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Free-energy-dissipative schemes for the Oldroyd-B model. (English) Zbl 1167.76018
Summary: 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 holds also for the numerical scheme. Among the analyzed numerical schemes, we consider some discretizations based on the log-formulation of the Oldroyd-B system proposed by R. Fattal and R. Kupferman in [J. Non-Newton. Fluid Mech. 123, No. 2–3, 281–285 (2004; Zbl 1084.76005)], for which solutions in some benchmark problems have been obtained beyond the limiting Weissenberg numbers for the standard scheme (see [M. A. Hulsen et al., J. Non-Newton. Fluid Mech. 127, 27–39 (2005)]). Our analysis gives some tracks to understand these numerical observations.

76M10 Finite element methods applied to problems in fluid mechanics
76A10 Viscoelastic fluids
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