Constitutive laws for the matrix-logarithm of the conformation tensor

Raanan Fattal, Raz Kupferman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

352 Scopus citations

Abstract

We show how to transform a large class of differential constitutive models into an equation for the (matrix) logarithm of the conformation tensor. Under this transformation, the extensional components of the deformation field act additively, rather than multiplicatively. This transformation is motivated by numerical evidence that the high Weissenberg number problem may be caused by the failure of polynomial-based approximations to properly represent exponential profiles developed by the conformation tensor. The potential merits of the new formulation are demonstrated for a finitely-extensible fluid in a two-dimensional lid-driven cavity at Weissenberg number Wi = 5.

Original languageAmerican English
Pages (from-to)281-285
Number of pages5
JournalJournal of Non-Newtonian Fluid Mechanics
Volume123
Issue number2-3
DOIs
StatePublished - 10 Nov 2004

Bibliographical note

Funding Information:
We are grateful to Alexandre Chorin, Erez Lapid and Lior Silberman for useful advice. This research was funded and supported in part by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities, and by the Applied Mathematical Sciences subprogram of the Office of Energy Research of the US Department of Energy under Contract DE-AC03-76-SF00098.

Keywords

  • Finite differences
  • High Weissenberg number problem
  • Matrix-logarithm

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