Volume 51, Number 3, May-June 2017
|Page(s)||1119 - 1144|
|Published online||07 June 2017|
Numerical approximation of viscoelastic fluids∗
Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213. USA.
Received: 9 September 2015
Revised: 27 July 2016
Accepted: 28 July 2016
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.
Mathematics Subject Classification: 65M60 / 65M12 / 76M10
Key words: Viscoelastic fluid / Oldroyd–B / high weissenberg number problem
© EDP Sciences, SMAI 2017
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