Numerical observations on the continuous spectrum of the linearized viscoelastic operator in shear dominated complex flows

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12 Scopus citations

Abstract

The eigenspectrum of the viscoelastic operator of the upper convected Maxwell (UCM) model in two-dimensional mixed-kinematic flows without internal stagnation points is contained on a line with real part given by - 1/De, where De denotes the Deborah number [9]. We examine the manifestation of this continuous spectrum in numerical simulations of viscoelastic journal bearing and eccentric Dean flows using a pseudo-spectral Chebyshev-Fourier collocation technique. Our numerical results show that for a given set of geometric parameters the maximum imaginary part of the continuous spectrum increases with the largest wavenumber that can be accomodated by the mesh. Hence, increasing azimuthal resolution for a given eccentricity introduces higher wavenumbers leading to an overall convergence that is poorer than that obtained for a coarser mesh. The eigenfunctions exhibit singular behavior in both the wall-normal and azimuthal directions. The locations of these singularities depend on the imaginary part of the eigenvalue. (C) 2000 Elsevier Science B.V. All rights reserved.

Original languageEnglish (US)
Pages (from-to)205-211
Number of pages7
JournalJournal of Non-Newtonian Fluid Mechanics
Volume94
Issue number2-3
DOIs
StatePublished - Nov 1 2000
Externally publishedYes

Keywords

  • Continuous spectrum
  • Oldroyd-B
  • Pseudo-spectral
  • Stability analysis
  • UCM
  • Viscoelastic

ASJC Scopus subject areas

  • Chemical Engineering(all)
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanical Engineering
  • Applied Mathematics

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