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characteristic method.

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Free-energy-dissipative schemes for the Oldroyd-B model
Sébastien Boyaval, Tony Lelièvre, Claude Mangoubi
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 43 / Issue 3 / May 2009

Published online by Cambridge University Press:

08 April 2009, pp. 523-561

Print publication:

May 2009
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In this article, we analyze the stability of various numerical schemes for differential models of viscoelastic fluids. More precisely, we consider the prototypical Oldroyd-B model, for which a free energy dissipation holds, and we show under which assumptions such a dissipation is also satisfied for the numerical scheme. Among the numerical schemes we analyze, we consider some discretizations based on the log-formulation of the Oldroyd-B system proposed by Fattal and Kupferman in [J. Non-Newtonian Fluid Mech.123 (2004) 281–285], for which solutions in some benchmark problems have been obtained beyond the limiting Weissenberg numbers for the standard scheme (see [Hulsen et al.J. Non-Newtonian Fluid Mech. 127 (2005) 27–39]). Our analysis gives some tracks to understand these numerical observations.