Lattice methods and their applications to reacting systems

Chen, S.; Dawson, Silvina Ponce; Doolen, Gary D.; Janecky, David R.; Ławniczak, Anna T.

doi:10.1016/0098-1354(94)00072-v

Computers &Amp; Chemical Engineering

1995

DOI: 10.1016/0098-1354(94)00072-v

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Lattice methods and their applications to reacting systems

S. Chen

Silvina Ponce Dawson²,

Gary D. Doolen

et al.

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Cited by 13 publications

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A lattice Boltzmann method for shock wave propagation in solids

Xiao

2006

Commun. Numer. Meth. Engng.

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SUMMARYThis paper proposes a new lattice Boltzmann (LB) method for the study of shock wave propagation in elastic solids. The method, which implements a flux-corrected transport (FCT) algorithm, contains three stages: collision, streaming, and correction. In the collision stage, distribution functions are updated. In the streaming stage, the distribution functions are shifted between lattice points. Generally, a partial differential equation (PDE) is solved in the streaming stage, and finite element methods are employed to support the use of unstructured meshes in the LB method. The FCT algorithm is used in the correction stage to revise the distribution functions at lattice points, so fluctuations behind shock wave fronts can be eliminated efficiently. In this method, schemes for shock wave reflection at fixed and free boundaries are developed based on the bounce-back technique. A similar technique is used to treat wave reflection and transmission at material interfaces of composites. Several one-dimensional examples show that this LB-FCT method can provide ideal depictions of shock wave propagation in structures, especially composite structures.

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A lattice Boltzmann method for shock wave propagation in solids

Xiao

2006

Commun. Numer. Meth. Engng.

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Lattice Boltzmann‐based single‐phase method for free surface tracking of droplet motions

Xing

Butler

Yang

2006

Numerical Methods in Fluids

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A 2D single-phase free surface tracking model, based on the lattice Boltzmann method (LBM) is developed for simulating droplet motion. In contrast to the conventional multi-phase models, it is not necessary to simulate the motion of the gas phase using this 2D single-phase algorithm, and thus improves the computational efficiency without sacrificing the underlying physics. A method for special treatment of the relevant boundary conditions in the single-phase algorithm is proposed and also validated. Numerical simulations are carried out for the motion of a free falling droplet with or without considering gravity and droplet spreading under gravity. The simulations of the LBM are found to be consistent with the results obtained from commercial computational fluid dynamics (CFD) software Fluent.

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A coupled lattice Boltzmann model for the shallow water‐contamination system

Huang

2008

Numerical Methods in Fluids

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SUMMARYA coupled numerical method for the direct simulation of shallow water dynamics and pollutant transport is formulated and implemented. The conservation equations of shallow water dynamics equations and the convection-diffusion equations are solved using the lattice Boltzmann (LB) method. The local equilibrium distribution of the pollutant has no terms of second order in flow velocity. And the relaxation time of the pollutant deviates from a constant for the flows with variable free surface water depth. The numerical tests show that this scheme strictly obeys the conservation law of mass and momentum. Excellent agreement is obtained between numerical predictions and analytical solutions in the pure diffusion problem and convection-diffusion problem. Furthermore, the influences on the accuracy of the lattice size and the diffusivity are also studied. The results indicate that the variation in the free surface water depth cannot affect the conservation of the model, and the model has the ability to simulate the complex topography problem. The comparison shows that the LB scheme has the capacity to solve the complex convectiondiffusion problem in shallow water.

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Lattice methods and their applications to reacting systems

Cited by 13 publications

References 0 publications

A lattice Boltzmann method for shock wave propagation in solids

A lattice Boltzmann method for shock wave propagation in solids

Lattice Boltzmann‐based single‐phase method for free surface tracking of droplet motions

A coupled lattice Boltzmann model for the shallow water‐contamination system

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