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

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.

Automated summary

This paper presents a numerical evaluation of two different artificial stress diffusion techniques for the stabilization of viscoelastic fluid flows at high Weissenberg numbers. The numerical simulations have shown that the proposed temporal stress diffusion method efficiently stabilizes the simulations and vanishes when the solution reaches a steady state, without affecting the final solution.