# Research on Parameter Spatialization and Adaptive Correction Models in Fluid Numerical Simulations

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.1.1. Data Introduction

#### DEM (Digital Elevation Model)

#### Initial data

#### Verification Data

#### 2.2. Model and Methods

- The spatial design of the Manning coefficient of the numerical simulation model in the calculation area;
- The logic of the adaptive adjustment of the Manning coefficient.

#### 2.2.1. Numerical Simulation Model

#### 2.2.2. Spatialized Design of the Manning Coefficient

#### 2.2.3. Cost Function

#### 2.2.4. Adaptive Correction Model

#### Logic-A

#### Logic-B

#### 2.2.5. Adaptive Correction Function

Algorithm 1:$\Delta t$ for adjustment of each gauge. |

#### 2.3. Model Running Conditions

#### 2.3.1. Boundary Conditions

#### 2.3.2. Stable Conditions

#### 2.4. Experimental Design

#### 2.4.1. Control Point Selection

#### 2.4.2. Parameter Settings

## 3. Results and Discussion

#### 3.1. Verification of the Logic and Stability of Adaptive Correction

#### 3.2. Verification of the Convergence of Adaptive Correction

- To analyze the effect of relaxation factor c, $a=0.2$ and $c=2$, 3, and 4 were set for three sets of data for the experiments.
- To analyze the effect of parameter a, $c=2$ and $a=0.2$, 0.35, and 0.5 were set for three sets of data for the experiments.

#### 3.3. Evaluation of the Accuracy of Adaptive Correction

## 4. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 7.**Relationship between the time error and Manning coefficient correction values for different parameters.

**Figure 10.**Error curve and learning curve of each gauge in logic A and logic B (${\mathbf{N}}_{2}$).

**Figure 11.**Error curve and learning curve of each gauge in logic-A and logic-B (${\mathbf{N}}_{3}$).

Gauge ID | X (m) | Y (m) | Water Arrival Time (s) | The Max Water Level (m) |
---|---|---|---|---|

6 | 4947.46 | 4289.71 | 9 | 84.2 |

7 | 5717.30 | 4407.61 | 100 | 49.1 |

8 | 6775.14 | 3869.23 | 180 | 54 |

9 | 7128.20 | 3162.00 | 270 | 40.2 |

10 | 8585.30 | 3443.08 | 400 | 34.9 |

11 | 9674.97 | 3085.89 | 600 | 27.4 |

12 | 10,939.15 | 3044.78 | 850 | 21.5 |

13 | 11,724.3 | 2810.41 | 970 | 16.1 |

14 | 12,723.70 | 2485.08 | 1130 | 12.9 |

G6 | G7 | G8 | G9 | G10 | G11 | G12 | G13 | G14 | ||
---|---|---|---|---|---|---|---|---|---|---|

Physical model | Water arrival time (s) | 9.00 | 100.00 | 180.00 | 270.00 | 400.00 | 600.00 | 850.00 | 970.00 | 1130.00 |

Max. water level (m) | 84.20 | 49.10 | 54.00 | 40.20 | 34.90 | 27.40 | 21.50 | 16.10 | 12.90 | |

Telemac-2D | Max. water level (m) | 87.97 | 54.43 | 53.25 | 47.91 | 36.51 | 25.37 | 19.13 | 17.65 | 12.76 |

RE (%) | 4.48 | 10.86 | 1.39 | 19.18 | 4.61 | 7.41 | 11.02 | 9.63 | 1.09 | |

MRE (%) | 7.74 | |||||||||

Without the spatialized design (n = 0.033) | Water arrival time (s) | 8.50 | 90.35 | 191.61 | 275.61 | 438.42 | 611.52 | 851.47 | 992.98 | 1273.12 |

RE (%) | 5.56 | 9.65 | 6.45 | 2.08 | 9.60 | 1.92 | 0.17 | 2.37 | 12.67 | |

MRE (%) | 5.61 | |||||||||

Max. water level (m) | 86.18 | 53.29 | 53.45 | 48.87 | 36.41 | 24.53 | 18.45 | 15.40 | 12.47 | |

RE (%) | 2.35 | 8.53 | 1.01 | 21.56 | 4.33 | 10.49 | 14.17 | 4.37 | 3.36 | |

MRE (%) | 7.80 | |||||||||

With the Spatialized design and adaptive correction | Water arrival time (s) | 8.50 | 94.30 | 185.61 | 269.31 | 399.98 | 598.03 | 842.87 | 947.79 | 1139.99 |

RE (%) | 5.56 | 5.70 | 3.11 | 0.26 | 0.01 | 0.33 | 0.84 | 2.29 | 0.88 | |

MRE (%) | 2.11 | |||||||||

Max. water level (m) | 86.55 | 53.77 | 54.29 | 47.65 | 37.38 | 25.69 | 18.79 | 15.92 | 11.50 | |

RE (%) | 2.79 | 9.52 | 0.53 | 18.53 | 7.11 | 6.25 | 12.61 | 1.14 | 10.87 | |

MRE (%) | 7.70 |

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**MDPI and ACS Style**

Qiao, C. Research on Parameter Spatialization and Adaptive Correction Models in Fluid Numerical Simulations. *Water* **2022**, *14*, 2671.
https://doi.org/10.3390/w14172671

**AMA Style**

Qiao C. Research on Parameter Spatialization and Adaptive Correction Models in Fluid Numerical Simulations. *Water*. 2022; 14(17):2671.
https://doi.org/10.3390/w14172671

**Chicago/Turabian Style**

Qiao, Changjian. 2022. "Research on Parameter Spatialization and Adaptive Correction Models in Fluid Numerical Simulations" *Water* 14, no. 17: 2671.
https://doi.org/10.3390/w14172671