Eddy viscosity of cellular flows by upscaling

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Abstract

The eddy viscosity is the tensor in the equation that governs the transport of the large-scale (modulational) perturbations of small-scale stationary flows. As an approximation to eddy viscosity the effective tensor, that arises in the limit as the ratio between the scales E → 0, can be considered. We are interested here in the accuracy of this approximation. We present results of computational investigation of eddy viscosity, when the small-scale flows are cellular, special periodic stationary flows with the stream function φ = sin y1 sin y2 + δ cos y1 cos y2, y = x/E, 0 ≤ δ ≤ 1. For small E we used a numerical upscaling method. We designed this method so that it captures the modulational perturbations for any E with O(E2) accuracy and independent of E complexity.

Original languageEnglish (US)
Pages (from-to)341-354
Number of pages14
JournalJournal of Computational Physics
Volume195
Issue number1
DOIs
Publication statusPublished - Mar 20 2004

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All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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