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Property preserving reformulation of constitutive laws for the conformation tensor

Jafari, Azadeh, Chitsaz, Alizera, Nouri, Reza and Phillips, Timothy N. 2018. Property preserving reformulation of constitutive laws for the conformation tensor. Theoretical and Computational Fluid Dynamics 32 (6) , pp. 789-803. 10.1007/s00162-018-0476-y
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Abstract

The challenge for computational rheologists is to develop efficient and stable numerical schemes in order to obtain accurate numerical solutions for the governing equations at values of practical interest of the Weissenberg numbers. This study presents a new approach to preserve the symmetric positive definiteness of the conformation tensor and to bound the magnitude of its eigenvalues. The idea behind this transformation is lies with the matrix logarithm formulation. Under the logarithmic transformation, the eigenvalue spectrum of the new conformation tensor varies from infinite positive to infinite negative. But, reconstruction the classical formulation from unbounded eigenvalues doesn't achieve meaningful results. This enhanced formulation, hyperbolic tangent, prevails the previous numerical failure by bounding the magnitude of eigenvalues in a manner that positive definite is always satisfied. In order to evaluate the capability of the hyperbolic tangent formulation we performed a numerical simulation of FENE-P fluids in a rectangular channel in the context of the finite element method. Under this new transformation, the maximum attainable Weissenberg number increases 21.4% and 112.5% comparing the standard log-conformation and classical constitutive equation respectively.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Springer
ISSN: 0935-4964
Date of First Compliant Deposit: 17 September 2018
Date of Acceptance: 24 August 2018
Last Modified: 10 Dec 2018 15:17
URI: http://orca.cf.ac.uk/id/eprint/114954

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