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| DOI：10.13522/j.cnki.ggps.2020182 |
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| Comparison and Optimization of Sparse Matrix Solution Methods in One-dimensional Saint-Venant Equation Difference Numerical Algorithm |
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WANG Haohua, GUAN Guanghua, XIAO Changcheng
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1. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China; 2. Power China HuaDong Engineering Corporation, Hangzhou 310014, China
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| Abstract: |
| 【Background】In order to alleviate the shortage of water resources, China has established many water transfer projects. Due to its long water transfer distance, large water delivery volume, and numerous water passing buildings along the line, the control process is very complicated. Unsteady flow will inevitably appear in the channel operation scheduling process, and the Saint-Venant equations are an important way to describe and solve the unsteady flow.【Objective】With the construction of large-scale water transfer projects and the complexity of the operation scheduling and control process, the traditional method of solving the sparse matrix of the original Saint-Venant equations has been unable to meet the requirements of calculation volume and calculation speed. In order to find efficient and stable algorithms for solving large and sparse linear equations to improve the speed of solving Saint-Venant equations.【Method】In this paper, four algorithms for solving Saint-Venant equations based on the four-point eccentric scheme are summarized and improved, and the calculation efficiency of different algorithms is compared through simulation experiments.【Result】From the simulation results, it can be seen that when the number of calculation sections is small (less than 500), the calculation time of all methods is basically the same; when the number of calculation sections is large (more than 500), the speed of the four algorithms is improved compared with the traditional algorithm.When the number of cross sections is 1520, the calculation speed of the four algorithms is 4 times that of the traditional algorithm. When the number of cross sections is 3040, the calculation speed is more than 10 times.【Conclusion】The improved GE and PM algorithms have faster calculation speed and higher calculation efficiency when the number of cross sections is larger. The results of this paper have reference value for improving the calculation speed of large channel non-constant flow simulation. The method can be applied to canal system automatic control technology such as MPC control, LQR control point, etc., to improve the running speed of simulation program. |
| Key words: one dimensional unsteady flow in open-channel; Saint-Venant Equations; large sparse matrices; calculation time of a single section |
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