Geodesic
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
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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
Keywords: Viscoelastic fluid, Roughness, Oldroyd model, Boundary layer 
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     title = {Viscoelastic flows in a rough channel: {A} multiscale analysis},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {483--508},
     year = {2017},
     publisher = {Elsevier},
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     number = {2},
     doi = {10.1016/j.anihpc.2016.01.002},
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     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2016.01.002/}
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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

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