Coupling a Lattice Boltzmann and a Finite Difference Scheme

Albuquerque, Paul; Alemani, Davide; Chopard, Bastien; Leone, Pierre

doi:10.1007/978-3-540-25944-2_70

Cited by 12 publications

(18 citation statements)

References 6 publications

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“…We are particularly interested in the spatial discretization error of the hybrid model. In [2,3,24], Albuquerque et al reported a second order discretization error in space (just like both the discretized PDE and LBM on the full domain). We will study this claim further and derive closed expressions for the error at steady state for some basic problems.…”

Section: Introductionmentioning

confidence: 99%

Accuracy of Hybrid Lattice Boltzmann/Finite Difference Schemes for Reaction-Diffusion Systems

Leemput¹,

Vandekerckhove²,

Vanroose³

et al. 2007

Multiscale Model. Simul.

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In this article we construct a hybrid model by spatially coupling a lattice Boltzmann model (LBM) to a finite difference discretization of the partial differential equation (PDE) for reaction-diffusion systems. Because the LBM has more variables (the particle distribution functions) than the PDE (only the particle density), we have a one-to-many mapping problem from the PDE to the LBM domain at the interface. We perform this mapping using either results from the Chapman-Enskog expansion or a point-wise iterative scheme that approximates these analytical relations numerically. Most importantly, we show that the global spatial discretization error of the hybrid model is one order less accurate than the local error made at the interface. We derive closed expressions for the spatial discretization error at steady state and verify them numerically for several examples on the one-dimensional domain.

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Section: Introductionmentioning

confidence: 99%

Accuracy of Hybrid Lattice Boltzmann/Finite Difference Schemes for Reaction-Diffusion Systems

Leemput¹,

Vandekerckhove²,

Vanroose³

et al. 2007

Multiscale Model. Simul.

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“…The coupling of FDM with LBM was conducted in Refs. [70] and [71], but the coupling computations were only implemented for the solution of one dimensional diffusion equation. A general coupling scheme, or a general reconstruction operator for transferring information from macroscale results to mesoscale parameters for multidimensional fluid flow is highly needed.…”

Section: Coupling Between Lbm and Fvm (Fdm And Fem)mentioning

confidence: 99%

Multiscale Simulations of Heat Transfer and Fluid Flow Problems

Tao

2012

Journal of Heat Transfer

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The multiscale problems in the thermal and fluid science are classified into two categories: multiscale process and multiscale system. The meanings of the two categories are described. Examples are provided for multiscale process and multiscale system. In this pa-per, focus is put on the simulation of multiscale process. The numerical approaches for multiscale processes have two categories: one is the usage of a general governing equation and solving the entire flow field involving a variation of several orders in characteristic geometric scale. The other is the so-called “solving regionally and coupling at the inter-faces. ” In this approach, the processes at different length levels are simulated by different numerical methods and then information is exchanged at the interfaces between different regions. The key point is the establishment of the reconstruction operator, which transforms the data of few variables of macroscopic computation to a large amount of variables of microscale or mesoscale simulation. Six numerical examples of multiscale simulation are presented. Finally, some research needs are proposed. [DOI: 10.1115/1.4005154

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“…And this is what we call multiscale simulation [2,3]. In recently years, many studies have been done about the coupling among different scale CFD models, such as FEM-MD-QM [4], MD-FVM [5,6], LBM-MD [7], DSMC-NS [8], FDM-LBM [9,10], FVM-LBM [11][12][13][14]. It is worth noting that the terminology ''multiscale'' is now used quite extensively.…”

Section: Introductionmentioning

confidence: 99%