On Multiple Solutions to the Steady Flow of Incompressible Fluids Subject to Do-nothing or Constant Traction Boundary Conditions on Artificial Boundaries

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11310%2F20%3A10406427" target="_blank" >RIV/00216208:11310/20:10406427 - isvavai.cz</a>

Alternative codes found

RIV/00216208:11320/20:10406427

Result on the web

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Eg27N.z1KV" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Eg27N.z1KV</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00021-019-0472-z" target="_blank" >10.1007/s00021-019-0472-z</a>

Result language

angličtina

Original language name

On Multiple Solutions to the Steady Flow of Incompressible Fluids Subject to Do-nothing or Constant Traction Boundary Conditions on Artificial Boundaries

Original language description

The boundary conditions prescribing the constant traction or the so-called do-nothing conditions are frequently taken on artificial boundaries in the numerical simulations of steady flow of incompressible fluids, despite the fact that they do not facilitate a well-posed problem, not allowing to establish the standard energy estimates. In a pursuit to understand better the possible consequences of using these conditions, we present a particular set of examples of flow problems, where we find none or two analytical or numerical solutions. Namely, we consider problems where the flow connects two such artificial boundaries. In the simple case of the isotropic radial flows where both steady and unsteady analytical solutions are derived easily, we demonstrate that while for some (large) boundary data all unsteady solutions blow up in finite time, for other data (including small or trivial) the unsteady flows either converge asymptotically to one of two steady solutions, or blow up in finite time, depending on the initial state. We then document the very same behavior of the numerical solutions for planar flow in a diverging channel. Finally, we provide an illustrative example of two steady numerical solutions to the flow in a three-dimensional bifurcating tube, where the inflow velocity is prescribed at the inlet, while the two outlets are treated by the do-nothing boundary condition.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10102 - Applied mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2020

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Mathematical Fluid Mechanics

ISSN

1422-6928

e-ISSN

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Volume of the periodical

22

Issue of the periodical within the volume

11

Country of publishing house

CH - SWITZERLAND

Number of pages

18

Pages from-to

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UT code for WoS article

000515533600008

EID of the result in the Scopus database

2-s2.0-85077028491