no. 2
Viscoelastic flows in a rough channel: A multiscale analysis
Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 2, pp. 483-508.

We investigate the influence of the rough boundaries on viscoelastic flows, described by the diffusive Oldroyd model. The fluid domain has a rough wall modeled by roughness patterns of size ε≪1. We present and rigorously justify an asymptotic expansion with respect to ε, at any order, based upon the definition of elementary problems: Oldroyd-type problems at the global scale defined on a smoothened domain and boundary-layer corrector problems. The resulting analysis guarantees optimality with respect to the truncation error and leads to a numerical algorithm which allows us to build the approximation of the solution at any required precision.

DOI : 10.1016/j.anihpc.2016.01.002
Mots clés : Viscoelastic fluid, Roughness, Oldroyd model, Boundary layer 
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Chupin, Laurent; Martin, Sébastien. Viscoelastic flows in a rough channel: A multiscale analysis. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 2, pp. 483-508. doi : 10.1016/j.anihpc.2016.01.002. http://archive.numdam.org/articles/10.1016/j.anihpc.2016.01.002/

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