Is a UCM fluid flow near a stationary point always singular?

TL;DR

This paper investigates whether the common numerical singularities observed in UCM viscoelastic fluid flows near stagnation points are genuine or artifacts, showing that such flows are actually regular at these points.

Contribution

The study provides analytical and numerical evidence that UCM flows near stagnation points are regular, challenging the notion that singularities are inevitable in these flows.

Findings

Flows are regular at stagnation points even at high Weissenberg numbers

Numerical and asymptotic solutions show good agreement

Singularities are not intrinsic to UCM flow near stationary points

Abstract

Frequently 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". The article argues this position, to which end it considers two typical flows with a stagnation point, often a place of the flows' singularity: counterflows and a flow spread over a wall. 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.