A sparse optimal closure for a reduced-order model of wall-bounded turbulence
File(s)
Accepted version
Author(s)
Khoo, Zhao Chua
Chan, Chi Hin
Hwang, Yongyun
Type
Journal Article
Abstract
In the present study, a set of physics-informed and data-driven approaches are examined towards the development of an accurate reduced-order model for a turbulent plane Couette flow. Based on the utilisation of the proper orthogonal decomposition (POD), a particular focus is given to the development of a reduced-order model where the number of POD modes are not large enough to cover the full dynamics of the given turbulent state, the situation directly relevant to the reduced-order modelling for turbulent flows. Starting from the conventional Galerkin projection approach ignoring the truncation error, three approaches enhanced by both physics and data are examined: (1) sparse regression of the POD-Galerkin dynamics; (2) Galerkin projection with an empirical eddy-viscosity model; (3) Galerkin projection with an optimal eddy viscosity obtained from a newly proposed sparse regression – an idea applying the sparse identification of nonlinear dynamics framework to an eddy-viscosity model. The sparse regression of the POD-Galerkin dynamics does not perform well, as the number of POD modes for the given chaotic dynamics appears to be too small. While the unsatisfactory performance of the Galerkin projection model with an empirical eddy viscosity is observed, the newly proposed approach, which combines the concept of an optimal eddy-viscosity closure with a sparse regression, more accurately approximates the chaotic dynamics than the other reduced-order models considered. This is demonstrated with the mean and time scales of the POD mode amplitudes as well as the first- and second-order turbulence statistics.
Date Issued
2022-05-25
Date Acceptance
2022-01-31
Citation
Journal of Fluid Mechanics, 2022, 939
ISSN
0022-1120
Publisher
Cambridge University Press
Journal / Book Title
Journal of Fluid Mechanics
Volume
939
Copyright Statement
© The Author(s), 2022. Published by Cambridge University Press. . This is a pre-copy-editing, author-produced version of an article accepted for publication in Journal of Fluid Mechanics following peer review. The definitive publisher-authenticated version is available online at: https://doi.org/10.1017/jfm.2022.161
Sponsor
The Leverhulme Trust
Engineering & Physical Science Research Council (E
Engineering & Physical Science Research Council (E
Grant Number
RPG-2019-123
EP/T009365/1
EP/V502354/1
Subjects
Fluids & Plasmas
01 Mathematical Sciences
09 Engineering
Publication Status
Published
Article Number
ARTN A11