# The Particle Generation Method Utilizing an Arbitrary 2D Model for Smoothed Particle Hydrodynamics Modeling and Its Application in the Field of Snowdrift

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## Abstract

**:**

## 1. Introduction

## 2. Introduction of SPH Equations

#### 2.1. Basic SPH Method Equations

#### 2.2. Smooth Radius and Support Domain

#### 2.3. Kernel Function

## 3. The Control Formula of Snow

#### 3.1. Model Initial Conditions

#### 3.2. Snow Particle Sublimation Control Formula

#### 3.3. Computational Parameters

## 4. The Control Formula of Snow

#### 4.1. Pixel Value Conversion

#### 4.2. Particle Generation of Embankment and Cutting Models

#### 4.3. Particle Generation of Complex Particle Size Models of Flat Snow Beds

## 5. Model Verification and Result Analysis

#### 5.1. Model Verification

^{−1}. The overall quantity of sublimation reduces with the rise in height, whereas the sublimation rate increases initially and eventually declines. This is due to the fact that when snow particles in the air increase, so does the sublimation rate. Particle number density is an important factor affecting the total sublimation rate, which is consistent with the experimental conclusion of Wever et al. (2009) [19].

#### 5.2. Simulation Analysis of Embankment and Cutting

#### 5.3. Analysis of Causes of Snow Disaster

#### 5.4. The Results of Adding a Snow Fence

#### 5.5. The Results of Increasing the Snow Fences

## 6. Conclusions

- In the start-up phase, the uppermost snow particles obtain almost the same speed under the influence of air drag force. The size and direction of snow particle velocity in the same layer change significantly over time. The pace at which snowflakes sublimate likewise alters as a result of this alteration. The SPH approach yielded a velocity probability distribution of snow particles that is consistent with the earlier experimental findings.
- The sublimation rates at different heights showed a trend of increasing first and then decreasing. Although the temperature and humidity at the low altitude changed significantly, which led to a significant increase in the negative feedback effect, the total sublimation amount showed the opposite trend with the increase in height due to the large particle density of sublimated snow particles. Before humidity stabilizes, it is the most important factor affecting the specific humidity. However, temperature is the primary factor impacting a given humidity level when the humidity is steady.
- Through the SPH simulation software established in this paper, targeted snow and sand prevention was implemented for typical embankment and cutting conditions of wind and snow disasters. Combined with the advantages of the structure of the embankment itself, the establishment of a vertical snow fence can achieve a good snow prevention effect, and the reduction in snow on the subgrade surface can reach more than 85%. For the forward-tilting 45-degree snow fence, the snow prevention effect on the subgrade surface of the cutting is significantly reduced as the friction wind speed increases, and the smallest effect is 30.59% prevention. For the condition of multiple snow fences in the cutting, the snow-proof effect of the subgrade surface reaches about 93%. For different working conditions, different preventive measures can be taken, and our contribution reduces the blindness when experimenting with those measures.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Support domain of particles. (

**a**) Support domain. (

**b**) Water vapor diffusion. (

**c**) Heat transfer.

**Figure 5.**Establishment of initial model. (

**a**) Embankment picture. (

**b**) Cutting picture. (

**c**) Embankment particle conversion. (

**d**) Cutting particle conversion.

**Figure 6.**Establishment of multi-particle size model. (

**a**) Effective particle size distribution of wind-blowing snow. (

**b**) Multi-particle size model.

**Figure 9.**The flux of snow on a flat surface. Black is an experiment, and the color is a simulation [21].

**Figure 11.**Variation in temperature and humidity. (

**a**) Temperature and humidity change with height. (

**b**) Time variation of humidity. (

**c**) Time change of temperature.

Gas | Snow | Other Parameters |
---|---|---|

Diameter ${d}_{s}=0.1\text{}\mathrm{m}\mathrm{m}$ | Density ${\rho}_{S}=910$ kgm^{−3} | Time step $\u25b3t=1.0\times {10}^{-6}\text{}$s |

Density ${\rho}_{g}=1.29$ kgm^{−3} | Viscosity $\text{}{\mu}_{g}=1.895\times {10}^{-5}\text{}$Nsm^{−1} | Coefficient of friction ${\mu}^{*}=0.4$ |

Coefficient of restitution $e=0.8$ | Karman constant $k=0.4$ |

D | A | B | C | |
---|---|---|---|---|

0.1 ms^{−1} | 63.56% | 38.41% | 94.57% | 100% |

0.13 ms^{−1} | 55.94% | 1.67% | 85.62% | 97.87% |

0.16 ms^{−1} | 48.24% | −30.61% | 85.41% | 98.92% |

D | A | B | C | |
---|---|---|---|---|

0.1 ms^{−1} | 66.00% | 27.64% | 86.44% | 88.00% |

0.13 ms^{−1} | 64.08% | 5.43% | 77.38% | 94.12% |

0.16 ms^{−1} | 50.47% | 11.34% | 60.00% | 72.73% |

D | A | B | C | |
---|---|---|---|---|

0.1ms^{−1} | 91.35% | 86.88% | 92.02% | 100% |

0.13 ms^{−1} | 91.92% | 82.46% | 93.60% | 98.52% |

0.16 ms^{−1} | 89.72% | 82.32% | 92.53% | 89.00% |

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**MDPI and ACS Style**

Zhang, S.; Jin, A.; Zheng, B.; Peng, H.
The Particle Generation Method Utilizing an Arbitrary 2D Model for Smoothed Particle Hydrodynamics Modeling and Its Application in the Field of Snowdrift. *Water* **2023**, *15*, 3763.
https://doi.org/10.3390/w15213763

**AMA Style**

Zhang S, Jin A, Zheng B, Peng H.
The Particle Generation Method Utilizing an Arbitrary 2D Model for Smoothed Particle Hydrodynamics Modeling and Its Application in the Field of Snowdrift. *Water*. 2023; 15(21):3763.
https://doi.org/10.3390/w15213763

**Chicago/Turabian Style**

Zhang, Shuzhi, Afang Jin, Bin Zheng, and Hao Peng.
2023. "The Particle Generation Method Utilizing an Arbitrary 2D Model for Smoothed Particle Hydrodynamics Modeling and Its Application in the Field of Snowdrift" *Water* 15, no. 21: 3763.
https://doi.org/10.3390/w15213763