一种大型河网洪水演进快速计算方法

对于大型河网洪水演进过程,一维圣维南方程组离散后的线性方程组规模较大,导致系数矩阵存储和方程组求解难度较大。对此,在矩阵存储方面,采用十字链表法和按行(列)压缩存储法,只存储非零元素,节省存储空间;在求解器方面,研究不同直接法和迭代法的求解效率,总结适合大型河网的求解方法。对三峡库区2014、2017年的洪水演进过程的复核计算结果表明,稀疏矩阵压缩存储方法能节约存储空间99.22%;LU分解法能在1ms左右求解线性方程组,效率明显高于传统多级解法。

A Method of Fast Flood Routing Computation for Large-scale River Network

For flood routing in large-scale river network, the coefficient matrix of discrete linear system of Saint-Venant equations is large and sparse, which is difficult to be stored and solved the linear system equations. To solve the problem, the orthogonal linked list and compressed storage row/column (CSR/CSC) were used to store the large-scale sparse matrix. The two structures only stored the nonzero elements, which could occupy less memory and avoid zeros to involve in computing. For the solver, several direct and iterative methods were studied to find the best solver for the linear system of river network. In experiment, it computed the flood routing process of Three Gorges Reservoir in years of 2014 and 2017. The experimental shows that the compressed storage method can reduce memory by 99.22%, and the LU factorization solver can solve the linear system in 0.001 seconds, which is more efficient than the traditional multistage methods.