A numerical stabilization framework for viscoelastic fluid flow using the finite volume method on general unstructured meshes

TL;DR

This paper introduces a robust finite volume framework for simulating viscoelastic fluid flows on unstructured meshes, effectively addressing high Weissenberg number challenges with enhanced stability and flexibility.

Contribution

It presents a general stabilization framework that combines various rheological models and stabilization techniques, with a novel stress interpolation correction for velocity-stress coupling.

Findings

Framework is robust across a wide range of Weissenberg numbers.

Significantly alleviates the high Weissenberg number problem.

Demonstrates accurate results through mesh convergence studies.

Abstract

A robust finite volume method for viscoelastic flow analysis on general unstructured meshes is developed. It is built upon a general-purpose stabilization framework for high Weissenberg number flows. The numerical framework provides full combinatorial flexibility between different kinds of rheological models on the one hand, and effective stabilization methods on the other hand. A special emphasis is put on the velocity-stress-coupling on co-located computational grids. Using special face interpolation techniques, a semi-implicit stress interpolation correction is proposed to correct the cell-face interpolation of the stress in the divergence operator of the momentum balance. Investigating the entry-flow problem of the 4:1 contraction benchmark, we demonstrate that the numerical methods are robust over a wide range of Weissenberg numbers and significantly alleviate the high Weissenberg number problem. The accuracy of the results is evaluated in a detailed mesh convergence study.