Browse > Article

Vector decomposition of the evolution equations of the conformation tensor of Maxwellian fluids  

Cho, Kwang-Soo (Department of Polymer Science and Engineering, Kyungpook National University)
Publication Information
Korea-Australia Rheology Journal / v.21, no.2, 2009 , pp. 143-146 More about this Journal
Abstract
Breakthrough of high Weisenberg number problem is related with keeping the positive definiteness of the conformation tensor in numerical procedures. In this paper, we suggest a simple method to preserve the positive definiteness by use of vector decomposition of the conformation tensor which does not require eigenvalue problem. We also derive the constitutive equation of tensor-logarithmic transform in simpler way than that of Fattal and Kupferman and discuss the comparison between the vector decomposition and tensor-logarithmic transformation.
Keywords
high Weisenberg number; vector decomposition; conformation tensor; nonlinear viscoelasticity; Maxwellian fluid;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 0  (Related Records In Web of Science)
연도 인용수 순위
1 Keunings, R., 1986, On the high Weissenberg number problem, J. Non-Newtonian Fluid Mech., 20, 209-226   DOI   ScienceOn
2 Leonov, A. I., 1976, Nonequilibrium thermodynamics and rheology of viscoelastic polymer media, Rheol. Acta, 15, 85-98   DOI
3 Kwon, Y., A. I. Leonov, 1995, Stability constraints in the formulation of viscoelastic constitutive equations, J. Non-Newtonian Fluid Mech., 58, 25-46   DOI   ScienceOn
4 Rosati, L., 2000, A novel approach to the solution of the tensor equation AX+XA=H, Int. J. Solids and Structures, 37, 3457-3477   DOI   ScienceOn
5 Fattal, R., and R. Kupferman, 2004, Constitutive laws for the matrix-logarithm of the conformation tensor, J. Non-Newtonian Fluid Mech., 123, 281-285   DOI   ScienceOn
6 Kwon, Y., 2004, Finite element analysis of planar 4:1 contraction flow with the tensor-logarithmic formulation of differential constitutive equations, Korea-Australia Rheol. J., 16, 183-191   과학기술학회마을