Is a UCM fluid flow near a stationary point always singular? - Part II

TL;DR

This paper investigates whether UCM viscoelastic fluid flows near stationary points are inherently singular, providing analytical and numerical evidence that such flows are regular at stagnation points, especially at high Weissenberg numbers.

Contribution

It offers new analytical and numerical insights showing that UCM flows near stagnation points are not necessarily singular, challenging previous assumptions of invincibility of such singularities.

Findings

Flows are regular at stagnation points at high Weissenberg numbers

Numerical and asymptotic solutions show good agreement

Contradicts the view that singularities are unavoidable in UCM flows

Abstract

Oftentimes observed divergence of numerical solutions to benchmark flows of the UCM viscoelastic fluid is a known and widely discussed issue. Some authors consider such singularities 'invincible'. Following the previous research, the article gives more arguments against this position, for which it considers two typical flows with a stagnation point, often a place of the flows' singularity. For the flow spread over a wall, as previously for the counterflows, numerical and asymptotic analytical solutions are presented. Both kinds of flows turn out regular in the stagnation points, in particular, for high Weissenberg numbers. A good accordance is demonstrated between the analytical and numerical results.