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Free-energy-dissipative schemes for the Oldroyd-B model

Abstract : 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, which have been reported to be numerically more stable than discretizations of the usual formulation in some benchmark problems. Our analysis gives some tracks to understand these numerical observations.
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https://hal.inria.fr/inria-00204620
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Submitted on : Tuesday, January 15, 2008 - 1:58:05 PM
Last modification on : Friday, November 29, 2019 - 12:42:01 PM
Long-term archiving on: : Tuesday, September 21, 2010 - 3:04:42 PM

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  • HAL Id : inria-00204620, version 2
  • ARXIV : 0801.2248

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Sébastien Boyaval, Tony Lelièvre, Claude Mangoubi. Free-energy-dissipative schemes for the Oldroyd-B model. [Research Report] RR-6413, INRIA. 2008, pp.53. ⟨inria-00204620v2⟩

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