A 1D–2D Coupled Lattice Boltzmann Model for Shallow Water Flows in Large Scale River-Lake Systems
Abstract
:1. Introduction
2. 1D and 2D Shallow Water Submodels and Their Coupling Strategy
2.1. 1D Shallow Water Submodel
2.2. 2D Shallow Water Submodel
2.3. The Coupling Strategy of 1D and 2D Submodels
- (1)
- Calculate the three unknown distribution functions of the coupling interface;
- (2)
- Calculate the macroscopic parameters (water depth and velocity) of the coupling interface by the distribution functions solved in the first step;
- (3)
- Calculate the unknown distribution functions at the coupling boundaries of the 2D domain by the above calculated macroscopic parameters.
2.4. Stability Requirements
3. Numerical Experiments
3.1. The Dam Break Flow
3.2. The Surge Waves in Tailrace Canal of a Hydropower Station
4. Simulation of Surge Waves in the Reservoir of a Run-of-River Hydropower Station
4.1. Computational Setup
4.2. Simulation Results
4.3. Computational Efficiency Analysis
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Methods | x1 | x2 | ||||
h (m) | AE (m) | RE (%) | h (m) | AE (m) | RE (%) | |
Analytic | 7.203 | - | - | 4.414 | - | - |
1D model | 7.180 | 0.023 | 0.32 | 4.411 | 0.003 | 0.07 |
2D model | 7.170 | 0.033 | 0.46 | 4.410 | 0.004 | 0.09 |
1D–2D model | 7.169 | 0.034 | 0.47 | 4.414 | 0 | 0 |
Methods | u (m/s) | AE (m/s) | RE (%) | u (m/s) | AE (m/s) | RE (%) |
Analytic | 0.906 | - | - | 4.557 | - | - |
1D model | 0.938 | 0.032 | 3.53 | 4.551 | 0.006 | 0.13 |
2D model | 0.952 | 0.046 | 5.08 | 4.550 | 0.007 | 0.15 |
1D–2D model | 0.951 | 0.045 | 4.97 | 4.544 | 0.013 | 0.28 |
Lattice Spacing (m) | 2D Grid | 1D Grid | Consumed Time (h) | Performance (MNUPS) | Speedup Ratio |
---|---|---|---|---|---|
= 17.28 | 400 300 | 2026 | 0.71 | 17.09 | - |
= 8.64 | 800 600 | 4051 | 1.90 | 25.54 | 1.46 |
= 4.32 | 1600 1200 | 8102 | 4.47 | 43.12 | 2.52 |
= 2.16 | 320 2400 | 16204 | 15.42 | 49.92 | 2.92 |
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Meng, W.; Cheng, Y.; Wu, J.; Zhang, C.; Xia, L. A 1D–2D Coupled Lattice Boltzmann Model for Shallow Water Flows in Large Scale River-Lake Systems. Appl. Sci. 2020, 10, 108. https://doi.org/10.3390/app10010108
Meng W, Cheng Y, Wu J, Zhang C, Xia L. A 1D–2D Coupled Lattice Boltzmann Model for Shallow Water Flows in Large Scale River-Lake Systems. Applied Sciences. 2020; 10(1):108. https://doi.org/10.3390/app10010108
Chicago/Turabian StyleMeng, Wanwan, Yongguang Cheng, Jiayang Wu, Chunze Zhang, and Linsheng Xia. 2020. "A 1D–2D Coupled Lattice Boltzmann Model for Shallow Water Flows in Large Scale River-Lake Systems" Applied Sciences 10, no. 1: 108. https://doi.org/10.3390/app10010108
APA StyleMeng, W., Cheng, Y., Wu, J., Zhang, C., & Xia, L. (2020). A 1D–2D Coupled Lattice Boltzmann Model for Shallow Water Flows in Large Scale River-Lake Systems. Applied Sciences, 10(1), 108. https://doi.org/10.3390/app10010108