High Order Finite Element Discretization of the Compressible Euler and Navier-Stokes Equations
We present a high order accurate streamline-upwind/Petrov-Galerkin (SUPG) algorithm for the solution of the compressible Euler and Navier-Stokes equations. The flow equations are written in terms of entropy variables which result in symmetric flux Jacobian matrices and a dimensionally consistent Fin...
| Main Authors: | , , |
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| Format: | Technical Report |
| Language: | en_US |
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Aerospace Computational Design Laboratory, Dept. of Aeronautics & Astronautics, Massachusetts Institute of Technology
2010
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| Online Access: | http://hdl.handle.net/1721.1/57597 |
| _version_ | 1811088659332464640 |
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| author | Wong, J. S. Darmofal, D. L. Peraire, J. |
| author_facet | Wong, J. S. Darmofal, D. L. Peraire, J. |
| author_sort | Wong, J. S. |
| collection | MIT |
| description | We present a high order accurate streamline-upwind/Petrov-Galerkin (SUPG) algorithm for the solution of the compressible Euler and Navier-Stokes equations. The flow equations are written in terms of entropy variables which result in symmetric flux Jacobian matrices and a dimensionally consistent Finite Element discretization. We show that solutions derived from quadratic element approximation are of superior quality next to their linear element counterparts. We demonstrate this through numerical solutions of both classical test cases as well as examples more practical in nature. |
| first_indexed | 2024-09-23T14:05:30Z |
| format | Technical Report |
| id | mit-1721.1/57597 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:05:30Z |
| publishDate | 2010 |
| publisher | Aerospace Computational Design Laboratory, Dept. of Aeronautics & Astronautics, Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/575972019-04-13T00:05:31Z High Order Finite Element Discretization of the Compressible Euler and Navier-Stokes Equations Wong, J. S. Darmofal, D. L. Peraire, J. Euler and Navier-Stokes equations Petrov-Galerkin entropy variables symmetric flux jacobian matrices high order accuracy We present a high order accurate streamline-upwind/Petrov-Galerkin (SUPG) algorithm for the solution of the compressible Euler and Navier-Stokes equations. The flow equations are written in terms of entropy variables which result in symmetric flux Jacobian matrices and a dimensionally consistent Finite Element discretization. We show that solutions derived from quadratic element approximation are of superior quality next to their linear element counterparts. We demonstrate this through numerical solutions of both classical test cases as well as examples more practical in nature. 2010-08-27T19:38:39Z 2010-08-27T19:38:39Z 2001-04 Technical Report http://hdl.handle.net/1721.1/57597 en_US ACDL Technical Reports;FDRL TR-01-1 application/pdf Aerospace Computational Design Laboratory, Dept. of Aeronautics & Astronautics, Massachusetts Institute of Technology |
| spellingShingle | Euler and Navier-Stokes equations Petrov-Galerkin entropy variables symmetric flux jacobian matrices high order accuracy Wong, J. S. Darmofal, D. L. Peraire, J. High Order Finite Element Discretization of the Compressible Euler and Navier-Stokes Equations |
| title | High Order Finite Element Discretization of the Compressible Euler and Navier-Stokes Equations |
| title_full | High Order Finite Element Discretization of the Compressible Euler and Navier-Stokes Equations |
| title_fullStr | High Order Finite Element Discretization of the Compressible Euler and Navier-Stokes Equations |
| title_full_unstemmed | High Order Finite Element Discretization of the Compressible Euler and Navier-Stokes Equations |
| title_short | High Order Finite Element Discretization of the Compressible Euler and Navier-Stokes Equations |
| title_sort | high order finite element discretization of the compressible euler and navier stokes equations |
| topic | Euler and Navier-Stokes equations Petrov-Galerkin entropy variables symmetric flux jacobian matrices high order accuracy |
| url | http://hdl.handle.net/1721.1/57597 |
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