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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

—

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

10101 - Pure mathematics

Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

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

Publication year

2017

Confidentiality

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

Name of the periodical

JOURNAL OF FLUIDS ENGINEERING-TRANSACTIONS OF THE ASME

ISSN

0098-2202

e-ISSN

1528-901X

Volume of the periodical

139

Issue of the periodical within the volume

1

Country of publishing house

US - UNITED STATES

Number of pages

9

Pages from-to

0112021-0112029

UT code for WoS article

000395119200006

EID of the result in the Scopus database

2-s2.0-84992391528