Runge-Kutta methods for the incompressible Navier-Stokes equations

Benjamin Sanderse, Barry Koren

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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 languageEnglish
Title of host publicationProceedings of the 21st AIAA Computational Fluid Dynamics Conference (San Diego CA, USA, June 24-27, 2013)
PublisherAmerican Institute of Aeronautics and Astronautics Inc. (AIAA)
PagesAIAA-2013-3085-
DOIs
Publication statusPublished - 13 Sep 2013
Event21st AIAA Computational Fluid Dynamics Conference - San Diego, CA, United States
Duration: 24 Jun 201327 Jun 2013

Conference

Conference21st AIAA Computational Fluid Dynamics Conference
CountryUnited States
CitySan Diego, CA
Period24/06/1327/06/13

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