Abstract
A standard model, one of the lattice Boltzmann models for incompressible flow, is broadly applied in mesoscopic fluid with obvious compressible error. To eliminate the compressible effect and the limits in 2D problems, three different models (He-Luo model, Guo’s model, and Zhang’s model) have been proposed and tested by some benchmark questions. However, the numerical accuracy of models adopted in complex geometry and the effect of structural complexity are rarely studied. In this paper, a 2D dimensionless steady flow model is proposed and constructed by fractal geometry with different structural complexity. Poiseuille flow is first simulated to verify the code and shows good agreements with the theoretical solution, supporting further the comparative study on four models to investigate the effect of structural complexity and grid resolution, with reference results obtained by the finite element method (FEM). The work confirms the latter proposed models and effectively reduces compressible error in contrast to the standard model; however, the compressible effect still cannot be ignored in Zhang’s model. The results show that structural error has an approximately negative exponential relationship with grid resolution but an approximately linear relationship with structural complexity. The comparison also demonstrates that the He-Luo model and Guo’s model have a good performance in accuracy and stability, but the convergence rate is lower, while Zhang’s model has an advantage in the convergence rate but the computational stability is poor. The study is significant as it provides guidance and suggestions for adopting LBM to simulate incompressible flow in a complex structure.
Highlights
The lattice Boltzmann Method (LBM) is one of the currently popular computational fluid dynamics (CFD) methods, successfully applied to fluid flows through porous media [1,2,3,4], multi-phase fluid flows [5,6,7,8], fluid structure interaction [9,10], particle-laden turbulent [11,12], non-Newtonian particle flow [13,14] and even medical engineering [15]
Compared with traditional CFD methods such as the finite element method (FEM) and finite volume method (FVM), by solving N–S equations via direct discretization, LBM computes the statistics of vast kinetic particles, which are regarded as fluid micelles with a different velocity and mass, and is different from the continuous fluid assumption
The different LBM models for incompressible flow with an MRT collision operator are investigated in terms of their numerical performance
Summary
The lattice Boltzmann Method (LBM) is one of the currently popular computational fluid dynamics (CFD) methods, successfully applied to fluid flows through porous media [1,2,3,4], multi-phase fluid flows [5,6,7,8], fluid structure interaction [9,10], particle-laden turbulent [11,12], non-Newtonian particle flow [13,14] and even medical engineering [15]. Compared with traditional CFD methods such as the finite element method (FEM) and finite volume method (FVM), by solving N–S equations via direct discretization, LBM computes the statistics of vast kinetic particles, which are regarded as fluid micelles with a different velocity and mass, and is different from the continuous fluid assumption. The most attractive advantage over other approaches is the straightforward construction of geometry; the structure is mapped to points set with different attributes to avoid the complicated and difficult meshing process in traditional CFD [20,21]. Song [26,27] and Li et al [28] compared different numerical methods to simulate image-based rock permeability and confirmed that the LBM has incomparable and remarkable advantages in microscopic flow, especially with complex geometry structures
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
