A monolithic FEM approach for the log-conformation reformulation (LCR) of viscoelastic flow problems

In this work, we discuss special numerical techniques for viscoelastic flow problems given in log-conformation reformulation (LCR). In particular, we consider Oldroyd-B and Giesekus-type fluids. We utilize a fully coupled monolithic finite element approach that treats all the numerical variables sim...

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Bibliographic Details
Published in:Journal of non-Newtonian fluid mechanics 2010-10, Vol.165 (19), p.1105-1113
Main Authors: Damanik, H., Hron, J., Ouazzi, A., Turek, S.
Format: Article
Language:English
Subjects:
Computational methods in fluid dynamics
Cylinders
EO-FEM
Exact sciences and technology
Finite element method
Fluid dynamics
Fluid flow
Fluids
Fundamental areas of phenomenology (including applications)
Giesekus
Log-conformation reformulation (LCR)
Mathematical analysis
Mathematical models
Monolithic Newton-multigrid
Non-newtonian fluid flows
Oldroyd-B
Physics
Viscoelastic flow
Viscoelasticity
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Summary:In this work, we discuss special numerical techniques for viscoelastic flow problems given in log-conformation reformulation (LCR). In particular, we consider Oldroyd-B and Giesekus-type fluids. We utilize a fully coupled monolithic finite element approach that treats all the numerical variables simultaneously. Thus, it is possible to do a direct steady approach and to avoid pseudo-time stepping with correspondingly small time step sizes in the case of a nonsteady approach. The Newton method handles the discrete nonlinear system, which results from the FEM discretization with consistent edge-oriented FEM stabilization techniques. In each nonlinear step, a direct sparse solver or a geometrical multigrid solver with special Vanka smoother deals with the resulting linear subproblems. Moreover, local grid refinement helps to reduce the computational efforts and to increase the accuracy of functional values. The merit of the presented methodology, for the well-known ‘flow around cylinder’ benchmark problem, is that we can obtain the discrete approximations by using a direct steady approach. Thus, the numerical effort can be rather independent of the examined We numbers. Furthermore, the ‘black box’ techniques can deal with any given viscoelastic models easily, hereby showing the same advantageous numerical convergence behaviour of the above mentioned fluids.
ISSN:0377-0257
1873-2631
DOI:10.1016/j.jnnfm.2010.05.008