Numerical and Analytical Spatial Coupling of a Lattice Boltzmann Model and a Partial Differential Equation

Leemput, Pieter Van; Vanroose, Wim; Roose, Dirk

doi:10.1007/3-540-35888-9_19

Cited by 5 publications

(15 citation statements)

References 16 publications

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“…Afterwards, these values propagate to a neighboring lattice site according to their velocity direction (left hand side of ( 4)). Diffusive collisions are modeled by the Bhatnagar-Gross-Krook (BGK) collision term −ω(f i (x, t)−f eq i (x, t)) in ( 4) as a relaxation to a local diffusive equilibrium f eq i (x, t) with relaxation coefficient ω [30,37], while reactions are modeled by the term R i (x, t) [30,13] as…”

Section: Lattice Boltzmann Model (Lbm)mentioning

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: Lattice Boltzmann Model (Lbm)mentioning

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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“…In this paper, LBM is adopted as the mesoscopic simulator. As indicated in [18,20] the macroscopic state variables are easy to be achieved. To transfer the micro/meso-scale parameters into macro parameters we need some restriction [22] or compression [29] operators.…”

Section: Derivation Of Non-equilibrium Distribution Function By Multimentioning

confidence: 99%

“…(77) can be determined directly by the right-hand side of Eq. (20). For any given initial velocity and density fields, each term in the right-hand side of Eq.…”

Section: Examination Of the Precision Of The Reconstruction Operatormentioning

confidence: 99%

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A lifting relation from macroscopic variables to mesoscopic variables in lattice Boltzmann method: Derivation, numerical assessments and coupling computations validation

Luan

et al. 2012

Computers & Fluids

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In this paper, analytic relations between the macroscopic variables and the mesoscopic variables are derived for lattice Boltzmann methods (LBM). The analytic relations are achieved by two different methods for the exchange from velocity fields of finite-type methods to the single particle distribution functions of LBM. The numerical errors of reconstructing the single particle distribution functions and the non-equilibrium distribution function by macroscopic fields are investigated. Results show that their accuracy is better than the existing ones. The proposed reconstruction operator has been used to implement the coupling computations of LBM and macro-numerical methods of FVM.The lid-driven cavity flow is chosen to carry out the coupling computations based on the numerical strategies of domain decomposition methods (DDM).The numerical results show that the proposed lifting relations are accurate and robust.

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Numerical and Analytical Spatial Coupling of a Lattice Boltzmann Model and a Partial Differential Equation

Cited by 5 publications

References 16 publications

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

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

Multiscale Simulations of Heat Transfer and Fluid Flow Problems

A lifting relation from macroscopic variables to mesoscopic variables in lattice Boltzmann method: Derivation, numerical assessments and coupling computations validation

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