Lattice Boltzmann method for polymer kinetic theory

Ammar, Amine

doi:10.1016/j.jnnfm.2010.05.006

Cited by 13 publications

(7 citation statements)

References 32 publications

(32 reference statements)

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“…This behavior can be associated with the shape of the PDF at steady-state, that for lower Wi m is closer to the initial condition. More details about error analysis of lattice Boltzmann methods for Fokker-Planck equations can be found in [13,16].…”

Section: Sub-grid Solution Analysismentioning

confidence: 99%

“…(10) from the lattice-BGK Eq. (17) via asymptotic expansion (Chapman-Enskog procedure) [13]. Tilde notation is omitted for readability.…”

Section: Appendix a Asymptotic Analysismentioning

confidence: 99%

“…The proposed approach relies on a previous work by Ammar [13] about a lattice Boltzmann solution of the Fokker-Planck equation for homogeneous flows. Recently this method has been also theoretically analyzed [14] and applied for the solution of a population balance equation [15] and for the Fokker-Planck equation [16].…”

Section: Introductionmentioning

confidence: 99%

“…Recently this method has been also theoretically analyzed [14] and applied for the solution of a population balance equation [15] and for the Fokker-Planck equation [16]. However, none of the previous works [13][14][15][16] deals with the coupling of the kinetic solution with macroscopic fields, thus we investigate efficient ways to exploit it in multi-scale simulations.…”

Section: Introductionmentioning

confidence: 99%

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Direct numerical simulation of complex viscoelastic flows via fast lattice-Boltzmann solution of the Fokker–Planck equation

Bergamasco¹,

Izquierdo²,

Ammar³

2013

Journal of Non-Newtonian Fluid Mechanics

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Micro-macro simulations of polymeric solutions rely on the coupling between macroscopic conservation equations for the fluid flow and stochastic differential equations for kinetic viscoelastic models at the microscopic scale. In the present work we introduce a novel micro-macro numerical approach, where the macroscopic equations are solved by a finite-volume method and the microscopic equation by a lattice-Boltzmann one. The kinetic model is given by molecular analogy with a finitely extensible non-linear elastic (FENE) dumbbell and is deterministically solved through an equivalent Fokker-Planck equation.The key features of the proposed approach are: (i) a proper scaling and coupling between the micro lattice-Boltzmann solution and the macro finite-volume one; (ii) a fast microscopic solver thanks to an implementation for Graphic Processing Unit (GPU) and the local adaptivity of the lattice-Boltzmann mesh; (iii) an operator-splitting algorithm for the convection of the macroscopic viscoelastic stresses instead of the whole probability density of the dumbbell configuration. This latter feature allows the application of the proposed method to non-homogeneous flow conditions with low memory-storage requirements. The model optimization is achieved through an extensive analysis of the lattice-Boltzmann solution, which finally provides control on the numerical error and on the computational time. The resulting micro-macro model is validated against the benchmark problem of a viscoelastic flow past a confined cylinder and the results obtained confirm the validity of the approach.

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Section: Sub-grid Solution Analysismentioning

confidence: 99%

“…(10) from the lattice-BGK Eq. (17) via asymptotic expansion (Chapman-Enskog procedure) [13]. Tilde notation is omitted for readability.…”

Section: Appendix a Asymptotic Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Direct numerical simulation of complex viscoelastic flows via fast lattice-Boltzmann solution of the Fokker–Planck equation

Bergamasco¹,

Izquierdo²,

Ammar³

2013

Journal of Non-Newtonian Fluid Mechanics

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“…Since 1990s, Qian [11] and Giraud [12] have been developed the lattice Boltzmann method to account for non-Newtonian behaviors, but they did not focus on the model with strong elastic effects. Later, several approaches have been proposed to incorporate constitutive equations in lattice Boltzmann simulations for viscoelastic fluids [13][14][15][16][17]. Recently, Papenkort et al [18] investigated viscoelastic shear-thinning fluid using lattice Boltzmann method; Wang et al [19] employed a multiple-relaxation-time lattice Boltzmann flux solver for non-Newtonian power-law fluid flows.…”

Section: Introductionmentioning

confidence: 99%

A Lattice Boltzmann Method and Asynchronous Model Coupling for Viscoelastic Fluids

Ouyang

2018

Applied Sciences

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The numerical algorithms of viscoelastic flows can appear a tremendous challenge as the Weissenberg number (Wi) enlarged sufficiently. In this study, we present a generalized technique of time-stably advancing based on the coupled lattice Boltzmann method, in order to improve the numerical stability of simulations at a high Wi number. The mathematical models of viscoelastic fluids include both the equation of the solvent and the Oldroyd-B constitutive equation of the polymer. In the two-dimensional (2D) channel flow, the coupled method shows good agreements between the corresponding exact results and the numerical results obtained by our method. In addition, as the Wi number increased, for the viscoelastic flows through contractions, we show that the prediction of our presented method can reproduce the same numerical results that were reported by previous studies. The main advantage of current method is that it can be applied to simulate the complex phenomena of the viscoelastic fluids.lattice Boltzmann method have been devised to solve the equations of an Oldroyd-B viscoelastic fluid in the reference [21], which did not need to adding extra distribution functions for the stress tensor. The coupled systems of the viscoelastic fluid include the macro scale constitutive equation and the mesoscopic lattice Boltzmann equation. There is a more disparity in timescales between the macro solver and meso solver. To distinguish this different time scale and enhance the computational efficiency, the asynchronously coupled method [22,23] was applied for the coupling time in reference [21]. That means, the data between macro constitutive equation and the lattice Boltzmann equation exchange at every time step. The constitutive solver may run at a slower pace than the meso-scale dynamics.The asynchronous coupling method allows for the coupled solvers to exchange the data at every loop, although the meso and macro time steps are unequal. This special treatment is actually a numerical approximation to the true solution. For viscoelastic fluids at low Wi number, asynchronously coupled method may get steady result in simulations if the macro time step can guarantee the adequate resolutions of each solvers because of the small scale-separation. However, for viscoelastic fluids at high Wi number, the computational stability of asynchronously coupling is greatly affected by the polymer stress as the elasticity interaction becomes relatively large. Therefore, the asynchronously coupling method has the limitations, such as poor numerical stability, which were limited to solve the low Wi number problem.The aim of the current paper is to develop a generalized technique for time advancing of the viscoelastic coupled lattice Boltzmann method, seeking to be immune to high Wi number problem. The basic idea of our new method is as follows. (i) Run the lattice Boltzmann solver using its own time step δt, while allowing for a flexible number of lattice Boltzmann solver steps N before the exchange of coupling variables; (ii) Run the constitutive ...

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