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Convergence limit in numerical modeling of steady contraction viscoelastic flow and time-dependent behavior near the limit

Authors
Kwon, YoungdonHan, JungHyun
Issue Date
Dec-2010
Publisher
KOREAN SOC RHEOLOGY
Keywords
viscoelastic flow; finite element; Leonov model; contraction flow; Deborah number; elastic instability
Citation
KOREA-AUSTRALIA RHEOLOGY JOURNAL, v.22, no.4, pp.237 - 245
Indexed
SCIE
SCOPUS
KCI
OTHER
Journal Title
KOREA-AUSTRALIA RHEOLOGY JOURNAL
Volume
22
Number
4
Start Page
237
End Page
245
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/115170
ISSN
1226-119X
Abstract
In the framework of finite element analysis we numerically analyze both the steady and transient 4:1 contraction creeping viscoelastic flow. In the analysis of steady solutions, there exists upper limit of available numerical solutions in contraction flow of the Leonov fluid, and it is free from the frustrating mesh dependence when we incorporate the tensor-logarithmic formulation (Fattal and Kupferman, 2004). With the time dependent flow modeling with pressure difference imposed slightly below the steady limit, the 1(st) and 2(nd) order conventional approximation schemes have demonstrated fluctuating solution without approaching the steady state. From the result, we conclude that the existence of upper limit for convergent steady solution may imply flow transition to highly elastic time-fluctuating field without steady asymptotic. However definite conclusion certainly requires further investigation and devising some methodology for its proof.
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