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

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/00216208:11320/20:10406427

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Journal of Mathematical Fluid Mechanics

ISSN

1422-6928

e-ISSN

—

Svazek periodika

22

Číslo periodika v rámci svazku

11

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

18

Strana od-do

—

Kód UT WoS článku

000515533600008

EID výsledku v databázi Scopus

2-s2.0-85077028491