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

Sébastien Boyaval; Tony Lelièvre; Claude Mangoubi

ESAIM: Mathematical Modelling and Numerical Analysis (2009)

  • Volume: 43, Issue: 3, page 523-561
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Boyaval, Sébastien, Lelièvre, Tony, and Mangoubi, Claude. "Free-energy-dissipative schemes for the Oldroyd-B model." ESAIM: Mathematical Modelling and Numerical Analysis 43.3 (2009): 523-561. <http://eudml.org/doc/250596>.

@article{Boyaval2009,
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 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. },
author = {Boyaval, Sébastien, Lelièvre, Tony, Mangoubi, Claude},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Viscoelastic fluids; Weissenberg number; stability; entropy; finite elements methods; discontinuous Galerkin method; characteristic method.; finite element method},
language = {eng},
month = {4},
number = {3},
pages = {523-561},
publisher = {EDP Sciences},
title = {Free-energy-dissipative schemes for the Oldroyd-B model},
url = {http://eudml.org/doc/250596},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Boyaval, Sébastien
AU - Lelièvre, Tony
AU - Mangoubi, Claude
TI - Free-energy-dissipative schemes for the Oldroyd-B model
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2009/4//
PB - EDP Sciences
VL - 43
IS - 3
SP - 523
EP - 561
AB - 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.
LA - eng
KW - Viscoelastic fluids; Weissenberg number; stability; entropy; finite elements methods; discontinuous Galerkin method; characteristic method.; finite element method
UR - http://eudml.org/doc/250596
ER -

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