Constitutive laws for the matrix-logarithm of the conformation tensor

Raanan Fattal; Raz Kupferman

doi:10.1016/j.jnnfm.2004.08.008

Constitutive laws for the matrix-logarithm of the conformation tensor

Raanan Fattal, Raz Kupferman^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

403 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 language	English
Pages (from-to)	281-285
Number of pages	5
Journal	Journal of Non-Newtonian Fluid Mechanics
Volume	123
Issue number	2-3
DOIs	https://doi.org/10.1016/j.jnnfm.2004.08.008
State	Published - 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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10.1016/j.jnnfm.2004.08.008

Cite this

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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.",

keywords = "Finite differences, High Weissenberg number problem, Matrix-logarithm",

author = "Raanan Fattal and Raz Kupferman",

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N2 - 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.

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Constitutive laws for the matrix-logarithm of the conformation tensor

Abstract

Bibliographical note

Keywords

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