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Research Papers: Fundamental Issues and Canonical Flows

High-Order Solution of Viscoelastic Fluids Using the Discontinuous Galerkin Method

[+] Author and Article Information
Ehsan Mirzakhalili

School of Mechanical Engineering,
College of Engineering,
University of Tehran,
North Karegar Avenue,
P.O. Box 11155-4563,
Tehran, Iran
e-mail: e.mirzakhalili@ut.ac.ir

Amir Nejat

Assistant Professor
School of Mechanical Engineering,
College of Engineering,
University of Tehran,
North Karegar Avenue,
P.O. Box 11155-4563,
Tehran, Iran
e-mail: nejat@ut.ac.ir

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received January 20, 2014; final manuscript received October 4, 2014; published online November 20, 2014. Assoc. Editor: D. Keith Walters.

J. Fluids Eng 137(3), 031205 (Mar 01, 2015) (9 pages) Paper No: FE-14-1035; doi: 10.1115/1.4028779 History: Received January 20, 2014; Revised October 04, 2014; Online November 20, 2014

In this paper, the high-order solution of a viscoelastic fluid is investigated using the discontinuous Galerkin (DG) method. The Oldroyd-B model is used to describe the viscoelastic behavior of the fluid flow. The high-order accuracy of the applied DG method is verified for a Newtonian benchmark problem with an exact solution. Next, the same algorithm is utilized to solve the viscoelastic flow by separating the stress tensor into the stress due to the Newtonian solvent and the stress due to the solved viscoelastic polymers. The high-order accuracy of the solution for viscoelastic flow is demonstrated by solving the planar Poiseuille flow. Then, the planar contraction problem is simulated as a benchmark for the viscoelastic flow. The obtained results are in good agreement with the results in the literature for both creeping and inertial flow when high-order polynomials were used even on coarse meshes.

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Figures

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Fig. 1

Domain of the Kovasznay flow

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Fig. 2

Numerical solution of Kovasznay flow

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Fig. 3

Norm of the error for y-velocity component in the Kovasznay flow

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Fig. 4

The numerical solution of viscoelastic stresses for simple channel flow (exact solutions are shown by symbols)

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Fig. 5

The geometry of benchmark problem

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Fig. 6

The computational grid of benchmark problem consisting of 360 elements

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Fig. 7

Variation of corner vortex length with We number for the creeping flow

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Fig. 8

Length of the corner vortex for the creeping flow

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Fig. 9

Intensity of the corner vortex for the creeping flow

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Fig. 10

Variation of corner vortex length with We number for the inertial flow

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Fig. 11

Length of the corner vortex for the inertial flow

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