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

Marília Pires and Tomáš Bodnár
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Marília Pires: Department of Mathematics and CIMA-UE, Technology Sciences School, University of Évora, Rua Romão Ramalho, 7000-671 Évora, Portugal
Tomáš Bodnár: Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67 Prague 1, Czech Republic

Mathematics, 2022, vol. 10, issue 3, 1-20

Abstract: 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.

Keywords: viscoelastic fluids; finite element method; Oldroyd-B model; numerical diffusion (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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