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非线性管道网络方程组的一个新解法

张建中,沈明刚   

  1. 上海师范学院 ;上海师范学院
  • 出版日期:1981-01-20 发布日期:1981-01-20

张建中,沈明刚. 非线性管道网络方程组的一个新解法[J]. 数值计算与计算机应用, 1981, 2(1): 29-36.

A NEW METHOD FOR NONLINEAR PIPE NETWORK EQUATIONS

  1. Zhang Jian-zhong;Shen Ming-gang Shanghai Teacher's College
  • Online:1981-01-20 Published:1981-01-20
求解非线性管道网络的压力——流量方程组,是输油、输气管道、给水排水管道以及通风巷道设计中经常遇到的计算问题.考虑连通的平面管网图G,这里的平面图是指可以嵌入到平面上,且使它们的边只在节点处相交的图.设G上有m个收点,M个发点,n条边(管段).诸发点均为定压输出,从而它们相对于参考点(取在某发点处)的压降向量
The current method for nonlinear pipe network equations is that of seccessive linearapproximation. This type of method, even though some improvements have been madein it so as to prove its convergence, has simply a rate of linear convergence in general. In this paper, however, we transform the pipe network equations into a problem ofunconstrained convex programming, and solve the latter with the conjugate gradientmethod. In this way, our algorithm possesses a superlinear rate of convergence. Further-more, in our method neither the node matrix nor the circuit matrix is needed. Hence thestorage in the computer is very economical on calculating. Numerical practices haveshown that good effects can be achieved with this new method.
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[2] 张建中,用线性逼近法求解非线性管道网络的收敛性,上海数学会1978年年会论文选集.
[3] N. Biggs, Algebraic graph theory, 1974.
[4] J. A. Bondy, U. S. R. Murty, Graph theory with applications, 1976.
[5] D. J. Wood, C. O. A. Charles, Rydraulic network analysis using linear theory, J. of the Hydraulics ASCE, Vol. 98, 1972. 1157-1172.
[6] R. W. Jeppson, Analysis of flow in pipe networks, 1976.
[7] G. P. McCormick, K. Ritter. Alternative proofs of the convergence properties of the conjugate gradient method. J. of Opt. Theory and Appl., Vol. 13. 1974. 497-518.
[8] 高桑哲男,闭管路方程式法配水管网解析,日本水道协会杂志,1975年2月号,15-26.
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