Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations I: Method Formulation
In this article we consider the development of discontinuous Galerkin finite element methods for the numerical approximation of the compressible Navier-Stokes equations. For the discretization of the leading order terms, we propose employing the generalization of the symmetric version of the interio...
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| Format: | Article |
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2005
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| Online Access: | https://eprints.nottingham.ac.uk/164/ |
| _version_ | 1848790352819912704 |
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| author | Hartmann, Ralf Houston, Paul |
| author_facet | Hartmann, Ralf Houston, Paul |
| author_sort | Hartmann, Ralf |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | In this article we consider the development of discontinuous Galerkin finite element methods for the numerical approximation of the compressible Navier-Stokes equations. For the discretization of the leading order terms, we propose employing the generalization of the symmetric version of the interior penalty method, originally developed for the numerical approximation of linear self-adjoint second-order elliptic partial differential equations. In order to solve the resulting system of nonlinear equations, we exploit a (damped) Newton-GMRES algorithm. Numerical experiments demonstrating the practical performance of the proposed discontinuous Galerkin method with higher-order polynomials are presented. |
| first_indexed | 2025-11-14T18:11:15Z |
| format | Article |
| id | nottingham-164 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:11:15Z |
| publishDate | 2005 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-1642020-05-04T20:30:33Z https://eprints.nottingham.ac.uk/164/ Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations I: Method Formulation Hartmann, Ralf Houston, Paul In this article we consider the development of discontinuous Galerkin finite element methods for the numerical approximation of the compressible Navier-Stokes equations. For the discretization of the leading order terms, we propose employing the generalization of the symmetric version of the interior penalty method, originally developed for the numerical approximation of linear self-adjoint second-order elliptic partial differential equations. In order to solve the resulting system of nonlinear equations, we exploit a (damped) Newton-GMRES algorithm. Numerical experiments demonstrating the practical performance of the proposed discontinuous Galerkin method with higher-order polynomials are presented. 2005-07 Article PeerReviewed Hartmann, Ralf and Houston, Paul (2005) Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations I: Method Formulation. Finite element methods discontinuous Galerkin methods compressible Navier-Stokes equations |
| spellingShingle | Finite element methods discontinuous Galerkin methods compressible Navier-Stokes equations Hartmann, Ralf Houston, Paul Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations I: Method Formulation |
| title | Symmetric Interior Penalty DG Methods for the Compressible
Navier-Stokes Equations I: Method Formulation |
| title_full | Symmetric Interior Penalty DG Methods for the Compressible
Navier-Stokes Equations I: Method Formulation |
| title_fullStr | Symmetric Interior Penalty DG Methods for the Compressible
Navier-Stokes Equations I: Method Formulation |
| title_full_unstemmed | Symmetric Interior Penalty DG Methods for the Compressible
Navier-Stokes Equations I: Method Formulation |
| title_short | Symmetric Interior Penalty DG Methods for the Compressible
Navier-Stokes Equations I: Method Formulation |
| title_sort | symmetric interior penalty dg methods for the compressible
navier-stokes equations i: method formulation |
| topic | Finite element methods discontinuous Galerkin methods compressible Navier-Stokes equations |
| url | https://eprints.nottingham.ac.uk/164/ |