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arXiv · 2207.06808

Reduced-order Galerkin models of plane Couette flow

André V. G. Cavalieri·Petrônio A. S. Nogueira
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Abstract

Reduced-order models were derived for plane Couette flow using Galerkin projection, with orthonormal basis functions taken as the leading controllability modes of the linearised Navier-Stokes system for a few low wavenumbers. Resulting Galerkin systems comprise ordinary differential equations, with a number of degrees of freedom ranging from 144 to 600, which may be integrated to large times without sign of numerical instability. The reduced-order models so obtained are also found to match statistics of direct numerical simulations at Reynolds number 500 and 1200 with reasonable accuracy, despite a truncation of orders of magnitude in the degrees of freedom of the system. The present models offer thus an interesting compromise between simplicity and accuracy in a canonical wall-bounded flow, with relatively few modes representing coherent structures in the flow and their dominant dynamics.

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André V. G. Cavalieri, Petrônio A. S. Nogueira. 2022-07-14. Reduced-order Galerkin models of plane Couette flow. https://arxiv.org/abs/2207.06808

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