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SUMMARY:Elastic-turbulence simulations: a cautionary tale - Dario Vincenzi
  (CNRS (Centre national de la recherche scientifique))
DTSTART:20240613T104000Z
DTEND:20240613T113000Z
UID:TALK214723@talks.cam.ac.uk
DESCRIPTION:\n\n\n\nSimulations of elastic turbulence\, the chaotic flow o
 f highly elastic and inertialess polymer solutions\, are plagued by numeri
 cal difficulties: The chaotically advected polymer conformation tensor dev
 elops extremely large gradients and can loose its positive definiteness\, 
 which triggers numerical instabilities. While efforts to tackle these issu
 es have produced a plethora of specialized techniques&mdash\;tensor decomp
 ositions\, artificial diffusion\, and shock-capturing advection schemes&md
 ash\;we still lack an unambiguous route to accurate and efficient simulati
 ons. In this work\, we show that even when a simulation is numerically sta
 ble\, maintaining positive-definiteness and displaying the expected chaoti
 c fluctuations\, it can still suffer from errors significant enough to dis
 tort the large-scale dynamics and flow-structures. We focus on two-dimensi
 onal simulations of the Oldroyd-B and FENE-P equations\, driven by a large
 -scale cellular body-forcing. We first compare two positivity-preserving d
 ecompositions of the conformation tensor: symmetric square root (SSR) and 
 Cholesky with a logarithmic transformation (Cholesky-log). While both simu
 lations yield chaotic flows\, only the latter preserves the pattern of the
  forcing\, i.e.\, its fluctuating vortical cells remain ordered in a latti
 ce. In contrast\, the SSR simulation exhibits distorted vortical cells whi
 ch shrink\, expand and reorient constantly. To identify the accurate simul
 ation\, we appeal to a hitherto overlooked mathematical bound on the deter
 minant of the conformation tensor\, which unequivocally rejects the SSR si
 mulation. Importantly\, the accuracy of the Cholesky-log simulation is sho
 wn to arise from the logarithmic transformation. We then consider local ar
 tificial diffusion\, a potential low-cost alternative to high-order advect
 ion schemes. Unfortunately\, the diffusive smearing of polymer stress in r
 egions of intense stretching is found to destabilize the adjacent vortices
 \, thereby modifying the global dynamics. We end with an example\, showing
  how the spurious large-scale motions\, identified here\, contaminate pred
 ictions of scalar mixing.\n\n\n\n
LOCATION:Seminar Room 1\, Newton Institute
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