一维圣维南方程差分数值算法中稀疏矩阵求解方法比较及优选研究  

Comparison and Optimization of Sparse Matrix Solution Methods in One-dimensional Saint-venant Equation Difference Numerical Algorithm

作　　者：王浩骅 管光华[1] 肖昌诚 WANG Haohua;GUAN Guanghua;XIAO Changcheng(State Key Laboratory of Water Resources and Hydropower Engineering Science,Wuhan University,Wuhan 430072,China;Power China HuaDong Engineering Corporation,Hangzhou 310014,China)

机构地区：[1]武汉大学水资源与水电工程科学国家重点实验室,武汉430072 [2]中国电建集团华东勘测设计研究院有限公司,杭州310014

出　　处：《灌溉排水学报》2021年第3期116-124,共9页Journal of Irrigation and Drainage

基　　金：国家自然科学基金项目(51979202,51439006,51009108);“十三五”国家重点研发项目(2016YFC0401810)。

摘　　要：【目的】寻找高效、稳定的大型稀疏线性方程组求解算法以提高圣维南方程组求解速度。【方法】归纳了4种基于四点偏心格式的圣维南方程组求解算法并加以改进,并通过仿真试验,对比了不同算法的计算效率。【结果】计算断面数较少时(小于500),所有方法的运算时间基本一致;当计算断面数较大时(大于500),4种算法的速度较传统算法有了一定的提高,在计算断面数为1520时,4种算法的计算速度是传统算法的4倍,在计算断面数为3040时,计算速度更是达到了10倍以上。【结论】改进后的高斯消元法和PM算法在计算断面数较大时计算速度较快,计算效率较高。该方法可应用于MPC控制、LQR控制等渠系自动化控制技术中,以提高仿真程序运算速度。【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 aut

关 键 词：明渠一维非恒定流 圣维南方程组 大型稀疏矩阵 单个断面运算时间 

分 类 号：TV133[水利工程—水力学及河流动力学]