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

Sébastien Boyaval (1, 2) , Tony Lelièvre (1, 2) , Claude Mangoubi (1, 2, 3)

1 MICMAC - Methods and engineering of multiscale computing from atom to continuum
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique
3 Einstein Institute of Mathematics

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.

Mots clés: Viscoelastic Fluids; Weissenberg Number; Stability; Entropy; Finite Elements Methods; Discontinuous Galerkin Method; Characteristic Method

Domaines: Analyse numérique [math.NA]

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⟩