New wall laws for the unsteady incompressible Navier-Stokes equations on rough domains

Gabriel R. Barrenechea, Patrick Le Tallec, Frédéric Valentin

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Different effective boundary conditions or wall laws for unsteady incompressible Navier-Stokes equations over rough domains are derived in the laminar setting. First and second order unsteady wall laws are proposed using two scale asymptotic expansion techniques. The roughness elements are supposed to be periodic and the influence of the rough boundary is incorporated through constitutive constants. These constants are obtained by solving steady Stokes problems and so they are calculated only once. Numerical tests are presented to validate and compare the proposed boundary conditions.
LanguageEnglish
Pages177-203
Number of pages26
JournalESAIM: Mathematical Modelling and Numerical Analysis
Volume36
Issue number2
DOIs
Publication statusPublished - 2002

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Incompressible Navier-Stokes Equations
Navier Stokes equations
Rough
Boundary conditions
Stokes Problem
Roughness
Asymptotic Expansion
Surface roughness
First-order
Influence

Keywords

  • Wall law
  • Navier-Stokes equations
  • asymptotic analysis
  • rough boundary
  • mathematical modelling
  • numerical analysis

Cite this

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abstract = "Different effective boundary conditions or wall laws for unsteady incompressible Navier-Stokes equations over rough domains are derived in the laminar setting. First and second order unsteady wall laws are proposed using two scale asymptotic expansion techniques. The roughness elements are supposed to be periodic and the influence of the rough boundary is incorporated through constitutive constants. These constants are obtained by solving steady Stokes problems and so they are calculated only once. Numerical tests are presented to validate and compare the proposed boundary conditions.",
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New wall laws for the unsteady incompressible Navier-Stokes equations on rough domains. / Barrenechea, Gabriel R.; Le Tallec, Patrick; Valentin, Frédéric.

In: ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 36, No. 2, 2002, p. 177-203.

Research output: Contribution to journalArticle

TY - JOUR

T1 - New wall laws for the unsteady incompressible Navier-Stokes equations on rough domains

AU - Barrenechea, Gabriel R.

AU - Le Tallec, Patrick

AU - Valentin, Frédéric

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N2 - Different effective boundary conditions or wall laws for unsteady incompressible Navier-Stokes equations over rough domains are derived in the laminar setting. First and second order unsteady wall laws are proposed using two scale asymptotic expansion techniques. The roughness elements are supposed to be periodic and the influence of the rough boundary is incorporated through constitutive constants. These constants are obtained by solving steady Stokes problems and so they are calculated only once. Numerical tests are presented to validate and compare the proposed boundary conditions.

AB - Different effective boundary conditions or wall laws for unsteady incompressible Navier-Stokes equations over rough domains are derived in the laminar setting. First and second order unsteady wall laws are proposed using two scale asymptotic expansion techniques. The roughness elements are supposed to be periodic and the influence of the rough boundary is incorporated through constitutive constants. These constants are obtained by solving steady Stokes problems and so they are calculated only once. Numerical tests are presented to validate and compare the proposed boundary conditions.

KW - Wall law

KW - Navier-Stokes equations

KW - asymptotic analysis

KW - rough boundary

KW - mathematical modelling

KW - numerical analysis

U2 - 10.1051/m2an:2002009

DO - 10.1051/m2an:2002009

M3 - Article

VL - 36

SP - 177

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JF - ESAIM: Mathematical Modelling and Numerical Analysis

SN - 0764-583X

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