Conserving elastic turbulence numerically using artificial diffusivity

TL;DR

This paper proposes a localized artificial diffusivity method for simulating elastic turbulence, reducing unphysical artifacts and maintaining turbulence features more accurately than traditional approaches.

Contribution

The authors introduce a region-specific artificial diffusivity technique that minimizes unphysical artifacts in elastic turbulence simulations, improving accuracy and efficiency.

Findings

Localized artificial diffusivity reduces unphysical artifacts.

Method retains all features of elastic turbulence.

Requires less numerical resolution for accurate results.

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.