Random generation of hydraulic networks for testing algorithms
Martínez F., Enrique Cabrera Marcet, Cucó F.
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Since the tune computers became readily available, numerous articles have appeared proposing new models and alternative methods for hydraulic network solutions. Some criticize convergence problems of the methods which solve iteratively the system of equations one by one, balancing flows in the nodes or head losses an the loops, such as the methods of Harry-Cross [1]. These critics propose improvements based on the appropriate selection of circuits [2] - [3], in certain modifications of the method [4], [5], in the use of acceleration factors [6], etc. Others praise methods which linearize the system of equations with a formulation by nodes [7], loops [8] or other alternative methods [9], [10], — [11]. In this case the improvements are oriented toward the optimization of memory [12], the reduction of solution tune for the system of linear equations [13], or the convergence acceleration depending on the linearization method employed: direct linearization [14], fixed point [15], Newton [16], quasi Newton [17], etc. This problem still remains and so far none of the proposed methods may be considered superior to any of the others. Neither are there any definitive criteria which indicate when a particular method should be used, especially in the case of convergence rates. The modeling of new components such as supply and booster pumps [18], check valves and pressure reducing valves (PRV), [19], [20] only makes the situation worse. One way of casting light on this problem consists in experimenting with a large number of real cases. Some authors have done this, [6], [21], but this type of experimentation is simply too time-consuming for most analysts and users. Nevertheless, thanks to the help of computers, it is possible to generate networks which closely resemble to real ones, and to test any proposed method with them. Thus the user’s time is saved by the computers capacity to model and properly design many particular cases.