A numerical method for incompressible non-Newtonian fluid flows based on the lattice Boltzmann method

Yoshino, Masato; Hotta, Yohei; Hirozane, Takafumi; Endo, Morinobu

doi:10.1016/j.jnnfm.2007.07.007

Cited by 116 publications

(62 citation statements)

References 28 publications

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“…The Power-Law model is commonly used to describe the behavior of non-Newtonian fluids [29][30][31]. The effective viscosity of the Power-Law fluid is given by…”

Section: Governing Equationsmentioning

confidence: 99%

“…(45) can be obtained by a predictor-corrector approach similar to the procedure from Eq. (30) to Eq. (34).…”

Section: Finite Element Discretization For the Poisson Equationmentioning

confidence: 99%

“…Figure 7 shows that the present time integration scheme is indeed second-order accurate. [29,30] is used to validate the present hybrid method for the generalized Newtonian flows. The Power-Law exponent n is set to 0.8, 1.0 and 1.2.…”

Section: An Analytical Solution Problem For the Newtonian Fluidmentioning

confidence: 99%

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A hybrid finite volume/finite element method for incompressible generalized Newtonian fluid flows on unstructured triangular meshes

Gao

Ru-xun

2009

Acta Mech Sin

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This paper presents a hybrid finite volume/finite element method for the incompressible generalized Newtonian fluid flow (Power-Law model). The collocated (i.e. non-staggered) arrangement of variables is used on the unstructured triangular grids, and a fractional step projection method is applied for the velocity-pressure coupling. The cell-centered finite volume method is employed to discretize the momentum equation and the vertex-based finite element for the pressure Poisson equation. The momentum interpolation method is used to suppress unphysical pressure wiggles. Numerical experiments demonstrate that the current hybrid scheme has second order accuracy in both space and time. Results on flows in the lid-driven cavity and between parallel walls for Newtonian and Power-Law models are also in good agreement with the published solutions.

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“…The Power-Law model is commonly used to describe the behavior of non-Newtonian fluids [29][30][31]. The effective viscosity of the Power-Law fluid is given by…”

Section: Governing Equationsmentioning

confidence: 99%

“…(45) can be obtained by a predictor-corrector approach similar to the procedure from Eq. (30) to Eq. (34).…”

Section: Finite Element Discretization For the Poisson Equationmentioning

confidence: 99%

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A hybrid finite volume/finite element method for incompressible generalized Newtonian fluid flows on unstructured triangular meshes

Gao

Ru-xun

2009

Acta Mech Sin

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“…Various interesting properties of granular flows and related motions are studied in [5][6][7][8][9][10][11][12][13][14], for example, and in the references below. First let us consider the current setting in a little more detail.…”

Section: Introductionmentioning

confidence: 99%

On the evolving flow of grains down a chute

Ellis¹,

Smith²

2010

J Eng Math

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A continuum model leads to a partial differential equation for the evolving flow of grains down a chute. This is addressed for different effective viscosities in the system. Solutions for small viscosity are obtained which describe separating grains and clashing grains. Steady-state solutions are also found for any viscosity value, these being considered as a large time limit. Restrictions on the steady-state solutions are discussed, along with cases which yield re-structuring within a finite time.

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“…(6) - (10) The advantages of the LBM are the simplicity of the algorithm, the accuracy of the mass and momentum conservations and the suitability for parallel computing. Thus, it is expected that the LBM has possibility of simulating the two-phase viscoelastic fluid flows.…”

Section: Introductionmentioning

confidence: 99%

Lattice Boltzmann Simulation of Two-Phase Viscoelastic Fluid Flows

Yoshino

Toriumi

Arai

2008

JCST

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A lattice Boltzmann method (LBM) for two-phase viscoelastic fluid flows is proposed. The method is mainly an extension of the LBM for two-phase flows with large density differences proposed by Inamuro et al. [Journal of Computational Physics Vol.198, No.2 (2004), pp.628-644]. The viscoelastic effects are introduced by the constitutive equation based on the Maxwell model, which has a spring and a dashpot connected with each other in series. The method is applied to simulations of a drop under shear flow in viscoelastic fluids and of a bubble rising in viscoelastic fluids. In the simulation of drop deformation under shear flows, the effects of viscoelasticity on the deformation and orientation angle are evaluated. In the simulation of bubble rising in viscoelastic fluids, a cusp configuration at the trailing edge is investigated and compared with the theoretical prediction and other numerical results.

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A numerical method for incompressible non-Newtonian fluid flows based on the lattice Boltzmann method

Cited by 116 publications

References 28 publications

A hybrid finite volume/finite element method for incompressible generalized Newtonian fluid flows on unstructured triangular meshes

A hybrid finite volume/finite element method for incompressible generalized Newtonian fluid flows on unstructured triangular meshes

On the evolving flow of grains down a chute

Lattice Boltzmann Simulation of Two-Phase Viscoelastic Fluid Flows

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