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An optimal order interior penalty discontinuous Galerkin discretization of the compressible Navier-Stokes equations

Hartmann, Ralf and Houston, Paul (2008) An optimal order interior penalty discontinuous Galerkin discretization of the compressible Navier-Stokes equations. Journal of Computational Physics, 227 (22), pp. 9670-9685. Elsevier.

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Abstract

In this article we propose a new symmetric version of the interior penalty discontinuous Galerkin finite element method for the numerical approximation of the compressible Navier-Stokes equations. Here, particular emphasis is devoted to the construction of an optimal numerical method for the evaluation of certain target functionals of practical interest, such as the lift and drag coefficients of a body immersed in a viscous fluid. With this in mind, the key ingredients in the construction of the method include: (i) An adjoint consistent imposition of the boundary conditions; (ii) An adjoint consistent reformulation of the underlying target functional of practical interest; (iii) Design of appropriate interior--penalty stabilization terms. Numerical experiments presented within this article clearly indicate the optimality of the proposed method when the error is measured in terms of both the L<sup>2</sup>-norm, as well as for certain target functionals. Computational comparisons with other discontinuous Galerkin schemes proposed in the literature, including the second scheme of Bassi and Rebay, the standard SIPG method outlined in [Hartmann,Houston-2006], and an NIPG variant of the new scheme will be undertaken.

Item URL in elib:https://elib.dlr.de/57072/
Document Type:Article
Title:An optimal order interior penalty discontinuous Galerkin discretization of the compressible Navier-Stokes equations
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Hartmann, RalfUNSPECIFIEDUNSPECIFIED
Houston, PaulUniversity of NottinghamUNSPECIFIED
Date:20 November 2008
Journal or Publication Title:Journal of Computational Physics
Open Access:Yes
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Volume:227
Page Range:pp. 9670-9685
Publisher:Elsevier
Status:Published
Keywords:Finite element methods, discontinuous Galerkin methods, adjoint consistency, compressible Navier-Stokes equations
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:06 Jan 2009
Last Modified:31 Jul 2019 19:23

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