An optimization method for chaotic turbulent flow

Chung, Seung Whan; Freund, Jonathan B.

doi:10.1016/j.jcp.2022.111077

Title: An optimization method for chaotic turbulent flow

Journal Article · 17 February 2022 · Journal of Computational Physics

DOI: https://doi.org/10.1016/j.jcp.2022.111077 · OSTI ID:1977280

^[1]; Freund, Jonathan B. ^[2]

Univ. of Illinois at Urbana-Champaign, IL (United States); OSTI
Univ. of Illinois at Urbana-Champaign, IL (United States)

Evidence indicates that quantities-of-interest in some turbulent flows can be controlled despite the overall chaotic dynamics. It is typically thought that this is via relatively deterministic, larger-scale components of the turbulence. However, finding such controls, if they exist, is challenging because chaos causes sensitivity gradients to explode and the search space to become intractably non-convex. This challenge is analyzed, and a penalty method is introduced to cope with it. In the new approach, the time domain is broken into segments approximately matching the chaos time scales, so that the solution within each segment is both physical and relatively deterministic. The initial condition of each segment is included in an adjoint-based gradient optimization, which temporarily introduces artificial Δq discontinuities in the overall solution. The optimization then proceeds in stages with increasing penalization of Δq. The method is developed and illustrated for a logistic map, the Lorenz Equation, and an advection augmented Kuramoto–Sivashinsky Equation. These examples show how the Δq temporarily increases the search scale prior to the strong Δq → 0 penalization that recovers a physical solution. It is then applied to turbulent Kolmogorov flow, for which it also far outperforms a standard adjoint-based gradient search. Finally, the utility of such an optimized chaotic solution is discussed.

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Research Organization:: Univ. of Illinois at Urbana-Champaign, IL (United States)

Sponsoring Organization:: USDOE; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0002374; NA0003963

OSTI ID:: 1977280

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 457; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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