A comparison of stabilisation approaches for finite-volume simulation of viscoelastic fluid flow

Abstract

In this work we compare different stabilisation approaches currently used in the simulation of viscoelastic fluid flow. These approaches are: the both-sides diffusion, the positive definiteness preserving scheme, the log-conformation tensor representation and the symmetry factorisation of the conformation tensor. The evaluation of these approaches is done regarding their implementation complexity, stability, accuracy, efficiency and applicability to complex problems. Their performances are examined for an Oldroyd-B fluid in the test cases of lid-driven cavity, flow past a cylinder and 4:1 contraction flow. We summarise the situations in which the different approaches can be recommended.

Keywords:

• viscoelastic fluid
• collocated finite-volume method
• high Weissenberg number problem
• stabilisation approach
• Oldroyd-B model

Acknowledgements

This work is supported by the ’Excellence Initiative’ of the German Federal and State Governments, the Center of Smart Interfaces and the Graduate School of Computational Engineering at Technische Universität Darmstadt.

Notes

^a Δr and Δs are the grid sizes in radial and tangential direction.

^a values in brackets are the critical values given in the corresponding literature.

^a values in brackets are the relative errors compared with the corresponding extrapolated values.