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

Author

Listed:
  • Marília Pires

    (Department of Mathematics and CIMA-UE, Technology Sciences School, University of Évora, Rua Romão Ramalho, 7000-671 Évora, Portugal
    Center for Mathematics and Applications (CEMAT), Instituto Superior Técnico, Avenue Rovisco Pais, 1049-001 Lisbon, Portugal
    Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67 Prague 1, Czech Republic)

  • Tomáš Bodnár

    (Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67 Prague 1, Czech Republic
    Department of Technical Mathematics, Faculty of Mechanical Engineering, Czech Technical University in Prague, Karlovo náměstí 13, 121 35 Prague 2, Czech Republic)

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.

Suggested Citation

  • Marília Pires & Tomáš Bodnár, 2022. "Temporal Artificial Stress Diffusion for Numerical Simulations of Oldroyd-B Fluid Flow," Mathematics, MDPI, vol. 10(3), pages 1-20, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:404-:d:735955
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