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On the simulation of a time‐dependent cavity flow of an Oldroyd‐B fluid
Author(s) -
Pan TsorngWhay,
Hao Jian,
Glowinski Roland
Publication year - 2008
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1919
Subject(s) - positive definiteness , weissenberg number , representation (politics) , flow (mathematics) , finite element method , mathematics , operator splitting , operator (biology) , scheme (mathematics) , tensor (intrinsic definition) , mathematical analysis , geometry , physics , positive definite matrix , biochemistry , eigenvalues and eigenvectors , chemistry , repressor , quantum mechanics , politics , political science , transcription factor , gene , law , thermodynamics
In this article we present a finite element method for simulating the time‐dependent flow of an Oldroyd‐B fluid in a lid‐driven cavity, which is a stringent test problem at high Weissenberg number. The key considerations for developing the methodology are the preservation of the positive definiteness of the conformation tensor via the log‐conformation representation and additional diffusion, from second‐order upwind scheme, to smooth the high‐frequency modes. The combination of the log‐conformation representation, finite element method, and an operator‐splitting Lie's scheme, gives us a robust and easy‐to‐implement scheme. We have obtained convergent results when simulating time‐dependent cavity flows. Copyright © 2008 John Wiley & Sons, Ltd.