Temporal artificial stress diffusion for numerical simulations of Oldroyd-B fluid flow

0552865 - MÚ 2023 RIV CH eng J - Journal Article
Pires, M. - Bodnár, Tomáš
Temporal artificial stress diffusion for numerical simulations of Oldroyd-B fluid flow.
Mathematics. Roč. 10, č. 3 (2022), č. článku 404. E-ISSN 2227-7390
R&D Projects: GA ČR(CZ) GA19-04243S
Institutional support: RVO:67985840
Keywords : finite element method * numerical diffusion * Oldroyd-B model * viscoelastic fluids
OECD category: Pure mathematics
Impact factor: 2.4, year: 2022
Method of publishing: Open access
https://doi.org/10.3390/math10030404

This paper presents a numerical evaluation of two different artificial stress diffusion techniques for the stabilization of viscoelastic Oldroyd-B fluid flows at high Weissenberg numbers. The standard artificial diffusion in the form of a Laplacian of the extra stress tensor is compared with a newly proposed approach using a discrete time derivative of the Laplacian of the extra stress tensor. Both methods are implemented in a finite element code and demonstrated in the solution of a viscoelastic fluid flow in a two-dimensional corrugated channel for a range of Weissenberg numbers. The numerical simulations have shown that this new temporal stress diffusion not only efficiently stabilizes numerical simulations, but also vanishes when the solution reaches a steady state. It is demonstrated that in contrast to the standard tensorial diffusion, the temporal artificial stress diffusion does not affect the final solution.
Permanent Link: http://hdl.handle.net/11104/0327958