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A ‘poor man's Navier–Stokes equation’: derivation and numerical experiments—the 2‐D case
Author(s) -
McDonough J. M.,
Huang M. T.
Publication year - 2004
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.657
Subject(s) - bifurcation , mathematics , compressibility , galerkin method , algebraic number , navier–stokes equations , simple (philosophy) , large eddy simulation , mathematical analysis , scale (ratio) , statistical physics , nonlinear system , physics , mechanics , turbulence , philosophy , epistemology , quantum mechanics
We present a systematic derivation of a discrete dynamical system directly from the two‐dimensional incompressible Navier–Stokes equations via a Galerkin procedure and provide a detailed numerical investigation (covering more than 107 cases) of the characteristic behaviours exhibited by the discrete mapping for specified combinations of the four bifurcation parameters. We show that this simple 2‐D algebraic map, which consists of a bilinearly coupled pair of logistic maps, can produce essentially any (temporal) behaviour observed either experimentally or computationally in incompressible Navier–Stokes flows as the bifurcation parameters are varied in pairs over their ranges of stable behaviours. We conclude from this that such discrete dynamical systems deserve consideration as sources of temporal fluctuations in synthetic‐velocity forms of subgrid‐scale models for large‐eddy simulation. Copyright © 2004 John Wiley & Sons, Ltd.