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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

1 Citation (Scopus)

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.

Original language	English
Title of host publication	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)
Pages	AIAA-2013-3085
DOIs	https://doi.org/10.2514/6.2013-3085
Publication status	Published - 13 Sept 2013
Event	21st AIAA Computational Fluid Dynamics Conference - San Diego, CA, United States Duration: 24 Jun 2013 → 27 Jun 2013

Conference

Conference	21st AIAA Computational Fluid Dynamics Conference
Country/Territory	United States
City	San Diego, CA
Period	24/06/13 → 27/06/13

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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.",

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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), pp. AIAA-2013-3085, 21st AIAA Computational Fluid Dynamics Conference, San Diego, CA, United States, 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. p. AIAA-2013-3085.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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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.

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ER -

Runge-Kutta methods for the incompressible Navier-Stokes equations

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