Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
Volume 81, Issue 9, Pages 523-557Publisher
WILEY
DOI: 10.1002/fld.4195
Keywords
characteristic finite element; characteristic finite difference; energy stable; viscoelastic fluids; high Weissenberg; logarithmic transformation
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Funding
- German Science Foundation [IRTG 1529, TRR 146]
- JSPS (the Japan Society for the Promotion of Science) under the Japanese-German Graduate Externship 'Mathematical Fluid Dynamics'
- [26800091]
- [24224004]
- Grants-in-Aid for Scientific Research [26800091] Funding Source: KAKEN
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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 (C) 2015 John Wiley & Sons, Ltd.
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