Temporal Artificial Stress Diffusion for Numerical Simulations of Oldroyd-B Fluid Flow

Mathematics

Marília Pires¹  Tomáš Bodnár² 

[1] Department of Mathematics and CIMA-UE, Technology Sciences School, University of Évora, Rua Romão Ramalho, 7000-671 Évora, Portugal;Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67 Prague 1, Czech Republic;

关键词: viscoelastic fluids;    finite element method;    Oldroyd-B model;    numerical diffusion;   

DOI  :  10.3390/math10030404

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown