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Energy dissipative characteristic schemes for the diffusive Oldroyd‐B viscoelastic fluid
Author(s) -
Lukáčová Medvid'ová Mária,
Notsu Hirofumi,
She Bangwei
Publication year - 2015
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.4195
Subject(s) - dissipative system , discretization , finite element method , mathematics , viscoelasticity , logarithm , mathematical analysis , energy (signal processing) , numerical analysis , finite difference , finite difference method , stability (learning theory) , transformation (genetics) , classical mechanics , physics , computer science , statistics , biochemistry , chemistry , quantum mechanics , gene , thermodynamics , machine learning
Summary In this paper, we propose new energy dissipative characteristic numerical methods for the approximation of diffusive Oldroyd‐B equations that are based either on the finite element or finite difference discretization. We prove energy stability of both schemes and illustrate their behavior on a series of numerical experiments. Using both the diffusive model and the logarithmic transformation of the elastic stress, we are able to obtain methods that converge as mesh parameter is refined. Copyright © 2015 John Wiley & Sons, Ltd.