Detailed analysis of the lattice Boltzmann method on unstructured grids

Marek Krzysztof Misztal; Anier Hernandez Garcia; Rastin Matin; Henning Osholm Sørensen; Joachim Mathiesen

doi:10.1016/j.jcp.2015.05.019

Detailed analysis of the lattice Boltzmann method on unstructured grids

Marek Krzysztof Misztal, Anier Hernandez Garcia, Rastin Matin, Henning Osholm Sørensen, Joachim Mathiesen

19 Citations (Scopus)

Abstract

The lattice Boltzmann method has become a standard for efficiently solving problems in fluid dynamics. While unstructured grids allow for a more efficient geometrical representation of complex boundaries, the lattice Boltzmann method is often implemented using regular grids. Here we analyze two implementations of the lattice Boltzmann method on unstructured grids, the standard forward Euler method and the operator splitting method. We derive the evolution of the macroscopic variables by means of the Chapman-Enskog expansion, and we prove that it yields the Navier-Stokes equation and is first order accurate in terms of the temporal discretization and second order in terms of the spatial discretization. Relations between the kinetic viscosity and the integration time step are derived for both the Euler method and the operator splitting method. Finally, we suggest an improved version of the bounce-back boundary condition. We test our implementations in both standard benchmark geometries and in the pore network of a real sample of a porous rock.

Original language	English
Journal	Journal of Computational Physics
Volume	297
Pages (from-to)	316-339
ISSN	0021-9991
DOIs	https://doi.org/10.1016/j.jcp.2015.05.019
Publication status	Published - 5 Sept 2015

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title = "Detailed analysis of the lattice Boltzmann method on unstructured grids",

abstract = "The lattice Boltzmann method has become a standard for efficiently solving problems in fluid dynamics. While unstructured grids allow for a more efficient geometrical representation of complex boundaries, the lattice Boltzmann method is often implemented using regular grids. Here we analyze two implementations of the lattice Boltzmann method on unstructured grids, the standard forward Euler method and the operator splitting method. We derive the evolution of the macroscopic variables by means of the Chapman-Enskog expansion, and we prove that it yields the Navier-Stokes equation and is first order accurate in terms of the temporal discretization and second order in terms of the spatial discretization. Relations between the kinetic viscosity and the integration time step are derived for both the Euler method and the operator splitting method. Finally, we suggest an improved version of the bounce-back boundary condition. We test our implementations in both standard benchmark geometries and in the pore network of a real sample of a porous rock.",

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T1 - Detailed analysis of the lattice Boltzmann method on unstructured grids

AU - Misztal, Marek Krzysztof

AU - Hernandez Garcia, Anier

AU - Matin, Rastin

AU - Sørensen, Henning Osholm

AU - Mathiesen, Joachim

PY - 2015/9/5

Y1 - 2015/9/5

N2 - The lattice Boltzmann method has become a standard for efficiently solving problems in fluid dynamics. While unstructured grids allow for a more efficient geometrical representation of complex boundaries, the lattice Boltzmann method is often implemented using regular grids. Here we analyze two implementations of the lattice Boltzmann method on unstructured grids, the standard forward Euler method and the operator splitting method. We derive the evolution of the macroscopic variables by means of the Chapman-Enskog expansion, and we prove that it yields the Navier-Stokes equation and is first order accurate in terms of the temporal discretization and second order in terms of the spatial discretization. Relations between the kinetic viscosity and the integration time step are derived for both the Euler method and the operator splitting method. Finally, we suggest an improved version of the bounce-back boundary condition. We test our implementations in both standard benchmark geometries and in the pore network of a real sample of a porous rock.

AB - The lattice Boltzmann method has become a standard for efficiently solving problems in fluid dynamics. While unstructured grids allow for a more efficient geometrical representation of complex boundaries, the lattice Boltzmann method is often implemented using regular grids. Here we analyze two implementations of the lattice Boltzmann method on unstructured grids, the standard forward Euler method and the operator splitting method. We derive the evolution of the macroscopic variables by means of the Chapman-Enskog expansion, and we prove that it yields the Navier-Stokes equation and is first order accurate in terms of the temporal discretization and second order in terms of the spatial discretization. Relations between the kinetic viscosity and the integration time step are derived for both the Euler method and the operator splitting method. Finally, we suggest an improved version of the bounce-back boundary condition. We test our implementations in both standard benchmark geometries and in the pore network of a real sample of a porous rock.

U2 - 10.1016/j.jcp.2015.05.019

DO - 10.1016/j.jcp.2015.05.019

M3 - Journal article

SN - 0021-9991

VL - 297

SP - 316

EP - 339

JO - Journal of Computational Physics

JF - Journal of Computational Physics

ER -

Detailed analysis of the lattice Boltzmann method on unstructured grids

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