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

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-...

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Veröffentlicht in:Journal of non-Newtonian fluid mechanics 2005-02, Vol.126 (1), p.23-37
Hauptverfasser: Fattal, Raanan, Kupferman, Raz
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0377-0257
1873-2631
DOI:10.1016/j.jnnfm.2004.12.003