Runge-Kutta methods for the incompressible Navier-Stokes equations

Benjamin Sanderse; Barry Koren

doi:10.2514/6.2013-3085

Runge-Kutta methods for the incompressible Navier-Stokes equations

Benjamin Sanderse, Barry Koren

Center for Analysis, Scientific Computing and Applications

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

1 Citaat (Scopus)

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Time integration of the incompressible Navier-Stokes equations with Runge-Kutta methods is not straightforward due to the differential-algebraic nature of the equations. In this work we investigate the temporal order of accuracy of velocity and pressure for both explicit and implicit methods. This is done by applying existing theory on Runge-Kutta methods for differential-algebraic equations to the incompressible Navier-Stokes equations. We focus on a specific class of Runge-Kutta methods, namely symplectic Runge-Kutta methods, which in the case of the incompressible Navier-Stokes equations are energy-conserving.

Originele taal-2	Engels
Titel	Proceedings of the 21st AIAA Computational Fluid Dynamics Conference (San Diego CA, USA, June 24-27, 2013)
Uitgeverij	American Institute of Aeronautics and Astronautics Inc. (AIAA)
Pagina's	AIAA-2013-3085
DOI's	https://doi.org/10.2514/6.2013-3085
Status	Gepubliceerd - 13 sep. 2013
Evenement	21st AIAA Computational Fluid Dynamics Conference - San Diego, CA, Verenigde Staten van Amerika Duur: 24 jun. 2013 → 27 jun. 2013

Congres

Congres	21st AIAA Computational Fluid Dynamics Conference
Land/Regio	Verenigde Staten van Amerika
Stad	San Diego, CA
Periode	24/06/13 → 27/06/13

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@inproceedings{4162e7d32157496ebf02c47406d8d29a,

title = "Runge-Kutta methods for the incompressible Navier-Stokes equations",

abstract = "Time integration of the incompressible Navier-Stokes equations with Runge-Kutta methods is not straightforward due to the differential-algebraic nature of the equations. In this work we investigate the temporal order of accuracy of velocity and pressure for both explicit and implicit methods. This is done by applying existing theory on Runge-Kutta methods for differential-algebraic equations to the incompressible Navier-Stokes equations. We focus on a specific class of Runge-Kutta methods, namely symplectic Runge-Kutta methods, which in the case of the incompressible Navier-Stokes equations are energy-conserving.",

author = "Benjamin Sanderse and Barry Koren",

year = "2013",

month = sep,

day = "13",

doi = "10.2514/6.2013-3085",

language = "English",

pages = "AIAA--2013--3085",

booktitle = "Proceedings of the 21st AIAA Computational Fluid Dynamics Conference (San Diego CA, USA, June 24-27, 2013)",

publisher = "American Institute of Aeronautics and Astronautics Inc. (AIAA)",

address = "United States",

note = "21st AIAA Computational Fluid Dynamics Conference ; Conference date: 24-06-2013 Through 27-06-2013",

}

Sanderse, B & Koren, B 2013, Runge-Kutta methods for the incompressible Navier-Stokes equations. in Proceedings of the 21st AIAA Computational Fluid Dynamics Conference (San Diego CA, USA, June 24-27, 2013). American Institute of Aeronautics and Astronautics Inc. (AIAA), blz. AIAA-2013-3085, 21st AIAA Computational Fluid Dynamics Conference, San Diego, CA, Verenigde Staten van Amerika, 24/06/13. https://doi.org/10.2514/6.2013-3085

Runge-Kutta methods for the incompressible Navier-Stokes equations. / Sanderse, Benjamin; Koren, Barry.
Proceedings of the 21st AIAA Computational Fluid Dynamics Conference (San Diego CA, USA, June 24-27, 2013). American Institute of Aeronautics and Astronautics Inc. (AIAA), 2013. blz. AIAA-2013-3085.

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

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AU - Sanderse, Benjamin

AU - Koren, Barry

PY - 2013/9/13

Y1 - 2013/9/13

N2 - Time integration of the incompressible Navier-Stokes equations with Runge-Kutta methods is not straightforward due to the differential-algebraic nature of the equations. In this work we investigate the temporal order of accuracy of velocity and pressure for both explicit and implicit methods. This is done by applying existing theory on Runge-Kutta methods for differential-algebraic equations to the incompressible Navier-Stokes equations. We focus on a specific class of Runge-Kutta methods, namely symplectic Runge-Kutta methods, which in the case of the incompressible Navier-Stokes equations are energy-conserving.

AB - Time integration of the incompressible Navier-Stokes equations with Runge-Kutta methods is not straightforward due to the differential-algebraic nature of the equations. In this work we investigate the temporal order of accuracy of velocity and pressure for both explicit and implicit methods. This is done by applying existing theory on Runge-Kutta methods for differential-algebraic equations to the incompressible Navier-Stokes equations. We focus on a specific class of Runge-Kutta methods, namely symplectic Runge-Kutta methods, which in the case of the incompressible Navier-Stokes equations are energy-conserving.

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BT - Proceedings of the 21st AIAA Computational Fluid Dynamics Conference (San Diego CA, USA, June 24-27, 2013)

PB - American Institute of Aeronautics and Astronautics Inc. (AIAA)

T2 - 21st AIAA Computational Fluid Dynamics Conference

Y2 - 24 June 2013 through 27 June 2013

ER -

Runge-Kutta methods for the incompressible Navier-Stokes equations

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