An Optimal Order Interior Penalty Discontinuous Galerkin Discretization of the Compressible Navier-Stokes Equations
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 evaluat...
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Elsevier
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| author | Hartmann, Ralf Houston, Paul |
| author_facet | Hartmann, Ralf Houston, Paul |
| author_sort | Hartmann, Ralf |
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| description | 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_2-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 & Rebay, cf. [11], the standard SIPG method outlined in [25], and an NIPG variant of the new scheme will be undertaken. |
| first_indexed | 2025-11-14T18:13:04Z |
| format | Article |
| id | nottingham-714 |
| institution | University of Nottingham Malaysia Campus |
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| last_indexed | 2025-11-14T18:13:04Z |
| publisher | Elsevier |
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| spelling | nottingham-7142020-05-04T20:34:37Z https://eprints.nottingham.ac.uk/714/ An Optimal Order Interior Penalty Discontinuous Galerkin Discretization of the Compressible Navier-Stokes Equations Hartmann, Ralf Houston, Paul 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_2-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 & Rebay, cf. [11], the standard SIPG method outlined in [25], and an NIPG variant of the new scheme will be undertaken. Elsevier Article NonPeerReviewed Hartmann, Ralf and Houston, Paul An Optimal Order Interior Penalty Discontinuous Galerkin Discretization of the Compressible Navier-Stokes Equations. Journal of Computational Physics . ISSN 0021-9991 (Submitted) Optimal Order Galerkin Discretization Compressible Navier-Stokes Equations http://www.elsevier.com/wps/find/journaldescription.cws_home/622866/description#description |
| spellingShingle | Optimal Order Galerkin Discretization Compressible Navier-Stokes Equations Hartmann, Ralf Houston, Paul An Optimal Order Interior Penalty Discontinuous Galerkin Discretization of the Compressible Navier-Stokes Equations |
| title | An Optimal Order Interior Penalty Discontinuous Galerkin Discretization of the Compressible Navier-Stokes Equations |
| title_full | An Optimal Order Interior Penalty Discontinuous Galerkin Discretization of the Compressible Navier-Stokes Equations |
| title_fullStr | An Optimal Order Interior Penalty Discontinuous Galerkin Discretization of the Compressible Navier-Stokes Equations |
| title_full_unstemmed | An Optimal Order Interior Penalty Discontinuous Galerkin Discretization of the Compressible Navier-Stokes Equations |
| title_short | An Optimal Order Interior Penalty Discontinuous Galerkin Discretization of the Compressible Navier-Stokes Equations |
| title_sort | optimal order interior penalty discontinuous galerkin discretization of the compressible navier-stokes equations |
| topic | Optimal Order Galerkin Discretization Compressible Navier-Stokes Equations |
| url | https://eprints.nottingham.ac.uk/714/ https://eprints.nottingham.ac.uk/714/ |