Detailed analysis of the lattice Boltzmann method on unstructured grids

JOURNAL OF COMPUTATIONAL PHYSICS

卷:297

Article

Misztal, Marek Krzysztof¹  Hernandez-Garcia, Anier¹  Matin, Rastin¹  Sorensen, Henning Osholm²  Mathiesen, Joachim¹ 

[1] Univ Copenhagen, Niels Bohr Inst, DK-2100 Copenhagen, Denmark

[2] Univ Copenhagen, Nanosci Ctr, Dept Chem, DK-2100 Copenhagen, Denmark

关键词: Lattice Boltzmann method;    Unstructured grids;    Flow in porous media;    Chapman-Enskog expansion analysis;   

DOI  :  10.1016/j.jcp.2015.05.019

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free