# Comparative Study of Lattice Boltzmann Models for Complex Fractal Geometry

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Lattice Boltzmann Models for Incompressible Flow

## 3. Methodology

#### 3.1. Flow Model

^{−7}and the criterion is stricter than previous work [56].

#### 3.2. Poiseuille Flow and Validation

## 4. Results and Discussion

#### 4.1. Grid Resolution

#### 4.2. Geometric Structure

#### 4.3. Flow Balance and Efficiency

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**(

**a**)The profiles of pressure at inlet boundary; (

**b**) The profiles of pressure at outlet boundary.

**Figure 6.**(

**a**,

**b**) The profiles of ${v}_{x}$ along vertical centerline of ROI (x = 140.5) in fractal I. (

**c**,

**d**) RE curves of ${v}_{x}$ along vertical centerline of ROI (x = 140.5) in fractal I.

**Figure 7.**(

**a**,

**b**) The profiles of ${v}_{x}$ along vertical centerline of ROI (x = 140.5) in fractal II. (

**c**,

**d**) RE curves of ${v}_{x}$ along vertical centerline of ROI (x = 140.5) in fractal II.

**Figure 8.**(

**a**,

**b**) The profiles of ${v}_{x}$ along vertical centerline of ROI (x = 140.5) in fractal III; (

**c**,

**d**) RE curves of ${v}_{x}$ along vertical centerline of ROI (x = 140.5) in fractal III.

**Figure 9.**(

**a**) MARE vary with different GRs in fractal I. (

**b**) MARE vary with different GRs in fractal II; (

**c**) MARE vary with different GRs in fractal III.

**Figure 10.**(

**a**) MARE curves vary with different fractal structures; (

**b**) MARE curves vary with different fractal structures after removing unreasonable points with great structural errors.

**Figure 12.**(

**a**) Flux curves of fractal I. (

**b**) Flux curves of fractal II. (

**c**) Flux curves of fractal III.

Length of x | Length of y | Length of ROI | Width of ROI | Viscosity | Density | Inlet Pressure | Outlet Pressure |
---|---|---|---|---|---|---|---|

281 | 81 | 81 | 81 | 0.2 | 1.0 | 0.3667 | 0.3333 |

Grid Size | 281 × 81 | 562 × 162 | 843 × 243 |
---|---|---|---|

Grid Resolution | 1 | 2 | 3 |

Viscosity | 0.2 | 0.4 | 0.6 |

τ_{s} | 0.9091 | 0.5882 | 0.4348 |

τ_{q} | 1.2308 | 1.5238 | 1.652 |

τ_{ρ}= τ_{d} | 1.0 | 1.0 | 1.0 |

τ_{e} = τ_{ε} | 0.8 | 0.8 | 0.8 |

281 × 81 | 562 × 162 | 843 × 243 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

MRT-S | MRT-H | MRT-G | MRT-Z | MRT-S | MRT-H | MRT-G | MRT-Z | MRT-S | MRT-H | MRT-G | MRT-Z | |

I | 16,168 | 21,395 | 20,792 | 14,584 | 34,613 | 40,178 | 38,268 | 21,292 | 44,250 | 54,450 | 50,544 | 32,749 |

II | 11,249 | 12,740 | 12,596 | 7395 | 31,938 | 29,092 | 24,638 | 14,696 | 34,240 | 40,168 | 38,125 | 18,764 |

II | 12,068 | 12,144 | 11,242 | 9275 | 16,765 | 22,794 | 20,959 | 13,252 | 36,541 | 37,805 | 35,254 | 21,600 |

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**MDPI and ACS Style**

Zhang, D.; Wang, E.; Liu, X.
Comparative Study of Lattice Boltzmann Models for Complex Fractal Geometry. *Energies* **2021**, *14*, 6779.
https://doi.org/10.3390/en14206779

**AMA Style**

Zhang D, Wang E, Liu X.
Comparative Study of Lattice Boltzmann Models for Complex Fractal Geometry. *Energies*. 2021; 14(20):6779.
https://doi.org/10.3390/en14206779

**Chicago/Turabian Style**

Zhang, Dong, Enzhi Wang, and Xiaoli Liu.
2021. "Comparative Study of Lattice Boltzmann Models for Complex Fractal Geometry" *Energies* 14, no. 20: 6779.
https://doi.org/10.3390/en14206779