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.
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