Preserving large-scale features in simulations of elastic turbulence
arXiv:2312.09165 · doi:10.1017/jfm.2024.858
Abstract
Simulations of elastic turbulence, the chaotic flow of highly elastic and inertialess polymer solutions, are plagued by numerical difficulties: The chaotically advected polymer conformation tensor develops extremely large gradients and can loose its positive definiteness, which triggers numerical instabilities. While efforts to tackle these issues have produced a plethora of specialized techniques -- tensor decompositions, artificial diffusion, and shock-capturing advection schemes -- we still lack an unambiguous route to accurate and efficient simulations. In this work, we show that even when a simulation is numerically stable, maintaining positive-definiteness and displaying the expected chaotic fluctuations, it can still suffer from errors significant enough to distort the large-scale dynamics and flow-structures. Focusing on two-dimensional simulations of the Oldroyd-B and FENE-P equations, we first compare two decompositions of the conformation tensor: symmetric square root (SSR) and Cholesky with a logarithmic transformation (Cholesky-log). While both simulations yield chaotic flows, only the Cholesky-log preserves the pattern of the forcing, i.e., its vortical cells remain ordered in a lattice as opposed to the vortices of the SSR simulations which shrink, expand and reorient constantly. To identify the accurate simulation, we appeal to a hitherto overlooked mathematical bound on the determinant of the conformation tensor, which unequivocally rejects the SSR simulation. Importantly, the accuracy of the Cholesky-log simulation is shown to arise from the logarithmic transformation. We then consider local artificial diffusion, a potential low-cost alternative to high-order advection schemes, and find unfortunately that it significantly modifies the dynamics. We end with an example, showing how the spurious large-scale motions identified here contaminate predictions of scalar mixing.
arXiv comment24 pages, 11 figures
References in corpus (26)
- Elastic turbulence in a polymer solution flow
- Efficient Mixing at low Reynolds numbers using polymer additives
- Elastic turbulence in curvilinear flows of polymer solutions
- Computing Nearly Singular Solutions Using Pseudo-Spectral Methods
- Frontiers of chaotic advection
- Spectra of turbulence in dilute polymer solutions
- Manifestations of Drag Reduction by Polymer Additives in Decaying, Homogeneous, Isotropic Turbulence
- Two-dimensional elastic turbulence
- Note on Global Regularity for 2D Oldroyd-B Fluids with Diffusive Stress
- Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction
- A continuous pathway between the elasto-inertial and elastic turbulent states in viscoelastic channel flow
- Elastic Alfven waves in elastic turbulence
- Effect of polymer-stress diffusion in the numerical simulation of elastic turbulence
- Elastically driven Kelvin-Helmholtz-like instability in planar channel flow
- Coherent structures in plane channel flow of dilute polymer solutions with vanishing inertia
- Elastic turbulence in two-dimensional Taylor-Couette flows
- Finite-amplitude elastic waves in viscoelastic channel flow from large to zero Reynolds number
- Two-dimensional, homogeneous, isotropic fluid turbulence with polymer additives
- Inertia-driven and elastoinertial viscoelastic turbulent channel flow simulated with a hybrid pseudo-spectral/finite-difference numerical scheme
- Melting of a nonequilibrium vortex crystal in a fluid film with polymers : elastic versus fluid turbulence
- New directions and perspectives in elastic instability and turbulence in various viscoelastic flow geometries without inertia
- Statistical properties of two-dimensional elastic turbulence
- Particle-laden two-dimensional elastic turbulence
- Characterizing elastic turbulence in the three-dimensional von Karman swirling flow using the Oldroyd-B model
- The mean conformation tensor in viscoelastic turbulence
- Elastic turbulence in two-dimensional cross-slot viscoelastic flows