Lattice Boltzmann computations for reaction-diffusion equations

Dawson, Silvina Ponce; Chen, S.; Doolen, Gary D.

doi:10.1063/1.464316

Cited by 354 publications

(64 citation statements)

References 14 publications

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“…Streaming describes the movement of the particles of each species and collision describes interactions between the particles of the same or different species. Further, these actions are combined in the LB equation for species i [4,7,10,11] (9) where is the PDF, the discrete streaming velocity, the collision term, Δt the simulation time step and the source term at any spatial location x and time t along the direction α. The collision term and the equilibrium function are specifi ed as (10) (11) (12) Where w a is the weight factor due to the placement of the particles in the grid, u i is the specifi c velocity contribution and τ i is the relaxation time for the specifi c species i.…”

Section: Governing Equationsmentioning

confidence: 99%

“…First, the reaction-advectiondiffusion equation can be written as [4,5]: (3) where C i is the concentration of species i, D is the diffusion coeffi cient, R r is the reaction rate for reaction with the specifi c species i, u is the velocity vector and t is the time. Secondly, the Navier-Stokes equations for conservation of momentum and the conservation of mass are presented as [4,5]: (4) (5) where p is the pressure in the fl uid, ν is the kinematic viscosity, F is the force term, u is the velocity and t is the time. The Bond number is used to characterize the shape of the bubble in the surrounding fl uid.…”

Section: Governing Equationsmentioning

confidence: 99%

“…The bubble formation and generation result in a complex set of optical and electrochemical phenomena at the semiconductor-catalyst-electrolyte interfaces. Semiconductor photo-electrodes for water splitting are most effi cient with surface features such as high-surface-area morphologies or heterogeneous catalysts [3,4].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Analysis of hydrogen bubble flow between nanorods using lattice boltzmann method

Paradis¹,

Grigoropoulos²,

Sundén³

2014

Int. J. CMEM

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Lattice Boltzmann method (LBM) is used to model the hydrogen production by splitting water by incident sunlight over Si nanorods. The purpose of this study is to investigate the transport and the formation of the hydrogen bubbles by electrochemical reactions with a 2D and a 3D numerical model using LBM. An ordered array of nanorods is created where each rod is 10 μm in high and 10 nm in diameter. The numerical models are simulated using MATLAB and parallel computing with the program Palabos. A reaction-advection-diffusion transport for two components is analyzed with electrochemical reactions. This process is further coupled with the momentum transport. The effect of different bond numbers and contact angels on the simulation results are analyzed.It has here been shown that LBM can be used to evaluate the transport processes at microscale and it is possible to include the effect of electrochemical reactions on the transport processes. An increased Bond number increases the bubble fl ow through the nanorod domain. A decreased contact angle facilitates the disconnection of the bubble to the nanorod at the top surface. The collection of the hydrogen bubbles at the top surface of the nanorods will be facilitated by an easy disconnection of the bubbles.

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Section: Governing Equationsmentioning

confidence: 99%

Section: Governing Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Analysis of hydrogen bubble flow between nanorods using lattice boltzmann method

Paradis¹,

Grigoropoulos²,

Sundén³

2014

Int. J. CMEM

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show abstract

“…This intrinsic feature enables the lattice BGK method to incorporate easily essential physics at microscopic or mesoscopic level. Several lattice BGK models for simulation of diffusion-reaction system have been proposed in the past several years [5][6][7][8][9]. Although each of the above lattice BGK diffusion-reaction models was built on different physical pictures and has a quite different appearance, a recent study by Yan et al [10] showed that all of them have an origin in the kinetic theory.…”

Section: Introductionmentioning

confidence: 99%

Lattice Bhatnagar–Gross–Krook model for the Lorenz attractor

Yan

2001

Physica D: Nonlinear Phenomena

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In this paper, we propose a new lattice Bhatnagar-Gross-Krook model for simulation of the Lorenz attractor. The new model is based on a nonlinear diffusion-reaction system. We formulate a lattice Bhatnagar-Gross-Krook model for the nonlinear diffusion-reaction system by using a method of higher moments of the lattice Boltzmann equation. As a special case where the diffusion effect disappears, we get the Lorenz equation. In the model, we obtain a series of lattice Boltzmann equations at different time scales, and the conservation law at time scale t 0 . The equilibrium distribution functions are simpler than those for the standard lattice Boltzmann model. The numerical examples show that the method can be used to simulate the Lorenz equation.

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“…A fourth line of development treats the Schrödinger equation and its nonlinear extensions as reaction-diffusion equations for complex wavefunctions [5][6][7], and adapts standard lattice Boltzmann techniques for reactiondiffusion equations [8]. The target partial differential equation then describes slowly varying solutions on some manifold within an enlarged state space for a dissipative system, just as in lattice Boltzmann formulations for hydrodynamics.…”

Section: Introductionmentioning

confidence: 99%

Quantum lattice algorithms: similarities and connections to some classic finite difference algorithms

Dellar¹

2015

ESAIM: Proc.

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Abstract. Quantum lattice algorithms originated with the Feynman checkerboard model for the onedimensional Dirac equation. They offer discrete models of quantum mechanics in which the complex numbers representing wavefunction values on a discrete spatial lattice evolve through discrete unitary operations. This paper draws together some of the identical, or at least unitarily equivalent, algorithms that have appeared in three largely disconnected strands of research. Treated as conventional numerical algorithms, they are all only first order accurate under refinement of the discrete space/time grid, but may be raised to second order by a unitary change of variables. Much more efficient implementations arise from replacing the evolution through a sequence of unitary intermediate steps with a short path integral formulation that expresses the wavefunction at each spatial point on the most recent time level as a linear combination of values at immediately preceding time levels and neighbouring spatial points. In one dimension, a particularly elegant reformulation replaces two variables at two time levels with a single variable over three time levels. The resulting algorithm is a variational integrator arising from a discrete action principle, and coincides with the Ablowitz-Kruskal-Ladik finite difference scheme for the Klein-Gordon equation.

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Lattice Boltzmann computations for reaction-diffusion equations

Cited by 354 publications

References 14 publications

Analysis of hydrogen bubble flow between nanorods using lattice boltzmann method

Analysis of hydrogen bubble flow between nanorods using lattice boltzmann method

Lattice Bhatnagar–Gross–Krook model for the Lorenz attractor

Quantum lattice algorithms: similarities and connections to some classic finite difference algorithms

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