Modeling of the unsteady flow through a channel with an artificial outflow condition by the Navier–Stokes variational inequality

We prove the global in time existence of a weak solution to the variational inequality of the Navier–Stokes type, simulating the unsteady flow of a viscous fluid through the channel, with the so‐called “do nothing” boundary condition on the outflow. The condition that the solution lies in a certain...

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Bibliographic Details
Published in:Mathematische Nachrichten 2018-08, Vol.291 (11-12), p.1801-1814
Main Authors: Kračmar, Stanislav, Neustupa, Jiří
Format: Article
Language:English
Subjects:
35Q30
65N30
76D05
Boundary conditions
Computational fluid dynamics
Computer simulation
Flow control
Fluid flow
Inequality
Navier-Stokes equations
Navier–Stokes equation
Outflow
Portfolio management
Unsteady flow
variational inequality
Viscous fluids
“do nothing” outflow boundary conditions
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Summary:We prove the global in time existence of a weak solution to the variational inequality of the Navier–Stokes type, simulating the unsteady flow of a viscous fluid through the channel, with the so‐called “do nothing” boundary condition on the outflow. The condition that the solution lies in a certain given, however arbitrarily large, convex set and the use of the variational inequality enables us to derive an energy‐type estimate of the solution. We also discuss the use of a series of other possible outflow “do nothing” boundary conditions.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201700228