IJE TRANSACTIONS C: Aspects Vol. 27, No. 9 (September 2014) 1331-1338    Article Under Proof

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N. Moosavian and M. R. Jaefarzadeh
( Received: September 26, 2013 – Accepted: May 22, 2014 )

Abstract    There are different methods for the hydraulic analysis of water supply networks. In the solution process of most of these methods, a large system of linear equations is solved in each iteration. This usually requires a high computational effort. Hardy Cross method is one of the approaches that do not need such a process and may converge to the solution through scalar divisions. However, this method has two shortcomings: first, initial discharges should satisfy continuity equation at each node; second a large number of iterations are required to converge to solution. In this article an algorithm is suggested for initial discharges that are close to the final results while the continuity equations are automatically established. This algorithm may be directly implemented in the Hardy Cross method. To reduce the number of iterations the Hardy Cross method is combined with third-order and sixteenth-order methods. The results of some numerical examples demonstrate that the use of the combined approach with the suggested initial guess reduces the number of iterations and hydraulic analysis time and the solutions converge with a high accuracy.


Keywords    Hydraulic Analysis, Modified Hardy-Cross, Water Supply Networks


چکیده    روش های بسیاری در تحلیل هیدرولیکی شبکه های آبرسانی وجود دارد. در هر تکرار از فرایند حل اکثر این روش ها، یک دستگاه معادله خطی حل می شود که معمولا هزینه محاسباتی زیادی دارد. روش هاردی کراس از جمله روش هایی است که در فرایند تحلیل نیازی به حل دستگاه معادلات خطی ندارد و با تقسیم های اسکالر به جواب همگرا می شود. اما روش هاردی کراس دو عیب دارد. اولا در این روش حدس اولیه باید به گونه ای باشد که معادلات پیوستگی در گره ها برقرار باشد، ثانیا تعداد تکرار برای رسیدن به همگرایی قابل توجه است. در این مقاله راهکاری برای انتخاب حدس اولیه پیشنهاد می شود که به جواب نهایی نزدیک است و در عین حال معادلات پیوستگی بطور خودکار برقرار می شود. بنابراین می تواند در روش هاردی کراس بکار برده شود. همچنین برای کاهش تعداد تکرار همگرایی، روش هاردی کراس را با دو روش مرتبه سه و شانزده ترکیب کردیم. نتایج حاصل از حل چند مثال عددی نشان می دهد روش ترکیبی به همراه انتخاب حدس اولیه پیشنهادی تعداد تکرار و زمان تحلیل هیدرولیکی را کاهش می دهد و جواب ها با دقت بسیار خوبی همگرا می شوند.



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