The Leray-αβ-deconvolution model: Energy analysis and numerical algorithms

Abigail L. Bowers, Tae Yeon Kim, Monika Neda, Leo G. Rebholz, Eliot Fried

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We study a fluid-flow regularization based on the Leray-α model that uses deconvolution in the nonlinear term and dissipation scale modeling in the viscous term. In particular, we establish that this 'Leray-αβ-deconvolution model' has an energy cascade with an enhanced energy dissipation that enlarges the microscale of the model relative to the Kolmogorov microscale, but captures more of the small scales than does the Leray-α model. These theoretical results are confirmed via numerically determined energy spectra. We also propose and analyze an efficient finite-element algorithm method for the proposed model. In addition to establishing stability of the method, the essential ingredient for any numerical study, we demonstrate convergence to a Navier-Stokes solution. A numerical experiment for the two-dimensional flow around an obstacle is also discussed. Results show that enhancing the Leray-α model with deconvolution and dissipation scale modeling can significantly increase accuracy.

Original languageBritish English
Pages (from-to)1225-1241
Number of pages17
JournalApplied Mathematical Modelling
Volume37
Issue number3
DOIs
StatePublished - 1 Feb 2013

Keywords

  • Approximate deconvolution
  • Dissipation scale modeling
  • Finite element method
  • Leray model
  • Navier-Stokes equations

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