Modelling of Hydrophobic Surfaces by the Stokes Problem with the Stick-Slip Boundary Conditions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F17%3APU119694" target="_blank" >RIV/00216305:26210/17:PU119694 - isvavai.cz</a>

Výsledek na webu

<a href="http://fluidsengineering.asmedigitalcollection.asme.org/article.aspx?articleid=2536532" target="_blank" >http://fluidsengineering.asmedigitalcollection.asme.org/article.aspx?articleid=2536532</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1115/1.4034199" target="_blank" >10.1115/1.4034199</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Modelling of Hydrophobic Surfaces by the Stokes Problem with the Stick-Slip Boundary Conditions

Popis výsledku v původním jazyce

Unlike the Navier boundary condition, the present paper deals with the case when the slip of a fluid along the wall may occur only when the shear stress attains certain bound which is given a-priori and does not depend on the solution itself. The mathematical model of the velocity-pressure formulation with this type of the threshold slip boundary condition is given by the so-called variational inequality of the second kind. For its discretization we use P1-bubble/P1 mixed finite elements. The resulting algebraic problem leads to the minimization of a non-differentiable energy function subject to linear equality constraints representing the discrete impermeability and incompressibility condition. To release the former one and to regularize the non-smooth term characterizing the stick-slip behavior of the algebraic formulation, two additional vectors of Lagrange multipliers are introduced. Further, the velocity vector is eliminated and the resulting minimization problem for a quadratic function depending on the dual variables (the discrete pressure, the normal and shear stress) is solved by the interior point type method which is briefly described. To justify the threshhold model and to illustrate the efficiency of the proposed approach, three physically realistic problems are solved and the results are compared with the ones solving the Stokes problem with the Navier boundary condition.

Název v anglickém jazyce

Modelling of Hydrophobic Surfaces by the Stokes Problem with the Stick-Slip Boundary Conditions

Popis výsledku anglicky

Unlike the Navier boundary condition, the present paper deals with the case when the slip of a fluid along the wall may occur only when the shear stress attains certain bound which is given a-priori and does not depend on the solution itself. The mathematical model of the velocity-pressure formulation with this type of the threshold slip boundary condition is given by the so-called variational inequality of the second kind. For its discretization we use P1-bubble/P1 mixed finite elements. The resulting algebraic problem leads to the minimization of a non-differentiable energy function subject to linear equality constraints representing the discrete impermeability and incompressibility condition. To release the former one and to regularize the non-smooth term characterizing the stick-slip behavior of the algebraic formulation, two additional vectors of Lagrange multipliers are introduced. Further, the velocity vector is eliminated and the resulting minimization problem for a quadratic function depending on the dual variables (the discrete pressure, the normal and shear stress) is solved by the interior point type method which is briefly described. To justify the threshhold model and to illustrate the efficiency of the proposed approach, three physically realistic problems are solved and the results are compared with the ones solving the Stokes problem with the Navier boundary condition.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

JOURNAL OF FLUIDS ENGINEERING-TRANSACTIONS OF THE ASME

ISSN

0098-2202

e-ISSN

1528-901X

Svazek periodika

139

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

9

Strana od-do

0112021-0112029

Kód UT WoS článku

000395119200006

EID výsledku v databázi Scopus

2-s2.0-84992391528