树状河网非恒定流的一则并行直接数值解法  

A Parallel Direct Numerical Method for Solving Unsteady Flow Issue of Tree-type River Networks

作　　者：张国义[1,2] 房明惠[3] 黄刘生[1,2] 陈国良[1,2] 

机构地区：[1]中国科学技术大学计算机科学与技术系 [2]国家高性能计算中心,安徽合肥230027 [3]中国科学技术大学地球与空间科学学院

出　　处：《系统仿真学报》2004年第12期2673-2676,2679,共5页Journal of System Simulation

基　　金：国家863高技术研究发展计划项目(2002AA104560)

摘　　要：描述了求解树状河网非恒定流问题的一则并行直接数值解法。该方法首先利用区域分解方法将河网划分成p个子块,然后利用串行双消除算法所隐含的自然并行性,以及树状河网支流交汇点水流连续方程组系数矩阵的特点,将计算任务分配到p个处理器进行多级直接数值求解。在曙光2000并行计算机上用消息传递方式实现了该算法并进行了性能测试,结果表明算法的数值稳定性好,并行效率可以达到90%以上。It is presents a parallel direct numerical method for solving unsteady flow issue of tree-type river networks. First, the river network is partitioned into p sub-networks using some graph-based domain decomposition techniques, and then an improved and parallelized Double Sweep Algorithm (DSA, described in reference [1] and [2]) is employed to perform DSA-styled three main steps in parallel: (1)elimination of linear discretized Saint Venant Equations (SVE) of each branch in every sub-network, (2)constructing and solving the flow continuity equations (FCE) around branch conjunction nodes, and (3)backward substitution. The coefficient matrix of FCE is a diagonal dominant sparse matrix. For solving FCE, we use a class of multi-level sparse direct numerical factorization method, and use the adjacent lists of each sub-network to guide the operations of 搊rdering? 損ermutation? etc. After factorization and selection, part of the FCE is transformed into a tridiagonal linear system that is solved by a parallel algorithm described in reference [11]. The numerical method present in this paper is implemented and tested on a homemade Dawning 2000 supercomputer equipped by National High Performance Center at Hefei (NHPCC@Hefei) using Message Passing programming method. The results show that not only the algorithm has high numerical stability, but also the parallel efficiency can reach higher than 90%.

关 键 词：树状河网 圣维南方程组 稀疏直接法 区域分解 并行算法 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]