Conserving elastic turbulence numerically using artificial diffusivity

Abstract

To simulate elastic turbulence, where viscoelasticity dominates, numerical solvers introduce an artificial stress diffusivity term to handle the steep polymer stress gradients that ensue. This has recently been shown [Gupta & Vincenzi, J. Fluid Mech. 870, 405-418 (2019); Dzanic, From & Sauret, J. Fluid Mech. 937, A31 (2022)] to introduce unphysical artifacts with a detrimental impact on simulations. In this Letter, we propose that artificial diffusion is limited to regions where stress gradients are steep instead of seeking the zero-diffusivity limit. Through the cellular forcing and four-roll mill problem, we demonstrate that this modified artificial diffusivity is devoid of unphysical artifacts, allowing all features of elastic turbulence to be retained. Results are found to conform with direct simulations, reducing the impact of artificial diffusivity from a qualitative scale to a quantitative scale while only requiring a fraction of the numerical resolution.

arXiv commentTo be published in Phys. Rev. E Letters

References in corpus (7)

• Elastic turbulence in a polymer solution flow
• Elastic turbulence in curvilinear flows of polymer solutions
• Two-dimensional elastic turbulence
• Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction
• Effect of polymer-stress diffusion in the numerical simulation of elastic turbulence
• Self-sustained elastoinertial Tollmien-Schlichting waves
• Elastic turbulence in two-dimensional cross-slot viscoelastic flows