An iterative stabilized CNBS–CG scheme for incompressible non-isothermal non-Newtonian fluid flow

Han, Xianhong; Li, Xikui

doi:10.1016/j.ijheatmasstransfer.2006.08.037

Cited by 14 publications

(6 citation statements)

References 24 publications

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“…By using the standard Galerkin procedure, the weak forms of Eqs. (26), (29), (22), (23) and (27) along with the weak forms of the corresponding natural boundary conditions can be respectively, written as…”

Section: Spatial Discretization Using the Finite Element Methodsmentioning

confidence: 99%

“…Refs. [21,23,36]). The numerical results for the 4:1 contraction viscoelastic flow problem display that the viscoelastic fluid at the zone far from the contraction region is subjected to a simple shear and that in the contraction channel is subjected to a pure extensional deformation along the centerline (elongation flow), while a mixture of shear and elongation flows exists near the re-entrant corners.…”

Section: Planar Contraction Flow Problemmentioning

confidence: 99%

“…Han and Li [23] simulated the incompressible non-isothermal nonNewtonian fluid flow by using a proposed iterative stabilized fractional step scheme, in which the Crank-Nicolson method based split (CNBS) scheme and the characteristic Galerkin (CG) method are respectively devised to discretize and solve the non-Newtonian momentum-mass conservation equations and the energy conservation equation in consideration of their convective character. Recently, Li et al [24] presented a self-adaptive method that coupled the finite element (FE) method and the meshfree (MF) method in the arbitrary Lagrangian-Eulerian (ALE) description for numerical simulation of injection molding processes.…”

Section: Introductionmentioning

confidence: 99%

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A numerical study of constitutive models endowed with Pom-Pom molecular attributes

Wang

Han

2010

Journal of Non-Newtonian Fluid Mechanics

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Section: Spatial Discretization Using the Finite Element Methodsmentioning

confidence: 99%

Section: Planar Contraction Flow Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A numerical study of constitutive models endowed with Pom-Pom molecular attributes

Wang

Han

2010

Journal of Non-Newtonian Fluid Mechanics

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“…Similar schemes for introducing the iterative procedure into the stabilized fractional step algorithms have been proposed for finite element analysis in Newtonian and non-Newtonian fluid mechanics [11,17,18], and result in saving computational efforts in a decisive manner. In this work the iterative procedure is particularly introduced to form an iterative pressure-stabilized DEVSS procedure using the Crank-Nicolson-based split scheme of the fractional step algorithm in the finite element method context, abbreviated as I_PS_DEVSS_CNBS scheme summarized as below:…”

Section: Spatial Discretization and The I_ps_devss_cnbs Schemementioning

confidence: 99%

A mixed finite element scheme for viscoelastic flows with XPP model

Han

2008

Acta Mech Sin

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A mixed finite element formulation for viscoelastic flows is derived in this paper, in which the FIC (finite incremental calculus) pressure stabilization process and the DEVSS (discrete elastic viscous stress splitting) method using the Crank-Nicolson-based split are introduced within a general framework of the iterative version of the fractional step algorithm. The SU (streamline-upwind) method is particularly chosen to tackle the convective terms in constitutive equations of viscoelastic flows. Thanks to the proposed scheme the finite elements with equal low-order interpolation approximations for stress-velocity-pressure variables can be successfully used even for viscoelastic flows with high Weissenberg numbers. The XPP (extended Pom-Pom) constitutive model for describing viscoelastic behaviors is particularly integrated into the proposed scheme. The numerical results for the 4:1 sudden contraction flow problem demonstrate prominent stability, accuracy and convergence rate of the proposed scheme in both pressure and stress distributions over the flow domain within a wide range of the Weissenberg number, particularly the capability in reproducing the results, which can be used to explain the "die swell" phenomenon observed in the polymer injection molding process.

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“…Ding et al [17] presented the simulation of the injection molding process by using the Taylor–Galerkin/pressure‐correction time‐stepping scheme. Han and Li [18] simulated the incompressible nonisothermal non‐Newtonian fluid flow by using a proposed iterative stabilized fractional step scheme [19], in which the Crank–Nicolson method based split scheme and the characteristic Galerkin (CG) method are, respectively, used to discretize and solve the non‐Newtonian momentum–mass conservation equations and the energy conservation equation in consideration of their convective character.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation and experimental verification of the filling stage in injection molding

Wang

Han

2011

Polymer Engineering & Sci

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The linear low‐density polyethylene melt is described by the modified Cross model, the dependence of melt viscosity on temperature incorporated with the Arrhenius equation, and the Moldflow second‐order model in this investigation. The mass, momentum conservation, and constitutive equations are discretized and solved by using the iterative stabilized fractional step algorithm along with the Crank–Nicolson implicit difference scheme. The energy conservation equation is discretized with the characteristic Galerkin approach. The free surface of molten polymer flow front is tracked by the arbitrary Lagrangian–Eulerian (ALE) method. It is demonstrated that good agreement of the numerical predictions given by the proposed ALE method with the results obtained by the injection short‐shot experiments is achieved in the locations and shape of the melt front. Furthermore, when the melt front completely reaches the wall of the mold cavity, the horizontal velocity distribution of counterflow at the section near the finally filling wall is exhibited in the present simulation. POLYM. ENG. SCI., 2012. © 2011 Society of Plastics Engineers

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An iterative stabilized CNBS–CG scheme for incompressible non-isothermal non-Newtonian fluid flow

Cited by 14 publications

References 24 publications

A numerical study of constitutive models endowed with Pom-Pom molecular attributes

A numerical study of constitutive models endowed with Pom-Pom molecular attributes

A mixed finite element scheme for viscoelastic flows with XPP model

Numerical simulation and experimental verification of the filling stage in injection molding

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