are then decomposed into sums
of local error indicators (the so-called goal-oriented or adjoint-based
indicators) which can be used in an adaptive mesh refinement algorithm
tailored to the accurate and efficient approximation of the target
quantity. After introduction of this adjoint-based error estimation and mesh
refinement approach for single target quantities (Section 8.1), it is extended
to the treatment of multiple target quantities (Section 8.2). Section 8.4
finalizes the adaptivity section with the derivation of residual-based
indicators. Not depending on an adjoint problem these indicators target at
resolving the overall flow field. Finally, in Section 9 the performance of
the adjoint-based error estimation, the adjoint-based mesh refinement and the
residual-based mesh refinement will be demonstrated for a number of
aerodynamic test cases of increasing compexity.
| elib-URL des Eintrags: | https://elib.dlr.de/90967/ | ||||||||||||
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| Dokumentart: | Beitrag im Sammelband | ||||||||||||
| Titel: | Higher order and adaptive DG methods for compressible flows | ||||||||||||
| Autoren: |
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| Datum: | 2014 | ||||||||||||
| Erschienen in: | 37th Advanced CFD Lecture Series: Recent developments in higher order methods and industrial application in aeronautics | ||||||||||||
| Referierte Publikation: | Nein | ||||||||||||
| Open Access: | Ja | ||||||||||||
| Gold Open Access: | Nein | ||||||||||||
| In SCOPUS: | Nein | ||||||||||||
| In ISI Web of Science: | Nein | ||||||||||||
| Band: | 2014 | ||||||||||||
| Seitenbereich: | Seiten 1-156 | ||||||||||||
| Herausgeber: |
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| Verlag: | Von Karman Institute for Fluid Dynamics | ||||||||||||
| Name der Reihe: | VKI lecture series | ||||||||||||
| ISBN: | ISBN-13978-2-87516-065-2 | ||||||||||||
| Status: | veröffentlicht | ||||||||||||
| Stichwörter: | Discontinuous Galerkin methods, adjoint consistency, error estimation, adjoint-based mesh refinement | ||||||||||||
| HGF - Forschungsbereich: | Luftfahrt, Raumfahrt und Verkehr | ||||||||||||
| HGF - Programm: | Luftfahrt | ||||||||||||
| HGF - Programmthema: | Flugzeuge | ||||||||||||
| DLR - Schwerpunkt: | Luftfahrt | ||||||||||||
| DLR - Forschungsgebiet: | L AR - Aircraft Research | ||||||||||||
| DLR - Teilgebiet (Projekt, Vorhaben): | L - Simulation und Validierung (alt) | ||||||||||||
| Standort: | Braunschweig | ||||||||||||
| Institute & Einrichtungen: | Institut für Aerodynamik und Strömungstechnik > C²A²S²E - Center for Computer Applications in AeroSpace Science and Engineering | ||||||||||||
| Hinterlegt von: | Hartmann, Dr.rer.nat. Ralf | ||||||||||||
| Hinterlegt am: | 28 Nov 2014 11:40 | ||||||||||||
| Letzte Änderung: | 28 Mär 2023 23:42 |
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