Finite-difference stable stencils based on least-square quadric fitting

Dupuy, P.M.; Svendsen, Hallvard F.; Patruno, L.E.; Jakobsen, Hugo A.

doi:10.1016/j.cpc.2010.06.004

Cited by 5 publications

(6 citation statements)

References 11 publications

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“…The SS stencil was verified to have stability while solving an ill-posed problem such as the anti-diffusion equation, and it has been tested stably in various cases, showing second-order accuracy as well [32]. Here, as what is implemented by Dupuy et al, we use the SS stencil to discretize the Laplacian term ∇ 2 T in the sub-operator equation L 2 :…”

Section: Temperature Fieldmentioning

confidence: 98%

“…Shu et al [31] has integrated LBM with FSM to simulate the high Reynolds number flow, but its splitting is ill-posed and without rigorous analysis, its accuracy, consistency and stability are not established. In our model the PS-TLBM is combined with the second-order Strang operator splitting method and SS finite difference scheme [32] in favor of better numerical stability.…”

Section: Introductionmentioning

confidence: 99%

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A fractional-step thermal lattice Boltzmann model for high Peclet number flow

Deng

Zhang

Wen

et al. 2015

Computers & Mathematics with Applications

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a b s t r a c tAs a promising approach in hydrodynamics and thermodynamics modeling, the lattice Boltzmann method (LBM) still suffers severe numerical instability when the temperature field of the flow is convection-dominant (high Peclet number). Despite a lot of research devoted to solve this problem worldwide, to simulate high Peclet number thermal flow at comparably few computational cost is still a hard work, making it inefficient in practical use. In this paper, we combine the LBM and the fractional-step method to propose a novel and stable thermal lattice Boltzmann scheme for high Peclet number flow without refining the lattice. By numerical tests of thermal Poiseuille flow and Couette flow, we quantify second-order accuracy of the proposed model, and through several cases of Peclet number from low to high, the superior stability and efficiency compared with existing thermal lattice Boltzmann model.

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Section: Temperature Fieldmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

A fractional-step thermal lattice Boltzmann model for high Peclet number flow

Deng

Zhang

Wen

et al. 2015

Computers & Mathematics with Applications

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“…In detail, as the LBM has optimal stability with the relaxation time of 1.0 (Sterling and Chen, 1996; Zhao, 2013), α 0 is accordingly set to be cs2δt(1−0.5). Other than ordinary central difference scheme, we use the SS stencil (Dupuy et al , 2010) to discretize the Laplacian term in the sub-operator equation L 2 : …”

Section: Lattice Boltzmann Implementationmentioning

confidence: 99%

Efficient numerical simulation of injection mold filling with the lattice Boltzmann method

Deng

Liang

Zhang

et al. 2017

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Purpose Lattice Boltzmann method (LBM) has made great success in computational fluid dynamics, and this paper aims to establish an efficient simulation model for the polymer injection molding process using the LBM. The study aims to validate the capacity of the model for accurately predicting the injection molding process, to demonstrate the superior numerical efficiency in comparison with the current model based on the finite volume method (FVM). Design/methodology/approach The study adopts the stable multi-relaxation-time scheme of LBM to model the non-Newtonian polymer flow during the filling process. The volume of fluid method is naturally integrated to track the movement of the melt front. Additionally, a novel fractional-step thermal LBM is used to solve the convection-diffusion equation of the temperature field evolution, which is of high Peclet number. Through various simulation cases, the accuracy and stability of the present model are validated, and the higher numerical efficiency verified in comparison with the current FVM-based model. Findings The paper provides an efficient alternative to the current models in the simulation of polymer injection molding. Through the test cases, the model presented in this paper accurately predicts the filling process and successfully reproduces several characteristic phenomena of injection molding. Moreover, compared with the popular FVM-based models, the present model shows superior numerical efficiency, more fit for the future trend of parallel computing. Research limitations/implications Limited by the authors’ hardware resources, the programs of the present model and the FVM-based model are run on parallel up to 12 threads, which is adequate for most simulations of polymer injection molding. Through the tests, the present model has demonstrated the better numerical efficiency, and it is recommended for the researcher to investigate the parallel performance on even larger-scale parallel computing, with more threads. Originality/value To the authors’ knowledge, it is for the first time that the lattice Boltzmann method is applied in the simulation of injection molding, and the proposed model does obviously better in numerical efficiency than the current popular FVM-based models.

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“…In the present work we are only interested in studying the momentum exchange, thus we provide only information on the pressure and momentum distribution modeled with Here f t i,x is the ith density function (or pseudoparticle) in node x at time t, and e i the discrete velocity vector of the pseudoparticle i. The collision term, Ω i , and the forcing terms, F i , are widely used in lattice Boltzmann schemes for modifying or adding extra terms to the equation system (1)- (3). Different expressions can be used for these source terms [7,12].…”

Section: The Lattice Boltzmann Modelmentioning

confidence: 99%

“…We use a first-order explicit in time finite difference technique for solving equation (16). The solution with two different stencils are studied, namely central differences (C) and a so-called stable stencil based on a least squares quadric fitting [3] for antidiffusion problems (SS). This last family of stencils computes correctly the actual curvature of the surfaces and at the same time counteracts the formation of ripples of a wavelength of two lattice units.…”

Section: Finite Difference Schemementioning

confidence: 99%

Fractional step two-phase flow lattice Boltzmann model implementation

et al. 2009

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A hybrid method that combines an advanced lattice Boltzmann model with traditional finite difference techniques is developed. An operator splitting technique is applied to separate the numerical scheme into two subproblems. Each subproblem is solved with different techniques, namely lattice Boltzmann and finite differences. This method is applied for the first time to a two-phase flow simulation case. Major simplifications are obtained in the lattice Boltzmann implementation. Simulations are presented to show these improvements and to validate the technique with kinematic viscosity down to 10−4 in lattice Boltzmann units. This technique does not add instabilities, and in contrast improves the stability behavior compared to reducing the relaxation time.

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Finite-difference stable stencils based on least-square quadric fitting

Cited by 5 publications

References 11 publications

A fractional-step thermal lattice Boltzmann model for high Peclet number flow

A fractional-step thermal lattice Boltzmann model for high Peclet number flow

Efficient numerical simulation of injection mold filling with the lattice Boltzmann method

Fractional step two-phase flow lattice Boltzmann model implementation

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