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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Main Authors: Hartmann, Ralf, Houston, Paul
Format: Article
Published: 2005
Subjects:
Online Access:https://eprints.nottingham.ac.uk/164/
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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.
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institution_category Local University
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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/