# Numerical Simulation of Sediment Transport in Unsteady Open Channel Flow

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## Abstract

**:**

## 1. Introduction

## 2. Governing Equations

#### 2.1. Nonequilibrium Sediment Transport Model

#### 2.2. Numerical Methods

#### 2.2.1. Godunov-Type Finite Volume Method

#### 2.2.2. HLLC Approximated Riemann Solver

#### 2.2.3. Well-Balanced Scheme for the VDSWEs

## 3. Results

#### 3.1. Case 1: Standing Contact-Discontinuity

#### 3.2. Case 2: One-Dimensional Dam-Break Flow over Mobile Bed

#### 3.3. Case 3: Two-Dimensional Dam-Break Flow over Mobile Bed

#### 3.4. Case 4: 1996 Lake Ha! Ha! Catastrophic Flood Event

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Solution of test case 1: (

**a**) surface profile; (

**b**) density profile; and (

**c**) velocity profile.

**Figure 3.**Measured and calculated results of test case 2: (

**a**) t = 0.25 s; (

**b**) t = 0.50 s; (

**c**) t = 0.75 s; (

**d**) t = 1.00 s (

**e**) t = 1.25 s; and (

**f**) t = 1.50 s [21].

**Figure 6.**Measured and calculated water levels of 2D dam-break flow at: (

**a**) Gauge 1; (

**b**) Gauge 2; (

**c**) Gauge 3; (

**d**) Gauge 4; (

**e**) Gauge 5; (

**f**) Gauge 6; (

**g**) Gauge 7; and (

**h**) Gauge 8.

**Figure 7.**Measured and calculated bed profiles of 2D dam-break flow: (

**a**) y = 0.20 m; (

**b**) y = 0.70 m; (

**c**) y = 1.45 m.

**Figure 10.**Measured and calculated bed cross sections of Lake Ha! Ha! flood event: (

**a**) cross section #20; (

**b**) cross section #70; (

**c**) cross section #120; (

**d**) cross section #170; (

**e**) cross section #220; (

**f**) cross section #270; and (

**g**) cross section #320.

**Figure 11.**Analysis of calculated bed cross sections of Lake Ha! Ha! flood event: (

**a**) RMSEs; (

**b**) MREs.

**Figure 13.**Measured and calculated thalwegs of Lake Ha! Ha! flood event: (

**a**) 0–12 km; (

**b**) 12–24 km; (

**c**) 24–36 km.

Time (s) | Water Level | Bed Elevation | ||
---|---|---|---|---|

RMSE (cm) | MRE (%) | RMSE (cm) | MRE (%) | |

0.25 | 1.13 | 3.35 | 0.45 | 23.20 |

0.50 | 0.57 | 1.80 | 0.38 | 25.09 |

0.75 | 0.78 | 2.79 | 0.39 | 26.47 |

1.00 | 0.84 | 3.37 | 0.33 | 22.24 |

1.25 | 0.82 | 3.58 | 0.35 | 23.75 |

1.50 | 0.87 | 4.83 | 0.32 | 27.35 |

Average | 0.84 | 3.29 | 0.37 | 24.68 |

Gauge Number | RMSE (cm) | MRE (%) |
---|---|---|

1 | 1.71 | 15.11 |

2 | 2.07 | 12.66 |

3 | 2.17 | 12.72 |

4 | 1.59 | 13.81 |

5 | 1.39 | 18.90 |

6 | 1.49 | 20.73 |

7 | 1.58 | 21.91 |

8 | 1.98 | 21.50 |

Average | 1.75 | 17.17 |

Bed Profile (m) | RMSE (cm) | MRE (%) |
---|---|---|

0.20 | 1.24 | 13.03 |

0.70 | 1.67 | 32.65 |

1.45 | 0.91 | 17.20 |

Average | 1.27 | 20.96 |

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**MDPI and ACS Style**

Duan, J.G.; Yu, C.; Ding, Y.
Numerical Simulation of Sediment Transport in Unsteady Open Channel Flow. *Water* **2023**, *15*, 2576.
https://doi.org/10.3390/w15142576

**AMA Style**

Duan JG, Yu C, Ding Y.
Numerical Simulation of Sediment Transport in Unsteady Open Channel Flow. *Water*. 2023; 15(14):2576.
https://doi.org/10.3390/w15142576

**Chicago/Turabian Style**

Duan, Jennifer G., Chunshui Yu, and Yan Ding.
2023. "Numerical Simulation of Sediment Transport in Unsteady Open Channel Flow" *Water* 15, no. 14: 2576.
https://doi.org/10.3390/w15142576