基于图论的多定压节点管网水力计算方法的研究

多定压节点管网具有复杂的拓扑关系,可充分发挥图论的优势对其进行水力计算.通过引入虚节最和虚环的概念将多定压节点问题转化为单定压节点问题,对相关矩阵按照定压和非定压节点、虚管段和实际管段、树支和链支管段进行分块表示.推导出了采用链支流量矩阵进行管网水力计算的解析表达式,在此基础上得到了适于计算机求解的离散模型,同时将此方法应用于实际算例并与Hardy Cross法的计算结果进行了对比.

Research on hydraulic computation of the multi-fixed head nodes network based on graph theory

With complicated topology in the multi-fixed head nodes network,hydraulic computation of the network is carried out with graph theory.The multi-fixed head nodes network is turned into a unique fixed head node network by adding pseudo-node and pseudo-loop,the relative matrix is blocked in terms of different types which include fixed and non-fixed head nodes,pseudo and real edge,tree and link.This paper deduces analytical formulas figured with link discharge matrix,based on which,the discrete model suitable for the numerical simulation is established.By computing the illustrative network,the result shows that the convergence and precision of the algorithm mentioned above is better than that of Hardy Cross method.