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

Raanan Fattal; Raz Kupferman

doi:10.1016/j.jnnfm.2004.12.003

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 journal › Article › peer-review

247 Scopus citations

Abstract

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 language	English
Pages (from-to)	23-37
Number of pages	15
Journal	Journal of Non-Newtonian Fluid Mechanics
Volume	126
Issue number	1
DOIs	https://doi.org/10.1016/j.jnnfm.2004.12.003
State	Published - 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.

Keywords

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

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10.1016/j.jnnfm.2004.12.003

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

abstract = "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.",

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author = "Raanan Fattal and Raz Kupferman",

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. ",

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AB - 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.

KW - Finite-differences

KW - High Weissenberg number problem

KW - Lid-driven cavity

KW - Matrix logarithm

KW - Oldroyd-B fluid

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

Abstract

Bibliographical note

Keywords

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