Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation

Raanan Fattal, Raz Kupferman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

234 Scopus citations


We present a second-order finite-difference scheme for viscoelastic flows based on a recent reformulation of the constitutive laws as equations for the matrix logarithm of the conformation tensor. We present a simple analysis that clarifies how the passage to logarithmic variables remedies the high-Weissenberg numerical instability. As a stringent test, we simulate an Oldroyd-B fluid in a lid-driven cavity. The scheme is found to be stable at large values of the Weissenberg number. These results support our claim that the high Weissenberg numerical instability may be overcome by the use of logarithmic variables. Remaining issues are rather concerned with accuracy, which degrades with insufficient resolution.

Original languageAmerican English
Pages (from-to)23-37
Number of pages15
JournalJournal of Non-Newtonian Fluid Mechanics
Issue number1
StatePublished - 20 Feb 2005

Bibliographical note

Funding Information:
We are grateful to Frank Baaijens, Alexandre Chorin, Martien Hulsen, Roland Keunings, Randy LeVeque, and Eitan Tadmor for precious advice and to Irad Yavneh for guiding us with multigrid methods. We are also grateful to Morton Denn for continual support. Part of this research was carried out while the authors were visiting the Department of Applied Mathematics at Lawrence Berkeley National Laboratory. This research was funded in part by the Applied Mathematical Sciences subprogram of the Office of Energy Research of the US Department of Energy under Contract DE-AC03-76-SF00098.


  • Finite-differences
  • High Weissenberg number problem
  • Lid-driven cavity
  • Matrix logarithm
  • Oldroyd-B fluid


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