Efficient computation of the eigenspectrum of viscoelastic flows using submatrix-based transformation of the linearized equations

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Abstract

Linear stability analysis of incompressible viscoelastic flows based on normal mode expansions of the eigenfunctions requires the numerical solution of a generalized eigenvalue problem (GEVP). The complex boundary layer structure of the leading eigenfunctions and the singular character of the continuous set of eigenvalues, necessitate the use of fine mesh sizes, leading to large algebraic GEVPs. In this paper, we present a submatrix-based transformation of the linearized equations (SubTLE) that converts the GEVP into a simple eigenvalue problem (EVP) of half the original dimension for the purely elastic isothermal and non-isothermal flows of an Oldroyd-B liquid. This leads to significant (up to an order of magnitude) reduction in the CPU time and memory required for the solution of the EVP. This is illustrated in the context of isothermal and non-isothermal shear flows.

Original languageEnglish (US)
Pages (from-to)75-85
Number of pages11
JournalJournal of Non-Newtonian Fluid Mechanics
Volume104
Issue number1
DOIs
StatePublished - Apr 20 2002
Externally publishedYes

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Keywords

  • Generalized eigenvalue problem
  • Non-isothermal
  • Oldroyd-B
  • Purely elastic
  • Stability analysis
  • Viscoelastic

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes

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