New Wall Laws for the Unsteady Incompressible Navier-Stokes Equations on Rough Domains
INRIA Projet M3N, Domaine de Voluceau, 78153 Le
Chesnay, France. Gabriel.Barrenechea@inria.fr.
2 Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile.
3 École Polytechnique, 91128 Palaiseau Cedex, France. Patrick.LeTallec@polytechnique.fr.
4 LNCC, Av. Getúlio Vargas, 333, 25651-070 Petrópolis - RJ, Brazil. Valentin@lncc.br.
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.
Mathematics Subject Classification: 76M45 / 76M10
Key words: Wall law / unsteady Navier-Stokes equations / asymptotic analysis / rough boundary.
© EDP Sciences, SMAI, 2002