Braack, Malte and Mucha, Piotr Boguslaw (2014) DIRECTIONAL DO-NOTHING CONDITION FOR THE NAVIER-STOKES EQUATIONS. Journal of Computational Mathematics, 32 (5). pp. 507-521. DOI 10.4208/jcm.1405-m4347.

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The numerical solution of flow problems usually requires bounded domains although the physical problem may take place in an unbounded or substantially larger domain. In this case, artificial boundaries are necessary. A well established artificial boundary condition for the Navier-Stokes equations discretized by finite elements is the "do-nothing" condition. The reason for this is the fact that this condition appears automatically in the variational formulation after partial integration of the viscous term and the pressure gradient. This condition is one of the most established outflow conditions for Navier-Stokes but there are very few analytical insight into this boundary condition. We address the question of existence and stability of weak solutions for the Navier-Stokes equations with a "directional do-nothing" condition. In contrast to the usual "do-nothing" condition this boundary condition has enhanced stability properties. In the case of pure outflow, the condition is equivalent to the original one, whereas in the case of inflow a dissipative effect appears. We show existence of weak solutions and illustrate the effect of this boundary condition by computation of steady and non-steady flows.

Document Type: Article
Additional Information: Times Cited: 0 0
Keywords: Boundary conditions, Navier-Stokes, Outflow condition, Existence
Research affiliation: OceanRep > The Future Ocean - Cluster of Excellence > FO-R11
Kiel University
Kiel University > Kiel Marine Science
OceanRep > The Future Ocean - Cluster of Excellence
Refereed: Yes
Open Access Journal?: No
DOI etc.: 10.4208/jcm.1405-m4347
ISSN: 0254-9409
Projects: Future Ocean
Date Deposited: 30 Mar 2015 12:01
Last Modified: 23 Sep 2019 20:18

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