JournalsaihpcVol. 34, No. 2pp. 483–508

Viscoelastic flows in a rough channel: A multiscale analysis

  • Laurent Chupin

    Université Blaise Pascal, Laboratoire de Mathématiques (CNRS UMR 6620), Campus des Cézeaux, 63177 Aubière cedex, France
  • Sébastien Martin

    Université Paris Descartes, Laboratoire MAP5 (CNR SUMR 8145), 45 rue des Saints-Pères, 75270 Paris cedex 06, France
Viscoelastic flows in a rough channel: A multiscale analysis cover
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Abstract

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 ε1\varepsilon \ll 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.

Cite this article

Laurent Chupin, Sébastien Martin, Viscoelastic flows in a rough channel: A multiscale analysis. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 2, pp. 483–508

DOI 10.1016/J.ANIHPC.2016.01.002