Geodesic
Solution of the problem of hydraulic calculation in networks using the method of stepwise dimensionality reduction
Journal of computational and engineering mathematics, Tome 1 (2014) no. 2, pp. 3-17.

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The paper describes a developed by the authors method of stepwise dimensionality reduction of the Kirchhoff equations for the flow distribution problem (hydraulic calculation) in networks. Our method allows to replace the original system of equations by an equivalent system with lower dimension from the solution of which you can recover the solution of the original system. Thus, the developed method allows to improve the convergence and searching speed of solution by existing iterative methods for solving of this problem. It is given the justification of the method and algorithm of its implementation. The examples of the implementation for developed algorithm are provided for various schemes of hydraulic networks.
Keywords: hydraulic network, flow distribution, Kirchhoff equations, method of contour expenses, method of stepwise dimensionality reduction. 
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A. S. Krasnov; I. G. Rusyak. Solution of the problem of hydraulic calculation in networks using the method of stepwise dimensionality reduction. Journal of computational and engineering mathematics, Tome 1 (2014) no. 2, pp. 3-17. http://geodesic.mathdoc.fr/item/JCEM_2014_1_2_a0/

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