Numerical approximation of viscoelastic fluids

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 ener...

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Bibliographic Details
Published in:ESAIM. Mathematical modelling and numerical analysis 2017-05, Vol.51 (3), p.1119-1144
Main Authors: Perrotti, Louis, Walkington, Noel J., Wang, Daren
Format: Article
Language:English
Subjects:
65M12
65M60
76M10
Computational fluid dynamics
Elastic deformation
Finite element method
Fluid flow
high weissenberg number problem
Mathematical models
Oldroyd–B
Robustness (mathematics)
Tensors
Viscoelastic fluid
Viscoelastic fluids
Viscoelasticity
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Summary: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.
ISSN:0764-583X
1290-3841
DOI:10.1051/m2an/2016053