Stable finite element schemes are developed for the solution of the equations modeling the flow of viscoelastic fluids. In contrast with classical statements of these equations, which introduce the stress as a primary variable, these schemes explicitly involve the deformation tensor and elastic energy. Energy estimates and existence of solutions to the discrete problem are established for schemes of arbitrary order without any restrictions on the time step, mesh size, or Weissenberg number. Convergence to smooth solutions is established for the classical Oldroyd–B fluid. Numerical experiments for two classical benchmark problems verify the robustness of this approach.
Accepté le :
DOI : 10.1051/m2an/2016053
Mots-clés : Viscoelastic fluid, Oldroyd–B, high weissenberg number problem
@article{M2AN_2017__51_3_1119_0,
author = {Perrotti, Louis and Walkington, Noel J. and Wang, Daren},
title = {Numerical approximation of viscoelastic fluids},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1119--1144},
publisher = {EDP-Sciences},
volume = {51},
number = {3},
year = {2017},
doi = {10.1051/m2an/2016053},
zbl = {1398.76122},
mrnumber = {3666659},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2016053/}
}
TY - JOUR AU - Perrotti, Louis AU - Walkington, Noel J. AU - Wang, Daren TI - Numerical approximation of viscoelastic fluids JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 1119 EP - 1144 VL - 51 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2016053/ DO - 10.1051/m2an/2016053 LA - en ID - M2AN_2017__51_3_1119_0 ER -
%0 Journal Article %A Perrotti, Louis %A Walkington, Noel J. %A Wang, Daren %T Numerical approximation of viscoelastic fluids %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 1119-1144 %V 51 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2016053/ %R 10.1051/m2an/2016053 %G en %F M2AN_2017__51_3_1119_0
Perrotti, Louis; Walkington, Noel J.; Wang, Daren. Numerical approximation of viscoelastic fluids. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 3, pp. 1119-1144. doi : 10.1051/m2an/2016053. http://archive.numdam.org/articles/10.1051/m2an/2016053/
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