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 . 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.
@article{AIHPC_2017__34_2_483_0, author = {Chupin, Laurent and Martin, S\'ebastien}, title = {Viscoelastic flows in a rough channel: {A} multiscale analysis}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {483--508}, publisher = {Elsevier}, volume = {34}, number = {2}, year = {2017}, doi = {10.1016/j.anihpc.2016.01.002}, zbl = {1381.76017}, mrnumber = {3610942}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2016.01.002/} }
TY - JOUR AU - Chupin, Laurent AU - Martin, Sébastien TI - Viscoelastic flows in a rough channel: A multiscale analysis JO - Annales de l'I.H.P. Analyse non linéaire PY - 2017 SP - 483 EP - 508 VL - 34 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2016.01.002/ DO - 10.1016/j.anihpc.2016.01.002 LA - en ID - AIHPC_2017__34_2_483_0 ER -
%0 Journal Article %A Chupin, Laurent %A Martin, Sébastien %T Viscoelastic flows in a rough channel: A multiscale analysis %J Annales de l'I.H.P. Analyse non linéaire %D 2017 %P 483-508 %V 34 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2016.01.002/ %R 10.1016/j.anihpc.2016.01.002 %G en %F AIHPC_2017__34_2_483_0
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://www.numdam.org/articles/10.1016/j.anihpc.2016.01.002/
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