Analytical Solution of the Classical Dam-Break Problem for the Gravity Wave–Model Equations

2016 ◽  
Vol 142 (5) ◽  
pp. 06016003 ◽  
Author(s):  
Ricardo Martins ◽  
Jorge Leandro ◽  
Slobodan Djordjević
Keyword(s):  
Analytical Solution ◽  
Gravity Wave ◽  
Wave Model ◽  
Dam Break ◽  
Model Equations

scholarly journals Assessing the Analytical Solution of One-Dimensional Gravity Wave Model Equations Using Dam-Break Experimental Measurements

Water ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 1261 ◽  
Author(s):  
Wenjun Liu ◽  
Bo Wang ◽  
Yunliang Chen ◽  
Chao Wu ◽  
Xin Liu
Keyword(s):  
Gravity Wave ◽  
Water Depth ◽  
Wave Model ◽  
Discontinuity Point ◽  
Weak Discontinuity ◽  
Dam Break ◽  
Experimental Results ◽  
Hydraulic Parameters ◽  
One Dimensional ◽  
Dimensional Gravity

The one-dimensional gravity wave model (GWM) is the result of ignoring the convection term in the Saint-Venant Equations (SVEs), and has the characteristics of fast numerical calculation and low stability requirements. To study its performances and limitations in 1D dam-break flood, this paper verifies the model using a dam-break experiment. The experiment was carried out in a large-scale flume with depth ratios (initial downstream water depth divided by upstream water depth) divided into 0 and 0.1~0.4. The data were collected by image processing technology, and the hydraulic parameters, such as water depth, flow discharge, and wave velocity, were selected for comparison. The experimental results show that the 1D GWM performs an area with constant hydraulic parameters, which is quite different from the experimental results in the dry downstream case. For a depth ratio of 0.1, the second weak discontinuity point, which is connected to the steady zone in the 1D GWM, moves upstream, which is contrary to the experimental situation. For depth ratios of 0.2~0.4, the moving velocity of the second weak discontinuity point is faster than the experimental value, while the velocity of the shock wave is slower. However, as the water depth ratio increases, the hydraulic parameters calculated by 1D GWM in the steady zone gradually approach the experimental value.

scholarly journals Dam-Break Flows: Comparison between Flow-3D, MIKE 3 FM, and Analytical Solutions with Experimental Data

2018 ◽  
Vol 8 (12) ◽  
pp. 2456 ◽  
Author(s):  
Hui Hu ◽  
Jianfeng Zhang ◽  
Tao Li
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Analytical Solution ◽  
Water Depth ◽  
3D Model ◽  
Real Life ◽  
Surface Profile ◽  
Dam Break ◽  
Computational Time ◽  
Free Surface Profile

The objective of this study was to evaluate the applicability of a flow model with different numbers of spatial dimensions in a hydraulic features solution, with parameters such a free surface profile, water depth variations, and averaged velocity evolution in a dam-break under dry and wet bed conditions with different tailwater depths. Two similar three-dimensional (3D) hydrodynamic models (Flow-3D and MIKE 3 FM) were studied in a dam-break simulation by performing a comparison with published experimental data and the one-dimensional (1D) analytical solution. The results indicate that the Flow-3D model better captures the free surface profile of wavefronts for dry and wet beds than other methods. The MIKE 3 FM model also replicated the free surface profiles well, but it underestimated them during the initial stage under wet-bed conditions. However, it provided a better approach to the measurements over time. Measured and simulated water depth variations and velocity variations demonstrate that both of the 3D models predict the dam-break flow with a reasonable estimation and a root mean square error (RMSE) lower than 0.04, while the MIKE 3 FM had a small memory footprint and the computational time of this model was 24 times faster than that of the Flow-3D. Therefore, the MIKE 3 FM model is recommended for computations involving real-life dam-break problems in large domains, leaving the Flow-3D model for fine calculations in which knowledge of the 3D flow structure is required. The 1D analytical solution was only effective for the dam-break wave propagations along the initially dry bed, and its applicability was fairly limited.

scholarly journals Analytical Solution of Shallow Water Equations for Ideal Dam-Break Flood along a Wet-Bed Slope

2020 ◽  
Vol 146 (2) ◽  
pp. 06019020 ◽  
Author(s):  
Bo Wang ◽  
Yunliang Chen ◽  
Yong Peng ◽  
Jianmin Zhang ◽  
Yakun Guo
Keyword(s):  
Analytical Solution ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Dam Break ◽  
Bed Slope
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