Geodesic
Numerical approximation of viscoelastic fluids
Perrotti, Louis1 ; Walkington, Noel J.1  ; Wang, Daren1
1 Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213. USA.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 3, pp. 1119-1144

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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.

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DOI : 10.1051/m2an/2016053
Classification : 65M60, 65M12, 76M10
Keywords: Viscoelastic fluid, Oldroyd–B, high weissenberg number problem

Perrotti, Louis 1 ; Walkington, Noel J. 1 ; Wang, Daren 1

1 Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213. USA. 
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     title = {Numerical approximation of viscoelastic fluids},
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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

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