Comparison of three numerical stabilization techniques of viscoelastic flows: vortex shedding behind a confined cylinder

TL;DR

This paper compares three numerical stabilization techniques for simulating viscoelastic flows past a confined cylinder, highlighting their effects on accuracy and stability across different polymer chain lengths.

Contribution

It evaluates the effectiveness of artificial viscosity, logarithmic reconstruction, and square root tensor methods in viscoelastic flow simulations using the FENE-P model.

Findings

Artificial viscosity slightly affects accuracy for short chains.

Overestimation of drag occurs with artificial dissipation for long chains.

Logarithmic reconstruction shows strong grid dependence and potential unphysical results.

Abstract

In this study, the OpenFOAM platform, based on the finite volume method, is applied to investigate the two-dimensional viscoelastic flow past a circular cylinder. The FENE-P model, which considers the bounded elongation of polymer molecules, is chosen to describe the elastic constitutive relationship of the polymer solution. The maximum molecular chain lengths of L = 10, 50, 100, and 200 are considered, which describe the molecular conformation characteristics of the polymer solution. To improve the numerical instability of the viscoelastic flow simulation, three different methods, i.e., the traditional method (Td) with the addition of artificial viscosity, the logarithmic reconstruction method (Log), and the square root tensor method (Sqrt), are evaluated. The results show that the artificial viscosity has a little effect on the accuracy for the simulation with a small molecular chain length (L = 10). However, for long molecular chain lengths such as L = 100 and L = 200, the addition of artificial dissipation tends to overestimate the drag, which indicates that special caution is needed to incorporate the artificial dissipation in the simulation. Moreover, the logarithmic reconstruction method shows a strong grid-dependent characteristics, which may produce unphysical results.