Pressure-driven flow in thin domains

被引：4

作者：

Fabricius, John ^{[1
]}

Miroshnikova, Elena ^{[1
]}

Tsandzana, Afonso ^{[2
]}

Wall, Peter ^{[1
]}

机构：

[1] Lulea Univ Technol, Dept Engn Sci & Math, SE-97187 Lulea, Sweden

[2] Eduardo Mondlane Univ, Dept Math & Informat, Praca 25 Junho,257 CP 257, Maputo, Mozambique

来源：

ASYMPTOTIC ANALYSIS | 2020年 / 116卷 / 01期

关键词：

Stokes equation; pressure boundary condition; two-scale convergence; thin domain; Bogovskii operator; Korn inequality;

D O I：

10.3233/ASY-191535

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the asymptotic behavior of pressure-driven Stokes flow in a thin domain. By letting the thickness of the domain tend to zero we derive a generalized form of the classical Reynolds-Poiseuille law, i.e. the limit velocity field is a linear function of the pressure gradient. By prescribing the external pressure as a normal stress condition, we recover a Dirichlet condition for the limit pressure. In contrast, a Dirichlet condition for the velocity yields a Neumann condition for the limit pressure.

引用

页码：1 / 26

页数：26

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