A stable and convergent scheme for viscoelastic flow in contraction channels

We present a new algorithm to simulate unsteady viscoelastic flows in abrupt contraction channels. In our approach we split the viscoelastic terms of the Oldroyd-B constitutive equation using Duhamel’s formula and discretize the resulting PDEs using a semi-implicit finite difference method based on...

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Bibliographic Details
Published in:Journal of computational physics 2005-05, Vol.205 (1), p.315-342
Main Authors: Trebotich, D., Colella, P., Miller, G.H.
Format: Article
Language:English
Subjects:
Computational techniques
Contraction channels
Exact sciences and technology
Mathematical methods in physics
Maxwell fluid
Oldroyd-B fluid
Physics
Projection methods
Viscoelastic flow
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Summary:We present a new algorithm to simulate unsteady viscoelastic flows in abrupt contraction channels. In our approach we split the viscoelastic terms of the Oldroyd-B constitutive equation using Duhamel’s formula and discretize the resulting PDEs using a semi-implicit finite difference method based on a Lax–Wendroff method for hyperbolic terms. In particular, we leave a small residual elastic term in the viscous limit by design to make the hyperbolic piece well-posed. A projection method is used to impose the incompressibility constraint. We are able to compute the full range of unsteady elastic flows in an abrupt contraction channel – from the viscous limit to the elastic limit – in a stable and convergent manner. We demonstrate the range of our method for unsteady flow of a Maxwell fluid with and without viscosity in planar contraction channels. We also demonstrate stable and convergent results for benchmark high Weissenberg number problems at We = 1 and We = 10.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2004.11.007