Viscoelastic Flows In A Rough Channel: A Multiscale Analysis

In this paper, we consider viscoelastic flows in a rough domain (with typical 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.

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