Volume 1, Issue 2, December 2016, Page: 26-35
A Hybrid Stabilized Finite Element/Finite Difference Method for Unsteady Viscoelastic Flows
Ahmed Elhanafy, Mathematics & Engineering Physics Department, Faculty of Engineering, Mansoura University, Mansoura, Egypt
Amr Guaily, Engineering Mathematics & Physics Department, Faculty of Engineering, Cairo University, Giza, Egypt
Ahmed Elsaid, Mathematics & Engineering Physics Department, Faculty of Engineering, Mansoura University, Mansoura, Egypt
Received: Sep. 10, 2016;       Accepted: Oct. 14, 2016;       Published: Oct. 21, 2016
DOI: 10.11648/j.mma.20160102.11      View  2994      Downloads  108
Abstract
The Oldroyd-B constitutive equation is used for the numerical simulation of unsteady incompressible viscoelastic flows. A novelty treatment is presented for the incompressibility constraint of the incompressible viscoelastic flow by using the modified continuity equation which allows using equal-order interpolation polynomials for all variables. The proposed technique circumvents the so-called LBB compatibility condition without pressure checkerboard and the solution instabilities with less computational costs compared with the traditional techniques. The discrete elastic-viscous stress-splitting method (DEVSS) is used to treat the instabilities resulting from the numerical simulation of viscoelastic flows. Two benchmark problems are simulated, namely, the flow through a channel with a bump and the flow inside a square cavity. Solutions are obtained for different Weissenberg number values and the results are compared with the published works.
Keywords
Unsteady Incompressible Viscoelastic Flow, Oldroyd-B Model, Pressure Stabilization Technique, The DEVSS Method, Galerkin Least Squares
To cite this article
Ahmed Elhanafy, Amr Guaily, Ahmed Elsaid, A Hybrid Stabilized Finite Element/Finite Difference Method for Unsteady Viscoelastic Flows, Mathematical Modelling and Applications. Vol. 1, No. 2, 2016, pp. 26-35. doi: 10.11648/j.mma.20160102.11
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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