Viscoelastic Flows In A Rough Channel: A Multiscale Analysis

TL;DR

This paper develops a multiscale asymptotic analysis for viscoelastic flows in rough channels, providing a rigorous mathematical framework that captures the effects of boundary roughness on flow behavior.

Contribution

It introduces a novel multiscale asymptotic expansion for viscoelastic flows in rough domains, rigorously justified at any order, linking global and boundary-layer problems.

Findings

Asymptotic expansion accurately models flow in rough channels.

Optimal error bounds are established for the expansion.

Framework applicable to complex viscoelastic flow problems.

Abstract

In this paper, we consider viscoelastic flows in a rough domain (with typical roughness patterns of size $\epsilon$ < 1). We present and rigorously justify an asymptotic expansion with respect to $\epsilon$, 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.