Numerical modelling of viscoelastic cavity driven flow using finite difference simulations

Demir, Hüseyin

doi:10.1016/j.amc.2004.04.107

Cited by 10 publications

(5 citation statements)

References 19 publications

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“…The velocity component u along the vertical centre line for different Re is shown in Figure 2A and Figure 2B and we use the u -velocity profiles in Figure 2 to test the Figure 2. U velocity profiles for (A) Re=100 and (B) Re=1000-Present, (C) Re=100 and (D) Re=1000- (Demir 2005), (E) Re=100 and (F) Re=1000- (Tosoka and Kakuda 1994).…”

Section: Resultsmentioning

confidence: 99%

“…The lid-driven cavity flow problem is a well investigated one using different continua (see Ottino and Chella 1983, Tosoka and Kakuda 1994, Demir 2005, and references therein). The problem serves as a benchmark for both forced convective, free convective and mixed convective problems in a cavity of the rectangular, square, shallow and slender slot types.…”

Section: Introductionmentioning

confidence: 99%

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New Algorithm for the Lid-driven Cavity Flow Problem with Boussinesq-Stokes Suspension

Süngü

Demi̇r

2018

KSEJ

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In the present investigation, a streamfunction-vorticity form for Boussinesq-Stokes liquids (with suspended particles) is suitably used to examine the problem of 2-D unsteady incompressible flow in a square cavity with moving top and bottom wall. A new algorithm is used for this form in order to compute the numerical solutions for high Reynolds numbers up to Re=2500. This algorithm is conducted as a combination of the multi-time-stepping temporal differential transform and the spatial finite difference methods. Convergence of the time-series solution is ensured by multi-time-stepping method. The classical benchmark results of the Newtonian liquid are recovered as a limiting case and the decelerating influence of the suspended particle on the Newtonian liquids’ flow field is clearly elaborated.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New Algorithm for the Lid-driven Cavity Flow Problem with Boussinesq-Stokes Suspension

Süngü

Demi̇r

2018

KSEJ

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“…[4,41,46,47,67,71]); finite difference methods (e.g. [16,22,62]); and mixed finite volume and finite element methods (e.g. [1,2,51,69]).…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

Oishi

Martins

Tomé

et al. 2011

Journal of Non-Newtonian Fluid Mechanics

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In this paper we present a finite difference method for solving two-dimensional viscoelastic unsteady free surface flows governed by the single equation version of the eXtended Pom-Pom (XPP) model. The momentum equations are solved by a projection method which uncouples the velocity and pressure fields. We are interested in low Reynolds number flows and, to enhance the stability of the numerical method, an implicit technique for computing the pressure condition on the free surface is employed. This strategy is invoked to solve the governing equations within a Marker-and-Cell type approach while simultaneously calculating the correct normal stress condition on the free surface. The numerical code is validated by performing mesh refinement on a two-dimensional channel flow. Numerical results include an investigation of the influence of the parameters of the XPP equation on the extrudate swelling ratio and the simulation of the Barus effect for XPP fluids

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“…In the last several years, many numerical methods have been developed and adopted for the prediction of complex flow patterns of viscoelastic fluids, including the finite difference method , the boundary element method , the finite element method , finite volume method , pseudospectral method , and the lattice Boltzmann method . Dimakopoulos presented a completely implicit, parallel algorithm for the simulation of transient free‐surface flows of multimode viscoelastic fluids based on the mixed finite element method for the velocity and pressure fields, an elliptic grid generator for the deformation of the mesh, and the discontinuous Galerkin method for the viscoelastic stresses.…”

Section: Introductionmentioning

confidence: 99%

Modeling and simulation of three‐dimensional extrusion swelling of viscoelastic fluids with PTT, Giesekus and FENE‐P constitutive models

Zhao

Chen

et al. 2013

Numerical Methods in Fluids

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SUMMARYThe investigation of the extrusion swelling mechanism of viscoelastic fluids has both scientific and industrial interest. However, it has been traditionally difficult to afford theoretical and experimental researches to this problem. The numerical methodology based on the penalty finite element method with a decoupled algorithm is presented in the study to simulate three‐dimensional extrusion swelling of viscoelastic fluids flowing through out of a circular die. The rheological responses of viscoelastic fluids are described by using three kinds of differential constitutive models including the Phan‐Thien Tanner model, the Giesekus model, and the finite extensible nonlinear elastic dumbbell with a Peterlin closure approximation model. A streamface‐streamline method is introduced to adjust the swelling free surface. The calculation stability is improved by using the discrete elastic‐viscous split stress algorithm with the inconsistent streamline‐upwind scheme. The essential flow characteristics of viscoelastic fluids are predicted by using the proposed numerical method, and the mechanism of swelling phenomenon is further discussed.Copyright © 2013 John Wiley & Sons, Ltd.

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Numerical modelling of viscoelastic cavity driven flow using finite difference simulations

Cited by 10 publications

References 19 publications

New Algorithm for the Lid-driven Cavity Flow Problem with Boussinesq-Stokes Suspension

New Algorithm for the Lid-driven Cavity Flow Problem with Boussinesq-Stokes Suspension

Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

Modeling and simulation of three‐dimensional extrusion swelling of viscoelastic fluids with PTT, Giesekus and FENE‐P constitutive models

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