Inertia-driven and elastoinertial viscoelastic turbulent channel flow simulated with a hybrid pseudo-spectral/finite-difference numerical scheme

TL;DR

This paper introduces a hybrid numerical scheme combining spectral and finite-difference methods to simulate viscoelastic turbulent flows accurately without artificial diffusion, revealing the impact of numerical methods on flow regimes.

Contribution

A novel hybrid pseudo-spectral/finite-difference numerical approach that stabilizes simulations of viscoelastic turbulence without artificial diffusion, enabling accurate study of elastoinertial turbulence.

Findings

Stable simulations at high Weissenberg numbers without artificial diffusion.

Artificial diffusion suppresses elastoinertial turbulence in simulations.

Hybrid method accurately captures flow statistics and structures.

Abstract

Numerical simulation of viscoelastic flows is challenging because of the hyperbolic nature of viscoelastic constitutive equations. Despite their superior accuracy and efficiency, pseudo-spectral methods require the introduction of artificial diffusion (AD) for numerical stability in hyperbolic problems, which alters the physical nature of the system. This study presents a hybrid numerical procedure that integrates an upwind total variation diminishing (TVD) finite-difference scheme, which is known for its stability in hyperbolic problems, for the polymer stress convection term into an overall pseudo-spectral numerical framework. Numerically stable solutions are obtained for Weissenberg number well beyond O(100) without the need for either global or local AD. Side-by-side comparison with an existing pseudo-spectral code reveals the impact of AD, which is shown to differ drastically between flow regimes. Elastoinertial turbulence (EIT) becomes unphysically suppressed when AD, at any level necessary for stabilizing the pseudo-spectral method, is used. This is attributed to the importance of sharp stress shocks in its self-sustaining cycles. Nevertheless , in regimes dominated by the classical inertial mechanism for turbulence generation, there is still an acceptable range of AD that can be safely used to predict the statistics, dynamics, and structures of drag-reduced turbulence. Detailed numerical resolution analysis of the new hybrid method, especially for capturing the EIT states, is also presented.